Shear-induced splitting of a plume outflow in a stratified ...

Indian Journal of Marine Sciences Vol. 34(2), June 2005, pp. 192-211

Shear-induced splitting of a plume outflow in a stratified enclosed basin

A. A. Bidokhti Institute of Geophysics, Tehran University, Tehran, PO Box 14155-6466, Iran

[E-mail: [email protected]] Received 19 April 2004, revised 4 February 2005

In this paper we review the outflow data for the Persian Gulf and report on laboratory experiments with outflows from turbulent plumes falling into a pre-established density stratification in a long box. The experiments show the formation of coarse vertical structure, a result of ‘shear layers’ generated by quasi-stationary internal wave modes. Applying a theory of Wong et al. [J. Fluid Mech., 434(2001) 209-244] for shear layers generated by plume outflows at the bottom of a tank, we interpret the intrusion structure in terms of downward-propagating low frequency waves excited by the outflow. In the presence of an upward mean advection driven by entrainment into the plume and displacement by the outflow a mode becomes stationary in the tank and causes the outflow to split into multiple horizontal (T, S) intrusions with thickness given by the dominant vertical wavelength. Central to this thesis are single-component experiments, which show that double-diffusive convection is not responsible for the coarse structure. When the laboratory plume is given both temperature and salinity contrasts from the surroundings, double-diffusive convection is evident and tends to modify the smooth gradients into interfaces and convecting layers. However, the convection is parasitic on the vertical T, S gradient perturbations generated by the shearing modes. In comparing the laboratory results and theory with the data for the Persian Gulf outflows, we tentatively propose that this outflow, as it passes over the sloped boundary, induces internal waves whose normal mode structure may fold up the outflow and create the coarse layers. We also find that the double-diffusive effects are too small to influence the shearing modes in ocean outflows.

[Key words: Stratified intrusions, shear modes, internal waves, double-diffusive convection, outflows, marginal seas, Persian Gulf]

1. Introduction Vertical profiles of temperature and salinity in the oceans reveal that fine-structure in the form of horizontally extensive mixed layers alternating with thin, large gradient interfaces is particularly prevalent in frontal regions and lateral intrusions1-3. In regions of strong horizontal gradients the formation of intrusive and mixed layers in the density field is commonly attributed to the action of double-diffusive convection4-7, because the overall vertical temperature and salinity (T-S) gradients through the layering are favourable to convection of either the diffusive (wherever ‘diffusive’ is mentioned in the text we mean the diffusive mode of double-diffusive convection) or salt finger kind, and because a clear mechanism for the formation of double-diffusive interleaving has been demonstrated8. The depths of layers (of order 10-50 m) are consistent with those predicted by the scaling established from laboratory experiments with double-diffusive fronts2,8-10. In some cases, interleaving layers extending across fronts are also found to slope across isopycnals, as expected for intrusions that are driven by double-diffusive density fluxes2,8,11.

On the other hand, inspection of vertical T-S profiles through outflows from marginal seas [e.g. Fig. 1] shows that they can be characterised by additional structure at larger vertical scales of 50-150 m (see Fig. 2). The outflows, where they form intrusions at their depth of neutral buoyancy rather than against the bottom, tend to split into several layers12. These multiple tongues then represent a greater number of large-scale T-S gradient inversions; potentially further enhancing double-diffusive convective fluxes. The tongues are strongly stratified and are not convecting layers. In recent experiments with turbulent plumes falling through stratified surroundings to form outflows at the base of long channels, it was noted that horizontal, counter-flowing ‘shear layers’ were formed by low frequency internal wave modes13,14 shearing layers were quasi-steady and more or less stationary in the tank. Similar shear layers are to be expected when a plume outflow intrudes at intermediate depths, and we ask whether they might represent a plausible mechanism for the formation of the course structure of large outflows. If so, then low frequency internal waves might play a role, alongside double-diffusive

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convection, in generating T-S structure, enhancing convective fluxes, and modifying the dispersion of outflow waters in the oceans. Outflows from marginal seas and gulfs are formed where relatively dense water flows over an exit sill into the deep ocean, sinks as a turbulent plume, entrains surrounding water, and intrudes into the ocean thermocline at a depth of neutral buoyancy12,15-17. The depth at which the outflow intrudes is determined by the ambient density gradient and the amount of entrainment. Outflows commonly carry relatively warm and saline water into the ocean, thus producing a broad T-S maximum in the water column and creating conditions favourable to double-diffusive convection: convecting layers separated by

Fig. 1—The geography and bathymetry of the Gulf of Oman, the receiving basin for outflow from the Persian Gulf. Depth contours are at 500 m intervals; SH - Strait of Hormuz.

salt fingering below the intrusion and diffusive interfaces above the intrusion. On the other hand, in experiments with double-diffusive sources placed at their neutral buoyancy depth in a density gradient, Turner9 demonstrated the formation of multi-layered intrusions and the spreading of the intrusion over a large depth range. This behaviour resulted from the vertical convective fluxes near the source. It was suggested that the observed ‘splitting’ of intrusions and sequential formation of new layers, in this type of experiment, might result from Stern’s18 collective instability of salt fingers19. Other experiments with density-compensated T-S fronts (starting with an initially vertical T-S interface) demonstrated the process of water mass interleaving driven by vertical thermohaline convective fluxes between the counter-flowing intrusions8. Even when outflows are strongly influenced by Coriolis effects and break up into geostrophic eddies (such as the ‘Meddies’ formed from the Mediterranean Outflow), the eddies are themselves influenced by double-diffusive interleaving layers formed around their perimeters2. Thus double-diffusive processes provide consistent explanations for the observed layering at 10-30m vertical scales. On the other hand, the formation of horizontally coherent T-S inversions having larger vertical scales, up to 150 m, and which are strongly stratified rather than convecting, has been

Fig. 2—Typical profiles of A) temperature and salinity, B) potential density, O2, and density ratio, and C) vertical gradients of T (heavy line) and S (light line), from the Persian Gulf outflow for winter (26 February 1992); from the station at (57.08 Long., 24.46 Lat.), NOAA Mt. Mitchell Cruise. In (B) R� is averaged over 2 to 3 m depth intervals, and is set to zero when either ∆T or ∆S vanishes across a measurement interval of approximately 1 m.

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attributed to a range of mechanisms. These include tidal pulsations, division of the descending slope plume into separate branches by irregular bottom topography, or seasonal variability in the source water characteristics1,12,16

The outflow from a dense turbulent plume falling to the bottom of a long channel of stratified fluid has been shown to excite a series of strong counter-flowing horizontal shear layers13. These layers have been interpreted as low frequency internal gravity waves excited by the bottom outflow current (a buoyancy-driven intrusion) and carrying energy and momentum upward14. The vertical scale of the dominant mode is successfully predicted by a matching of the downward phase speed of the travelling waves to the upward advection speed present throughout the tank (where it was assumed that the dominant modes have a horizontal wavelength equal to twice the length of the channel and that the bottom boundary had perfect slip). The advection is driven by the entrainment volume flux into the plume, and this ‘filling-box’ circulation20 is closed by the vertical displacement required by the plume outflow. The wave speed-mean flow matching leads to the excitation of a preferred wave number. The number of layers observed in experiments was between 4 and 6 (from the base of the tank to the level of the plume source). Wong et al.14 also conclude that the internal wave dynamics determine the thickness of the bottom outflow intrusion: this thickness becomes the height from the base to the first reversal in horizontal velocity. Internal wave dynamics have not been investigated for cases in which the outflow intrudes at intermediate depths. In that case, energy and momentum can be radiated both upward and downward through the water column, and the outflow depth, thickness and structure will be influenced by both the outflow dynamics and any feedback to the entrainment into the plume. A mean vertical advection can be driven by the plume and outflow only at depths above the outflow, and we expect strong shear layers to be possible at those depths. This is a difficult problem to tackle through ocean measurements, as the slow vertical advection and stationary internal waves cannot be measured directly and we can only make inferences from the T, S structure of oceanic outflows. Laboratory experiments suffer due to some of the same difficulties, but the vertical and horizontal velocities and outflow evolution are more readily determined from a range of measurements.

Another process not yet studied is the interaction of low frequency internal waves and double-diffusive convection in plume outflows posing a T-S contrast to the surroundings. Single component experiments only were reported by Wong & Griffiths13: the shearing layers were not convecting layers and were associated with only very small perturbations to the density gradient. The shear layer mechanism has been utilized to generate a horizontal shear that was sinusoidal in the vertical in a deep two-component density stratification supporting salt fingers21. In that case the shear was excited by inflow at one corner (as the gradient region was filled) and the interaction of salt fingers with the shear led to modification of the local density structure in each layer. In the case of plume outflows, we speculate that double-diffusive convection and shear layers might have significant effects on each other if the vertical scales of the two processes are comparable. On the other hand, if shear layers are strong and their vertical scale is large, they may be responsible for generating much of the T, S gradient structure on which convective layering occurs.

In section 2 we present some hydrographical data derived from that complied by Bower et al.12, showing the structure of outflows from the Persian Gulf into the Gulf of Oman Sea. Then we begin to explore the possibility that internal wave dynamics may provide an alternative mechanism for the formation of multiple tongues, as well as for controlling the vertical thickness of the outflow. In section 4 results are given for laboratory experiments with intrusions generated by dense turbulent plumes falling into stratified environments such that the outflow is at intermediate depths. As the ambient stratification we used both linear density gradients and non-linear (“filling box”) gradients generated by a previous plume of greater buoyancy flux. Both single-component flows and two-component (double-diffusive) cases are used to investigate the relative roles of internal waves and double-diffusive convection, and interactions between these two mechanisms. In section 5 the laboratory observations are compared with predictions based on the theoretical solution for the simpler case of bottom outflows, and with the data for the ocean outflow. Although there are a number of difficulties in applying the theory to the ocean, (e.g. internal waves here may be generated by the outflow plume passing the sloping boundary22 and they may not be stationary as in the laboratory case) we tentatively conclude that


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low frequency internal waves may be responsible for multiple, strongly stratified intrusion tongues in the outflow studied, while double-diffusive convection remains responsible for the smaller scales of layering characterised by convecting layers and steps. 2. Some properties of the outflows from semi-enclosed seas (Persian Gulf) Evaporation of the Persian Gulf water [Fig. 1] (at about 2 m/yr) exceeds the precipitation (about 0.5 m/yr) and causes an “inverse estuary” flow through the strait. As it enters the Gulf of Oman over a shallow sill 80 m deep, the outflow is 45 m thick and is intensified toward the southern boundary of the Strait by the Coriolis effect12. The outflow forms a down-slope plume in the Gulf of Oman and leads to a large lateral intrusion at depths between about 200 and 400 m (Fig. 3). The intrusion forms a narrow boundary current, less than 10 km wide, along the south west coast of the Gulf. Whereas the temperature maxima in the water column are most commonly found at a depth of 250 m, Bower et al.12 reported that in a summer survey there were “only a few warm temperature maxima below 200 m and a number of much warmer maxima between 75 and 200 m” (see Plate 8 of Bower et al.12 for a compilation of a large number of overlaid temperature profiles). They also

concluded from model simulations that the product waters end up at about the same depth in summer and winter. The averaged annual dilution factor of the outflow, as estimated by Bower et al.12, is approximately four. This is larger than that for many other outflows, and was attributed to the relatively small volume flux and large density difference. Characteristics of the outflow and surrounding waters are summarised below, based on Bower et al.12.

Parameter value Parameter Value

Ws (km) 30 Ds (m) 80 Us (m/s) 0.17 (w)

0.17 (s) Hs (m) 45 (w)

45 (s)

Di (m) intrusion 200 – 400 H (m) 200 (w) 320 (s) W (km) intrusion < 10

g′ (m/s2) 0.032 (w) 0.0194 (s)

N (s-1) sill outflow 0.021(w) 0.031(s)

F (m4s-3) 7344 (w) 4452 (s)

N (s-1) intrusion 0.007 N (s-1) ambient ocean 0.005

Here Ws is the width, Hs the thickness and Us the speed of the outflow (source) current in the strait; g′ = g∆σt/σt is the reduced gravity between the outflow in the source strait and the surrounding waters at the sill depth; F is the source buoyancy flux based on g′ and the volume exchange flux HsWsUs; DS is the sill depth; Di is the depth of the intrusion; H is the height through which the plume falls (from

Fig. 3—Typical profiles of A) temperature and salinity, B) potential density and density ratio R�, and C) vertical gradients of T (solid line) and S (broken line), from the Persian Gulf outflow for summer (4 June 1992); from the station at (57.24.46 Long., 24.58.92 Lat.), NOAA Mt. Mitchell Cruise. Data for only the upper 600 m of the water column are shown. Density ratio is averaged over 3m depth intervals and is plotted as R� = 0 when either ∆T = 0 or ∆S = 0 across a measuring interval.


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effective source depth to intrusion base); W is the estimated width of the intrusion; and N is the buoyancy frequency, given for the outflow layer in the strait, the intrusion (climatological values evaluated at the intrusion mid-depth) and ambient oceanic conditions (evaluated at 11.5°N, 45 °E, 25.5°N, 57.5°E and at sill depth); w, winter; s, summer. The receiving basin, the Gulf of Oman, is approximately 3000 m deep and 160 km wide at a depth of 250 m. It opens to the Arabian Sea some 600 km east of the Strait, but is partially enclosed at depth by a NE-SW trending ridge less than 2000 m deep. The intrusion of PG outflow water is found largely in a current less than 10km wide along the southwest boundary of the Gulf. Figures 2 and 3 show, typical profiles of temperature T, salinity S, dissolved oxygen O2 (available only for winter), potential density σt, and stability ratio Rρ through the Persian Gulf outflow for summer and winter of 1992. We calculate the stability ratio defined as Rρ = (α∂T/∂z)/(β ∂S/∂z) …(1) Stability ratios Rρ > 1 are salt finger favourable, 0 < Rρ < 1 are favourable to thermohaline convective layering of the diffusive type, Rρ = 0 implies a uniform temperature (probably a result of convection within a layer) and Rρ < 0 implies stable gradients of both T and S. Within most of the intrusion the gradient regions are favourable to either salt fingers or diffusive interfaces1 . Interfacial regions at and below the base of the outflow have stability ratios largely in the range 1 < Rρ < 2, which indicates strong salt fingering activity. There are a large number of fine layers with stepped structure in T, S and density on vertical scales of 10 to 30 m. In addition to the fine structure, there is an obvious coarse structure in the T and S profiles at scales of 50 to 100 m. At this larger vertical scale the intrusion(s) is stratified rather than overturning. It is this coarse structure that is the main interest in this paper and which we will tentatively associate with internal wave horizontal shearing modes. The stability ratio can also be represented as the Turner angle φρ (e.g. Ruddick & Walsh7), where: tan(φρ) = {(β∂S/∂z+α∂T/∂z)/(β∂S/∂z-α∂T/∂z)} …(2)

For -45° > φρ > -90° the gradients are favourable to salt finger convection and for 45° < φρ < 90° diffusive convection is expected. There is no vertical density gradient where ⏐φρ⏐ = 90°, gravitational instability is possible for ⏐φρ ⏐ > 90° and the water column is ‘doubly stable’ for ⏐φρ⏐ < 45°. Figure 4A shows an example of the profile of Turner angle for the T-S profiles of Fig. 3 (where we calculated φρ for local gradients averaged over a moving 10 point window corresponding to a 1 m depth interval): again the presence of alternating salt fingering and diffusive steps are clear within the outflow intrusion, with a predominance of salt fingering regions beneath the intrusion and a weaker prevalence of gradients favourable to diffusive convection in a small interval in the upper part of the intrusion beneath a depth of 150 m. The distribution of φρ seen in Fig. 4A is typical of profiles in both Persian Gulf (PG) and Red Sea Water (RSW) outflows – it tends to increase with depth in the upper predominantly diffusive layered region, oscillate between +90° and –90° in the central depths of the outflow, and increase from –90° to –60° through the salt finger favourable region below the outflow. The wave number (kz) power spectrum of φρ reveals two distinctive peaks at about kz

-1 ~ 50 m and 20 m (Fig. 4B). Our calculation of the Turner angle in the PG outflow reveals a similar pattern. We note that a similar distribution of layer thickness has also been found from φρ profiles through the Mediterranean outflow intrusion7. In searching for explanations of the various observed scales of layering, we begin by considering the double-diffusive frontal interleaving mechanism9,11, for which the thickness of interleaving layers across a T-S front (i.e. one having no initial horizontal density gradient) in laboratory experiments is found to be: hDD = (3/2)(1-γ)(gβ∆S/N2) … (3) where g is the gravitational acceleration, β is the coefficient of density change due to S, ∆S is the horizontal S difference across the front, N is the buoyancy frequency, and γ is the ratio of density fluxes associated with T and S fluxes due to salt fingering (γ = 0.56 for salt/heat fingers, and γ = 0.88 for analogue experiments using sugar and salt). For the intrusion formed by the Persian Gulf outflow at depths between 100 m and 400 m we find hDD ~ 23 m.


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Fig. 4—A) Vertical profile of Turner angle φρ from the data of figure 2 (the data are averaged over 10 points, or approximately 7 m depth intervals); and (B) the power spectrum of the Turner angle.

This is similar to the scales of the fine layer structure observed in the ocean outflows. In addition, Rρ is close to one. Hence double-diffusive interleaving is the probable cause of the fine-structure. Another mechanism potentially responsible for generation of fine-scale layering is local turbulent mixing within the mean density gradient23. This mechanism is expected to generate layer thicknesses comparable to the Ozmidov scale ε1/2N-3/2 (where ε is the rate of dissipation of turbulent kinetic energy), which we estimate to be of the order of a few metres and smaller than the finest stepped structure observed. We conclude that the coarse layers are much too thick to be attributed to double-diffusive interleaving instability. The presence of statically stable density stratification throughout the thicker layers, too, argues against convection as a cause or driving mechanism. Seasonal variation in source properties and fluxes remains a possible contributor, although Bower et al.12 also concluded that both summer and winter Red Sea Water intrudes at the same depth. These authors identified two bottom stream paths delivering Red Sea outflow water to the two major intrusions at 600 m and 1200 m. However, this bifurcation does not explain the multiple T, S maxima at 100 m scales. In order to investigate the possibility that low frequency internal wave shearing modes provide another, as yet unexplored, mechanism responsible

for the splitting of outflow intrusions into multiple layers, we have carried out laboratory experiments with turbulent plumes falling into pre-existing stratifications in a long stratified channel such that the plume outflow intrudes at intermediate depths. 3. Experiments Experiments were designed to allow an investigation of outflow structure and horizontal shearing modes generated by a plume outflow at depths remote from the tank bottom. A second aim was to investigate interactions between shear layers and double-diffusive convection. The experiments captured in the simplest possible system the basic elements thought to be important in ocean outflows, in particular, a dense plume that mixes and entrains as it descends to a depth of neutral buoyancy, an ambient stratification, and a resulting mid-depth intrusion. In the experiments the tanks is necessarily closed and of finite horizontal size, whereas the receiving basins for ocean outflows are at least partially open (see also section 5). We also aimed to make the intrusions (but not the descending plumes) as two-dimensional as possible, thus facilitating easier observations, measurements and comparison with theoretical analysis. Hence we chose to use a long rectangular channel. A related simplification was to study non-rotating cases. The omission of Coriolis effects gave


198

was successfully predicted using a previous empirical result24

the advantages of two-dimensionality and an understanding of the non-rotating flows that will assist in future work with the corresponding three-dimensional rotating flows. In the rotating case the outflows will intrude along a side boundary, free of Coriolis forces in the flow direction at the boundary, as in the non-rotating case, but will have a width set by the Rossby radius and baroclinic eddies rather than the basin width. In order to cover a wider range of parameters, experiments were carried out with two different initial ambient density stratifications: a nonlinear “filling box” gradient and a linear gradient (see below). Because we expect no mean vertical flow below the outflow depth, and therefore little effect of internal wave activity in that region (only unsteady evanescent waves), we treated the overall depth of water as irrelevant. Hence, without unduly restricting our investigation of the relevant parameter space, we set the plume characteristics such that the plume outflow initially intruded near mid-depth in the tank and did not vary the underlying water depth. Finally, we used only a constant source flux, in order to clearly separate shear layer effects from multiple intrusions formed by varying (seasonal) fluxes.

Fig. 5—Diagram of the experimental set-up, with the plume source at one end of the channel.

All experiments were carried out in a glass tank 1.8 m long, 0.15 m wide and 0.3 m deep (Fig. 5). In cases where a “filling box” stratification20 was to be used, the tank was initially filled with fresh water to a depth of 0.22 m. The water was then stratified using a plume of dense sugar or salt solution falling from the end of a small tube placed at 0.20 m from the base. This plume was stopped after running for a few ‘filling box’ ventilation time scales20, so that the first front of plume modified water had approached very close to the source depth. The resulting buoyancy frequency N(z) is given by the ‘filling box’ analysis: N = F*1/3(2E)-2/3π-1/3D-4/3[2.18(z/D)-5/3+0.279(z/D)-2/3

+0.0831(z/D)1/3….]1/2 …( 4) where F* is the source buoyancy flux of the stratifying plume, D is the depth from the plume source to the bottom, E is the entrainment coefficient and z is the vertical coordinate measured downward from the source. Hence the density profile has the same shape whatever the variable values chosen, and the magnitude of the density gradient can be changed by using different values of buoyancy flux F* or water depth D. For convenience, and without any loss of generality, we chose to vary only the buoyancy

flux (Table 1). The ambient “filling box” density gradients were necessarily very small, as a result of the large volume entrainment into the dense plume. In some runs the tank was instead stratified with a linear density profile using the double bucket method. Although the nonlinear ‘filling box’ stratification formed by a turbulent plume is the more similar in shape to typical ocean density profiles, the linear initial density profile enabled us to use both larger density gradients and larger values of ∆S (in both single and two components cases) between the outflow source and the tank. After setting up the initial stratification the tank was left for sometime for any motion to die away. In the “filling box” stratifications it was noticed that fine layers were sometimes formed in the very weakly stratified bottom region. This was found to be due to very small temperature differences between the tank water and ambient air across the tank wall, despite environmental conditioning of the laboratory. The observed scales of the layers, h ~ 2 cm, and the buoyancy frequency N near the base imply a wall temperature difference ∆T = ρN2/(αg) ≈ 0.25 °C. These layers were not important in the later outflow experiment as they were very thin and contained little horizontal motion compared to the later outflow. To produce the outflow intrusions a nozzle of 3 mm diameter was placed at the top of the stratified region, near the end of the tank and equidistance from the three proximate walls. A peristaltic pump provided a constant volume flux of salt solution to the nozzle, generating a turbulent plume with buoyancy flux F. The buoyancy flux was chosen such that the plume initially fell to a maximum depth H slightly less than half the full depth from the source to the base (see Fig. 7 below). The buoyancy flux required for this


199

= m3(H )

e buoyancy frequency at midnd H was typically about 0.1 m. The plume source

ution and to use a salty

the outflow appeared as a perturbation to the initial

conductivity ient, no i sions p le. The conductivity probe had an output voltage that was

ncentration

d

component case (salt plume into a salt-stratified tank)

wh

F

πN /5)4 … (5

where Nm was th -depth awas dyed to reveal the distribution of outflow water, and dye crystals were dropped through the flow to reveal the horizontal velocities, advection and mixing. A shadowgraph image of the flow was recorded on videotape for analysis and vertical profiles of conductivity were taken. Typical value of highly concentrated plume source volume flux was about 1 cc per minute which is very small in order to alter the level of water in the tank. In most of the two-component runs we chose to stratify the tank with sugar solsource plume (salt, referred to as T, and sugar, referred to as S, are used to model heat and salt in the oceans; Turner9. We emphasised this case because conductivity profiles more clearly revealed the outflow water as an anomaly relative to the ambient low-conductivity sugar solution. Indeed, T and S inversions (like those in ocean outflows) can only occur in two component cases (irrespective of whether double diffusive instabilities occur). In a few runs we used a sugar outflow into a salt environment: in this case, as in all of the single component experiments (salty outflow into a salty environment),

linear with salt concentration for the small concentrations recorded in the outflows

grad with nver ossib

25. The variables are: the salt concentration difference ∆T between the source and the environment at the source depth; the corresponding sugar co

ere a plume was first used to stratify the tank with a ‘filling box’

difference ∆S; the volume flux q of the source; the epth of plume fall from the source H; the initial

buoyancy frequency N0 (evaluated at the base of the tank, z = D for the filling box profiles); and the width W and length L of the tank. Fixed quantities include the gravitational acceleration g, the water depth D, the kinematic viscosity ν, the molecular diffusivities of salt κT and sugar κS, and the corresponding coefficients of density change due to salt α and sugar β. The depths D and H have fixed values in this study and are not independent because we set source properties to give an initial intrusion at mid-depth. The plume buoyancy flux at the source level is F = qg∆ρ/ρ, where ∆ρ/ρ = α∆T + β∆S (∆ρ > 0 since the plume is denser than the surroundings at the depth of the source). A velocity scale is U = (F/D)1/3. We used a range of fluxes F over more than one order of magnitude (Table 1). The dimensionless parameters for the single

Table 1—Summary of the experimental conditions. In those cases gradient, the stratifying plume of flux F* was run for 2 hours 17 minu

–1large time

–1

o3.0 209 3.0 0.31 0.25 0.02 209 15 0.13

6.25 .75

Linear grad

0.006 142 0.19 r-salt 0.97 3.00 0.008 89 15 0.31

tes. The buoyancy frequency N is given at the initial outflow depth H for both the initial gradient (N0) and within the later intrusion (Nm, near the time that the intrusion base reached the bottom of the tank). The density difference between the plume and surrounding at the source was set to a large value (approximately 60 kg m-3 in runs with “filling box” stratifications and 180 kg m-3 in those with linear gradients) in all runs in order to minimise the source volume flux, as well as to maximise double-diffusive effects (which would otherwise have remained unimportant) in two-component outflows.

Run number

Composition (outflow-environment)

F∗

(10-7 m4s3) N0 (z=H)

initial F

(10(s )

-7 m4s3) F/(H4N0

3) (initial value)

ϑ

Profile position x/H

Nm (z=H)

(s ) ‘Filling b

1 Sugar-salt x’ gradient

0.25

0.02

15

0.31 0.13 2 Salt-sugar 3 Salt-sugar 3.0 0.31 0.25 0.02 209 -18 0.13 4 Salt-sugar 6.0 0.40 0.42 0.017 124 7.5 0.16 5 Salt-sugar 6.0 0.40 0.80 0.03 65 7.5 0.16 6 Salt-salt 6.0 0.40 0.42 0.017 0 7.5 0.16 7 Salt-salt

6.0 0.40 0.80 0.03 0 7.5

ient

0.66

0.74

7.5

8 Salt-sugar 9 Suga

10 Salt-sugar 0.65 3.00 0.027 36 7.5 0.31 11 Salt-sugar 0.60 1.48 0.016 71 7.5 0.25 12 Salt-salt 0.60 1.48 0.016 0.0 5.6 0.25


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which have fixed values in this

ource to

on ill have no significant effect on the buoyancy fluxes

lo ϑ conv

ral results f this work. Outflows from a salt plume into a salt

vidence of the presence of s layered structure in

are: the Prandtl number Pr = ν/κT, aspect ratios L/H and W/H (all three of study), a dimensionless source buoyancy flux F/(D4N0

3) (equivalent to the cube of the Froude number U/ND), and Peclet number Pe = F1/3D2/3/κT. The Prandtl and Peclet numbers were extremely large and we assumed diffusion played no role in the (single component) flows. This left us with only the dimensionless buoyancy flux as a variable. Only very small variations in this parameter were practicable with ambient “filling box” gradients and, even with the linear gradients (where there was more flexibility in N0), its value was partially fixed by the requirement of a mid-depth outflow. Hence only a limited number of single component runs were used after testing for reproducibility. For bottom outflows, Wong & Griffiths13 used several aspect ratios L/H and found only a quantitative difference in the results. For two-component cases additional dimensionless parameters are the diffusivity ratio τ = κS/κT ≈ 1/80 and a density ratio Rρ = α∆T/β∆S. The density ratio is most easily defined in terms of the senvironment differences at the source depth. However, it is not a particularly useful parameter. For plumes falling into gradients with fresh water at the source depth Rρ is either vanishingly small or extremely large, depending on whether the plume carries T or S. In all cases, the density difference δρ(z) between the plume and its surroundings must vanish at the spreading depth. Therefore, the value of the ratio αδT/βδS = δρ/ρβδS - 1 = -1 at the spreading depth, independent of Rρ. The effects of double-diffusive convection within the falling plume are negligible, but the intrusion will have salt fingering at the top if the source is rich in salt, or along its lower side if the source is rich is sugar. A parameter that more directly indicates the magnitude of double-diffusive effects can be defined as the ratio ϑ of the two vertical sugar (S) fluxes, FDDC, owing to double-diffusive convection within the outflow and FS from the source. Here we use the expression for the vertical flux through one or more salt finger interfaces and convecting layers (Turner24)*, which becomes FDDC ≈ κS

2/3 (gβ/ν)1/3 (∆S)4/3 LW, where in our case we use ∆S as the S difference at the source depth and we have omitted a numerical constant. The source salt flux is simply FS = q∆S. These definitions lead to:

ϑ ≡ FDDC /FS = κS

2/3 (gβ∆S /ν)1/3 q-1 LW …(6)

Thus ϑ = 0 for single component cases (∆S = 0). For small values of ϑ weak double diffusive convectiwor outf w structure. For large values of ection may transport S effectively in the vertical (and possibly horizontal) direction and influence the buoyancy available for horizontal motions. 4. Experimental results 4.1 Single component intrusions Single component runs provide the centogradient showed strong ehorizontal shear layers, as well atracer concentration, in a reproducible pattern. For those runs with nonlinear initial density profiles, the mid-depth outflow initially spread at the depth predicted from Eq. (5). At early times the speed of the nose of the outflow increased with time. The intrusion also thickened, and eventually split to generate a new tongue of dyed plume water growing beneath the first layer. The new intruding layer corresponded to additional structure that had already appeared in the vertical profile of horizontal velocity far ahead of the nose of the longest intruding layer. As the plume volume flux was re-directed into the new intrusion, the spreading rate of the older layer above tended to slow down, and sometimes reversed. The older layer began to be re-entrained into the plume. Thus the advance differed from Manins’27 constant nose velocity (U∝(QN)1/2, where Q is the volume flux per unit width) observed for laminar intrusions produced by a source at its neutral buoyancy level. In time the formation of a new layer was repeated. The dye tracer in the outflow water was slowly advected upward (without reaching the far end of the channel) to replace water entrained into the plume at shallower depths, and eventually reached the level of the source.

________ ∗ Note that, if external conditions impose the salt (and buoyancy) flux, the S (or T) flux does not necessarily become small when q is small. Also, for the case of a plume containing S falling into a stratification purely of T (or a plume containing only T falling into an S gradient), the plume S (or T) flux is initially invariant with depth from the source to the spreading depth. In this case δρ(z) and the buoyancy flux F vanish at the spreading depth. For a plume driven by an S anomaly and falling into an S gradient, on the other hand, the plume S flux decreases with increasing depth z. Both fluxes FS and F and concentration anomaly ∆S vanish at the spreading depth, where δρ vanishes. Thus in Eq. (6) we evaluate ∆S (and FS) at the plume source.


201

from the ng decayed substantially

The plume also penetrated progressively deeper in the tank until it eventually reached the bottom. Figure 6 shows a sequence of photographs taken during an intrusion of a salt plume into a salt-stratified tank initially having a ‘filling box’ profile (run 7 in Table 1). The intrusion, marked by dye plume source reservoir, began as a wedged-shaped structure with a sloping interface beneath. The dye tracer from the plume reveals several distinct layers in tracer concentration in C) to e). The layer of furthest extent in C) is being overtaken by a layer beneath (seen developing in A) and B), and in D) the lower of these has moved ahead while the upper intrusion has pulled back toward the plume. At the same time the water and dye layers have moved upward relative to

the tank and the velocity structure shown by the initially vertical dye steaks. The presence of quasi-steady layering was clear in the horizontal velocity structure throughout the length of the tank and at heights above the spreading depth. The magnitude of the sheariwith height. Although internal waves can propagate down into the stratification, there can be no vertical advection beneath the intrusion and hence we saw no evidence of significant shearing beneath the base of the outflow. This is consistent with the prediction (Wong et al.14) that shear layers are formed where the vertical phase speed of low frequency waves is opposed by a vertical advection. For larger plume buoyancy fluxes we observed larger horizontal shear

Fig. 6- Photographs of the evolution of a salt outflow into a ‘filling box’ salt gradient, for F = 0.8×10-7 m4s-3 and N = 0.395 s-1 (at the initial outflow depth) (Run 7). The plume source water was marked with blue dye. Images were taken at times A) 22min:42s, B) 24:11, C) 27:20, D) 30:57 and E) 36min:43s after the plume flow was started. Only the left 0.9 m (approx.) of the channel length is shown.


202

ontal shear layers in the ambient

n of

layer velocities in the surroundings and more obvious branching in the intrusion. In addition to the shearing structure, the outflow tended to form a number of intrusions or tongues of dyed plume water. These are more difficult to see in the still photographs (Fig. 6) but were a distinctive feature of these flows. The multiple intruding tongues were advected upward. The formation of new tongues (and new ambient shear layers), as the flow evolved, can be attributed to upward advection of the existing intrusions (owing to entrainment of overlying water into the plume) and deeper penetration of the plume (owing to the increasing density of the water column above the outflow depth and the consequent increasing density of the plume itself). The observed flow structure has some similarity to that for the case of a turbulent plume falling onto the base of a tank and exciting large amplitude velocities in a sequence of horizstratification. However, the intermediate depth intrusions tended to be thicker and the overlying horizontal velocity structure had smaller amplitude, possibly as a result of the time-dependent depth of penetration and spreading. New intruding tongues of dyed water did not occur with bottom outflows, because the outflow water in that case spread all the way to the end of the channel and was then advected upward, giving a smooth vertical gradient in tracer concentration below the first upward moving front of dye. Horizontal gradients of tracer were insignificant. In the present case, however, the shearing layers worked on the horizontal gradients of dye tracer between the outflow and the surroundings to give rise to multiple intrusions of plume water. In an ocean situation, these tongues would present T, S inversions on the same vertical scale as the shearing layers. Figure 7 shows density profiles obtained from conductivity profiles through an outflow into an initial ‘filling box’ stratification (run 5 in Table 1). For comparison, Fig. 8 shows the time evolutiodensity profiles for an outflow into a linear gradient (salt into salt). In both cases the slow increase in density everywhere in the upper half of the water column was due to the addition of salt to that region from the plume via the horizontal intrusion and the upward ‘filling box’ advection above the spreading depth. In the case of an initial linear density profile, the profile in the upper portion of the tank evolved towards a ‘filling box’ profile. The only qualitative difference between the two cases was that the length

of the intrusion into a linear gradient grew larger than that in a ‘filling box’ stratification before branching into multiple tongues began (as marked by dye tracer). We attribute this to the larger density gradient and smaller aspect ratio of the outflow. The velocities in the shear layers (Fig. 9) were larger in the linear gradient case owing to the larger buoyancy flux (and therefore the magnitude was more similar to those in the experiments of Wong et al.14, where the plume flux was not limited by the requirement that spreading occur before the plume reached the bottom). The conductivity profiles reveal little structure related to the shear layers because the layers are associated with only small perturbations to the density (and salt) gradient.

Fig. 7—Density profiles (at x = 0.6 m from the plume location) through a single-component intrusion produced by a salt plume in a ‘filling box’ salt gradient, with F = 0.42×10-7 m4s-3, N = 0.395 s-1 (run 6).

Fig. 8—Density profiles (at x = 0.6 m) for a case of single-component intrusion into a linear gradient at a sequence of times (shown in minutes) from the start of the plume outflow (F = 1.48×10-7 m4s-3, N = 0.6 s-1, run 12).


203

rs. The salt and sugar

of penetration. Horizontal shear

ttempt to

as

4.2 Two-component intrusions Experiments involving double-diffusive convection were included in this study to investigate interactions between the formation of convective layering and the generation of shear layeconcentration differences that could be achieved were again limited by the large entrainment into the initial stratifying plume and were too small for differential diffusion of salt and sugar to have any detectable effect within the falling plume. However, we used the maximum possible property contrasts by adding only one component in the surroundings and only the other property in the plume source. Convection was obvious within the outflows in videos and less clear in the still pictures.

The outflows branched into multiple tongues as before, and proceeded to thicken through both the upward ‘filling box’ advection above the outflow and increasing depth layers were again clear, in both the intrusions and the surroundings, at and above the outflow depth (Fig. 10). For an outflow from a salt plume into a sugar gradient, salt fingering occurred at the top of each layer (as sugar solution lays above salt solution) and a sharp diffusive density interface developed at the bottom of each layer (as sugar solution lays below salt solution). Convection was visible within each intruding layer in flow visualization (not shown in still pictures). The important point is that the shear layers (inside and outside the intrusions) and the convection appeared to be very closely coupled, with layering being the same as that in the single component runs. We conclude that the convection developed on the T, S structure ‘imposed’ by horizontal advection in the shear layers, at least at early stages of a run, and took the same vertical scale. As a result of convection, a small slope developed on the layers, the nose of the intrusions dipping

downward across the horizontal isopycnal surfaces. This sloping behaviour was similar to that observed in the double-diffusive source experiments of Turner9 and the T-S front experiments of Ruddick & Turner8. For a sugar plume into a salt gradient the step-like diffusive interface occurred at the top of each intruding layer (below a region of reverse flow toward the plume end of the tank) and again the horizontal velocity profiles and vertical scales were identical to that in the single component case. In this case each layer tended slightly upward across isopycnal surfaces. As the outflow evolved the behaviour became more difficult to interpret, and the velocity structure appeared to at least partially follow the upward advection of the double diffusive layers and interfaces. We conclude that the convection was at that stage influencing the velocity structure. In the two-component experiments we focus on conductivity profiles, rather than the density profiles. Density was in this case determined only from a set of discrete sampling points, and we did not ameasure independently the profiles of sugar concentration. However, the sugar concentrations used for stratification of the environment were so small that they had only a very small effect on the conductivity. Hence conductivity remained a direct indication of salt concentration. All of the salt present in the tank was introduced from the plume source. Conductivity profiles through an outflow from a salt plume into a sugar ‘filling box’ gradient (taken at x = 1.2 m from the plume end of the tank) are shown in Fig. 11 (in this experiment the environment wpreviously stratified by a plume of sugar solution run for a period of 2 hour 15 minutes (effective plume fall H = 0.2 m). Note that the slight increase in the conductivity with depth in the sugar-stratified environment was attributed to a slight increase in temperature with depth. The final profile was taken

Fig. 9—Velocity structure generated by a single-component outflow (salt into salt) in an initially linear density gradient, for F = 1.48×10-7m4s-3 and N = 0.6s-1. Image taken a large time (116min: 32s) after the plume flow was started. Approximately 0.6 m of the channel length is shown (run 12).


204

Fig. 10—Photographs of a salt plume outflow intruding into a sugar ‘filling box’ gradient, with F = 0.8×10-7 m4s-3, N = 0.4 s-1 (run 5). Salt finger convection was evident near the top, of the intrusion. Images were taken at times A) 26min:08s, B) 29:04, C) 31:19, D) 32:04, E) 42:38, F) 43:21, G) 51:09 and H) 52min:07s after starting the plume source. Approximately 0.9 m of the channel length is visible.


205

fter the time that the bottom interface of the intrusion lded and produced another intrusion near the bottom

f the tank, and this was also after the intrusion had ached the far end of the tank). These profiles show

is experiment was

rapid

ion was larger as a

afoorethat salinity variations with depth are not as clear and regular as the velocity structure, most probably as a result of salt finger convection, which tended to extend throughout the layer depth and reduced vertical gradients over the thickness of a fingering region. However, small salinity maxima tended to be coincident with horizontal velocity maxima of the shear layers moving to the right (away from the plume), and salinity minima corresponded to shear layers moving toward the plume. Near the top of the water column the salinity variations corresponded to structure produced at earlier times by the shear layers at larger depths and thereafter advected upwards. Threpeated and conductivity profiles were taken almost simultaneously at different distances from the plume (Fig. 12). Fine structure was most obvious in the upper parts of the intrusion. The fine structure also had a larger amplitude at greater distances from the plume. Allowing for the difference in ambient conductivity gradients, the profiles of Figs. 11 and 12 show structure qualitatively similar to the coarse structure in the ocean outflows (Figs. 2A, 3A). Figure 13 shows salinity profiles from another experiment with a salt plume of larger buoyancy flux falling into a (larger) ‘filling box’ profile of sugar concentration. In this case there was a moredeepening of both the plume penetration and the base of the outflow (see also Fig. 10). This deepening involved the formation of new intrusive layers below

the existing intrusion (profiles 2 and 3). The formation of each new layer tended to be followed by an obvious retreat of the previous intrusion toward the plume, as though mass was withdrawn from it (this process was very obvious in visual observations). We attribute this behaviour to advection of that intrusion upward from a shear layer in which the horizontal velocity was positive (away from the plume) to a depth where the shear layer velocity was negative (as Wong et al.14 have observed). With the greater plume buoyancy flux the shear layer structure remained quasi-stationary in the tank while the water (with intrusions) was displaced upward. Conductivity profiles from an experiment with a salt plume falling into an initially linear density profile of sugar (run 10, Table 1) are shown in Fig. 14. The thickness of the intrus

Fig. 12—Conductivity profiles for the same experiment as in Fig. 11 but for different distances (m) from the source of the outflow intrusion taken approximately 2 hours 54 minutes after the source was started. The final profile shown, however, was taken after 3 hour 54 minutes. F = 0.25×10-7 m4s-3, N = 0.31 s-1 (run 3).

Fig. 13—Evolution of the conductivity profiles with time at x = 0.6 m for a two-component outflow into a ‘filling box’ density gradient; F = 0.42×10-7 m4s-3, N = 0.4 s-1. Note in particular the second and third profiles, where a new intrusion is growing below the previous one (run 4).

Fig. 11—Conductivity profiles taken at x = 1.2 m from the location of a salt plume falling into a sugar ‘filling box’ density gradient, shown for a sequence of times; for F = 0.25×10-7 m4s-3, N = 0.31 s-1 (The position of each profile has been shifted in conductivity by 0.2 units in order to avoid overlapping, run 2).


206

m, t=42 min.) for

extending the ngth of the channel and a splitting of the outflows

trusive layers of plume water which

result of stronger convection driven by the larger ∆S. Small salinity variations again coincided with the shear layers revealed by dye streaks. Figure 15 shows conductivity profiles for a run (#8) having a similar environment but a smaller plume buoyancy flux. In this case signs of layering in the salinity were very weak, and dye lines also showed weaker shearing structure. The ratio ϑ of convective S (sugar) flux due to double-diffusion (to the source plume salt flux) within the outflow in experiment #8 was about four times greater than that in experiment run #10. We conclude that, when the buoyancy flux of the plume was reduced relative to the double diffusive fluxes, convection played a greater role in transporting salt, thereby reducing the salinity perturbations associated with each intrusion tongue. Since convection was not

present in the single component (non-convecting) experiments, these showed the strongest and clearest shear layer structure in the horizontal velocity, and also the most stationary structure. In limited cases the vertical profiles of velocity and conductivity were plotted. As an example is shown in Fig. 16, in which the conductivity deviations from local mean is plotted (at x=50 c

Fig. 14—Conductivity profiles taken at x = 0.6 m (except for one at x = 1.1 m) and different times after the start of a two-component experiment with a salt plume outflow into an initial linear sugar gradient ; large plume buoyancy flux F = 3.0×10-7 m4s-3, N = 0.65 s-1 (run 10).

Fig. 15—Conductivity profiles taken at x = 0.6 m at different times, again for a salty plume outflow into a linear sugar gradient, but a small buoyancy flux; F = 0.74×10-7 m4s-3, N = 0.66 s-1 (run 8).

Fig. 16- Conductivity (deviations from local means) and velocity profiles for run 5 (at x=50 cm, t=42 min.).

exp. 5 to show how well the layered structures in them correspond to each other. The velocity layers are associated with local variations in conductivity. In conductivity profile finer layers are observed which may be the result of the older layers, which have been formed and advected upwards. Finer layers correspond well with velocity maxima. 5. Discussion The mid-depth outflows in the laboratory generated counter-flowing horizontal shear layers leinto multiple inmoved out from the base of the plume. The velocity layering was initially the same in experiments with two components as in single component runs. Convection formed in a parasitic fashion on the existing shear layers. For example, in the case of T outflows into an S gradient, fingering and diffusive density interfaces developed respectively above and below each positive horizontal velocity maximum (which were also T maxima). This close association is to be expected when two mechanisms tend to generate


207

l of the plume source. The velocity structure

to

et al. , who solved

re E is an trainment coefficient (about 0.13 in unconstrained

comparable vertical scales, and it is not possible to use conditions under which the double diffusive instabilities in the laboratory would generate layer thicknesses much smaller than the shear layer scale. However, only for the weakest plume buoyancy fluxes (i.e. the weakest internal wave motions) did the velocity structure in the surroundings became locked to the convecting layers as they moved upward, and this was only well after the initial convecting layers formed. This was despite using the maximum possible T-S contrast by having only T (or only S) in the plume. In our tank the number of peaks in the vertical profile of horizontal velocity reached 5 or 6, with the amplitude decaying very markedly with height up to the levewas quasi-stationary, with no clear propagation of phase relative to the tank. The water, solute and dye tracer, on the other hand, were advected upwards from the outflow depth to the source depth, passing through the velocity structure. Thus there was good evidence of a downward propagation of phase of low frequency internal wave modes relative to the water at and above the outflow depth. The mid-depth outflows were somewhat more complicated than plume outflows at the bottom of the tank, as a result of the unconstrained lower boundary of the intrusion. In particular, the addition of density to the water column above the outflow depth, and not below that depth, led to a slow evolution of the depth of plume penetration and of the overall flow, including a slowly changing internal wave field above the outflow level. The lower sloping interface bounding the outflow water periodically ‘folded’ to give rise to a new intrusion of plume water. Each new intrusion coincided with a horizontal shearing layer (across the length of the channel) in both single and two component cases. A similar intrusion splitting process was observed by Turner9 and Nagasaka et al.19 in experiments where double-diffusive intrusions were produced by slowly releasing a small volume of sugar solution ina linear salt stratification at its own density level. Multiple intruding layers formed along with upstream horizontal columnar wave modes. Nagasaka et al.19 attributed the branching and layering to “collective instability” of salt fingers near the source. In those experiments, strong double-diffusive convection occurred near the source and provided the only buoyancy flux in the flow (i.e. there was no input buoyancy flux as in a plume). They found that, for a

given source volume flux, the intrusion speed was substantially reduced below that for a single intrusion formed in the absence of convection, and that the vertical scale was determined by convection above and below the source. This case is therefore significantly different from that studied in the present experiments, in which: a) there was a direct buoyancy input and a very much larger volume flux at the outflow level; b) there was a mean vertical advection associated with a ‘filling box’ ventilation; and c) layering was not dependent on double-diffusive convection. Indeed, double-diffusive effects were negligible within the plume. The two types of experiment become more comparable when the plume buoyancy flux in the present experiments is made small, so that double diffusive effects begin to take over the forcing of velocity structure. However, it is possible that low-frequency internal waves played some role in those earlier double-diffusive experiments, perhaps serving to initialise the layer thicknesses and to communicate this scale horizontally into the surrounding stratification far ahead of the advancing intrusions (Griffiths and Turner, private communication). The layer thickness, outflow velocity and exponential decay height of the shear layers in the laboratory or ocean outflows can be estimated from the theoretical solution of Wong 14

for viscous internal waves modes excited by a plume outflow at the bottom of a basin. The theory does not rely on the stratification being produced by the same plume (it can be of arbitrary magnitude). The analysis assumed a stress-free bottom, which is an appropriate boundary condition to apply at the outflow depth in the present case. We can also reasonably assume that evanescent waves below the outflow play no significant role, in which case the total depth of water is irrelevant. The thickness and velocity of the outflow are predicted to be determined by the dominant internal wave mode excited by the outflow. This is the mode having a downward phase speed equal to the upward advection speed, in this case induced by the outflow volume flux. The thickness of the outflow (identified as the lower most shear layer) in a long narrow channel (where the outflow can be considered two-dimensional) is given by: λ ≈ 2πE(H/W)1/2H …(7) from Eq. (42) of Wong et al.(

en14), whe


208

lume and W is the width of the basin. The outflow

plume buoyancy flux. These quantities re therefore independent of the length L of the basin.

uoyancy flux. The predicted exponential decay

the basin aspect ratio and Re = NmH /ν a Reynolds number based on the buoyancy

Applying Eqs. (7-9) to our experiments with mid-

.13, H ≈ 0.12 m, W = 0.15

a

the buoyancy available to drive intrusions. Using in

. Taking

vertically falling plumes), H is the height of fall of the pvelocity is given by (combining Eqs. (6) and (45) of Wong et al.14) U ≈ 1.37E1/3F1/3H1/6W-1/2 …(8) where F is the aThe layer thickness λ is also independent of the bheight γ is γ = 2πRe(H/L)(λ/2πH)4H = (2πNm/νL)(λ/2π)4 …(9) where H/L is 2

isfrequency at the outflow. depth outflows and using the initial buoyancy frequency, with Nm ≈ 0.2 s-1, ν ≈ 10-6 m2s-1 (the molecular viscosity), E ≈ 0m and L = 1.5 m (for experiments as run numbers 5, 6 and 8), we predict λ ≈ 0.08 m and a vertical decay scale γ ≈ 0.03 m which are the s me for most of the experimental runs. The predicted thickness of shear layers is in good agreement with the experimental results. The decay height is up to a factor of two smaller than that observed (although the empirical value had a large uncertainty because the decay distance was not much greater than the distance between the velocity maxima). This discrepancy may be the result of the free lower boundary to the outflow or the slow evolution of the flow and deepening of the outflow depth with time. In any case, the theory indicates that, at the laboratory scale, viscosity can cause the observed decay of the shearing velocities within a height less than 0.1 m above the outflow depth. Turning to ocean outflows, we may apply the same theoretical solution given above (at least for some time after the start of the experiments and not for long time after which the laboratory outflow had occupied a significant portion of the enclosure), while keeping in mind the two dimensional and non-rotating simplifications in the analysis. The internal waves in ocean outflows may also be generated by the sloped boundary and are not usually stationary as in the laboratory case22. However, we should also ask whether double diffusive convection will influence

Eq. (6) values for the Persian Gulf in summer (see section 2, particularly ∆S = 4.1 kgm-3, β∆S = 3.0, q = 2.3×105 m3s-1), along with molecular quantities κS = 1.3×10-9 m2s-1, ν = 10-6 m2s-1, we estimate the source salt flux FS = 9.4×105 kgs-1, the salt finger interface flux FDDC = 7.5×105 kgs-1 and the ratio ϑ = 0.80. In contrast with the two component experiments (Table 1) this is a very small value. It indicates that double diffusive convection is too weak to influence the outflow buoyancy and shearing motions. The outflow is predicted to behave as a single component flow (apart from any small scale structure produced by convective instabilities) and we may proceed to apply the results (Eqs. 7-9). We also tentatively use N ≈ 0.007 s-1 (see section 2), ν ≈ 10-5 m2s-1 (an estimate for the turbulent vertical viscosity in this density gradient), an entrainment coefficient E ≈0.1 for the plume on a sloped boundary27 and outflow depth H ≈ 400 msome account of the highly irregular width (due to eddies) of the boundary current formed by the outflow, we use W ≈ 5000 m (and this is also the internal Rossby radius for the outflow). The relevant basin length in (9) is more problematic, as the Gulf of Oman is not closed at its eastern end at the outflow depth. We propose instead that the dominant wave mode might be the fundamental mode across the Gulf, implying L ≈ 105 m; or it may be taken as the distance along the Oman Gulf in which an internal Rossby adjustment (based on potential vorticity conservation, the distance from the Strait where the outflow vanishes) of the outflow may occur28, which is about the same. Friction and Coriolis effects might also influence the effective length of low frequency motions in the Gulf. With these values Eqs. (7) and (9) give λ ≈ 70 m and γ ≈300 m. For comparison, the data collated by Bower et al.12, Plate 8) and that in Fig. 2 show temperature maxima at 30 to 80 m depth intervals, typically throughout a 200 to 300 m range of depths. Hence the predicted values seem to match the observed structure. The prediction for the Red Sea outflow, which has a larger height of plume fall (Bower et al.12, Plate 8), is λ ≈ 100 m and γ ≈ 600 m. Collated temperature profiles for the Red Sea Water (Bower et al. 12, Plate 3, noting the February to June periods in particular) show a 200 m scale in histograms of the depths of temperature maxima, and would require a decay height of order 300-400 m. Individual vertical profiles, on the other hand, show temperature maxima separated by less than 100 m. Hence the predictions are not inconsistent. To an


209

ection. We have not established whether

pth intervals. The evidence

flows from arginal seas may be a result of low frequency

. Our experiments demonstrate that

tions): it leads to a modification of the

extent, the differences between the two outflows are correctly predicted. It should be noted that we are here assuming an association between vertical structure in temperature and horizontal velocity similar to that found in the experiments. No provision has been made for seasonal variations of outflow depth and volume flux, which will tend to increase the overall thickness of the outflow and allow a smaller value of γ. We are forced to refrain from further quantitative comparisons because the analysis of Wong et al.14 and the present experiments involve internal wave modes that are standing in the horizontal and travelling in the vertical dirhorizontally standing modes are relevant in ocean outflows, where the basin is generally not bounded in all directions, or what value to place on the basin length L. Furthermore, the assumption of a two-dimensional and non-rotating flow is likely to lead to quantitative differences, given that ocean outflows are essentially three-dimensional and have a plan form strongly influenced by Coriolis effects. Thus it is not clear what value should be used for the outflow width W. All of these factors influence the mean vertical advection available to make low frequency modes quasi-stationary. There are also significant seasonal variations in source buoyancy and volume fluxes. We therefore emphasise the fundamental mechanism that may contribute to outflow structure, and the qualitative similarity between the ocean and laboratory observations. Returning to the finer scales of T, S structure in the ocean outflows, Figs. 2C, 3C illustrate that these are characterised by a “staircase” of mixed layers (small or vanishing vertical gradients) and thin high-gradient interfaces at 10-30 m deremains strong that these are maintained by double-diffusive convection. Thus the ocean outflows exhibit a degree of separation of scales, the convective layers being significantly smaller than the coarse structure discussed in this paper. As a result, there is likely to be less interaction between the two processes than was observed in the experiments, where each of the two mechanisms on its own would generate a comparable (velocity or convection) layer thickness and where we found that the shear layers controlled the initial scale for convection. The coarse scales in the ocean are, however, associated with local T and S gradients that are enhanced above the average vertical

gradients, and to that extent the shear layer mechanism can increase convective activity and vertical fluxes. Shear layers will also increase the rate of horizontal dispersion of outflow water. 6. Conclusion Laboratory simulations of plume outflows lead us to conclude that the coarse vertical structure evident in vertical T and S profiles through outminternal wavesquasi-stationary horizontal shearing modes are excited by the outflow from a plume of dense water spreading into stratified surroundings. It was clear that water, dye tracer and salt were slowly displaced upward at depths above the outflow depth while the shearing layers remained stationary in the tank. We conclude that the shear modes have a downward component of phase velocity equal and opposite to the upward advection velocity of the water. The shear layers led to a number of counter-flowing layers within the intrusion and (as a consequence of the horizontal T, S gradients between the outflow and the surroundings) had associated local vertical maxima in temperature and salinity. In the presence of both T and S gradients double-diffusive convection can be active. At the laboratory scale the convection is parasitic on the shearing modes (owing to T, S inversions generated by the horizontal movertical gradients initially generated by the shearing modes into thin diffusive density interfaces and reduced gradients in salt fingering regions. When the source buoyancy flux is large enough (ϑ < 102), the thickness of the shear layers is unchanged by the convection. There is evidence that weak shearing layers and strong double-diffusive effects (ϑ > 102) can lead to the velocity structure becoming locked to the convecting layers, after which the two structures are advected upward together. In the case of ocean outflows the coarse vertical scales of order 100 m that we tentatively attribute to quasi-stationary internal wave modes are significantly larger than the fine structure commonly attributed to double-diffusive convection. This separation of scales is likely to minimise interaction between the two mechanisms (one of which creates thin convecting mixed layers and steps, the other produces large stratified regions of enhanced T, S gradients). We also showed that ϑ = 0.80 which is further evidence that double diffusive convection cannot influence the shearing modes. On


210

utflow water

r. We also thank Heather unt (WHOI, Woods Hole) for providing us a report

l data of the Persian Gulf region.

ean salt lens - intrusion slopes and dynamical mechanisms, J. Phys.

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7 ns which drive thermohaline intrusions, in

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ffusive convection, Geophysical Monograph 94,

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22 died by ERS-

ARSS'94), Vol. IV, (Pasadena, California, USA), 1994, pp. 2023-2025.

the other hand, the level of convective activity will be enhanced by the T, S inversions that are generated by the horizontal shearing modes in the presence of the horizontal T, S gradients in the outflow. Splitting of the plume outflow and growth of new layers beneath the initial intrusion is a distinct feature of the laboratory flows, with and without double-diffusive convection. The process appears as a folding of the sloping lower boundary of the oand may be dependent on the slow evolution of the flow as density is added to the water column above the outflow depth and the outflow depth increases. This long-time evolution probably does not occur in the oceans (especially with regard to the vertical advection as in the laboratory model), where the outflows are persistent, as a result of larger scale horizontal exchange with the Indian Ocean. Quantitative predictions for the ocean outflows are also hampered by complexities resulting from three-dimensionality, geostrophic flow, and an open end to the receiving basins, and seasonal variations of the source water characteristics. Further experiments should include the effects of rotation and seasonal buoyancy fluxes, while further theoretical analysis is required to investigate the roles of geostrophic flow and partially open basins. Acknowledgement We thank Prof. Ross Griffiths (ANU, Canberra) for providing valuable comments and corrections on the early version of this papeHon the hydrographicaWe thank T. Beasley and R. Wylde-Browne for their technical assistance with the experiments. A. A. Bidokhti was supported from the Tehran University while on sabbatical leave at the Research School of Earth Sciences, Australian National University, Canberra, Australia. Hence the support of Tehran University is also greatly acknowledged. References

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