Proc. 8th Hawaiian Winter Workshop, P. Muller & D. Henderson (eds.),University of Hawaii at Manoa, January 17-20,1995, pp. 43-56.

Waves Trapped To Discrete Topography:Existence and Implications

D.S. LutherSchool of Ocean and Earth Science and Technology, University of Hawaii, Honolulu. Hawaii

Abstract The characteristics of observed energetic waves trapped to discrete topographic features, especially

islands and mid-ocean ridge segments, are discussed. Resonant oscillations may occur due to closed propagation

paths or zero group velocity along isobaths. The waves are forced directly by fluctuating winds, and may also beforced indirectly through the atrnosphere's excitation of open ocean waves that subsequently impinge upon thetopography. Evidence of energy leakage from one resonant island trapped wave to a resonant wave trapped to aneighboring island is reviewed. The potential importance of the poorly understood island and ridge trapped waves toteleconnections, mixing at the water-earth boundary, effluent dispersal, and general circulation simulations is noted.

Introduction

Perhaps the most important characteristic of theocean's many types of free waves is their ability to pro-pagate information about a disturbance from the regionof forcing to an otherwise quiescent distant location.Waveguides, produced for example by topography at acoast (e.9., yielding refractive trapping to the coast), orby the reversal of sign of the vertical Coriolis parirmeterat the equirtor (equatorially+rapped waves), etc.,enhance this characteristic by reducing the energy lossthat would otherwise occur if the wave were to pro-pagate in all directions indiscriminately. The wave isfocused in a particular direction so that its energy den-sity is not diminished by dispersal in multiple direc-tions. For example, long period waves (periods greaterthan a day) trapped to,continental coastlines are nowwell respected for their impact on currents and tempera-ture fields far from the point of origin (e.g., Brtnk,l99l). Long period waves trapped to the equator play avariety of roles in the onset and maturation of climati-cally significant phenomena by propagating informationabout atmospheric changes across ocean basins (e.g., theEl Niflo phenomenon; Philander, 1990).

This note reviews some wave types whose existencehas received minimal attention in the literature, andwhose impact has been noted only briefly but could besubstantial in both the teleconnection sense outlinedabove and the local sense of how strong the ocean'sresponse will be to imposed forcing. The waves in ques-tion are those trapped to discrete topography, by whichis meant topography of limited extent, though this con-cept will not be made precise for this review. Suchtopographic features as islands, seamounts, ridge seg-ments and plateaus enable many kinds of free waves toexist that are trapped to the topography in a stratifiedocean and therefore are guided to freely propagate in(usually) only one direction, i.e., along isobaths.

The reason the scale of the 'discrete' topography willnot be defined rigorously is that some 'of the more

interesting observations that have arisen lately are ofwaves trapped to a mid-ocean ridge segment, e.g., theJuan'dq Fuca Ridge. These waves raise the question ofexistenc'e and propagation for long distances along themid-ocean ridges. If a ridge-trapped wave were gen-

erat€d by a storm in the South Pacific Ocean could itpropagate up to the equator along the East Pacific Rise?This paper will concentrate on discussing those obsewa-tions of waves trapped to more discrete features, espe-cially the Hawaiian Islands and the Juan de Fuca ridgesegment. Waves trapped to se:rmounts, which have beenfound to reach amplitudes up to 40 cm/s (Eriksen,

l99l), are treated by other authors in this volume.There are now quite a few observations of narrow-

band (in frequency) wave motions that appear to beresonances of the oceanic fluid system in the presenceof discrete topographic features. These resonant wavesare the most easily identifiable members of the wholeclass of oscillations which can exist at discrete topogra-phy, but are just a small portion of this class. The reso-nance can occur because the wavelength of a particularwave neatly circumscribes the discrete topography in anintegral number of wavelengths, or because the charac-teristic dispersion of the trapped oscillations admits azero group velocity point in the (single) direction ofpropagation thus allowing energy to accumulate.Perhaps what is most remarkable about these resonancesis their existence at all, and especially their existence asunderdamped oscillations in the presence of highlyirregular topography that intuitively would be expectedto cause strong damping. As will be seen, the irregulartopography of such features as mid-ocean ridges doesnot seem to inhibit the existence of resonances whichnecessarily have been studied with only the smoothestof ideal geometries.

The resonant oscillations are easy to study, and havebeen studied with datasets not specifically intended for

that purposeo because their amplification at discrete fre-

43

44 LUTHER

quencies makes them identifiable in autospectra of oce-anic variables taken at widely separated locations, and,because being narrow-band in frequency usually impliessmall wavenumber bandwidth, leading to relatively highhorizontal coherence. Thus it is easier to describe thesephenomena from a sparse iuray of instruments than it isto describe broad-band phenomena.

An important practical consequence of narow-bandresonance among trapped waves is that the resonantwaves are reservoirs of energy well above what wouldbe present at the topographic boundary due to ambientopen ocean variability. Such reservoirs must have animpact on mixing at the boundaries, or on dispersal ofthe products of such mixing, especially since thetrapped waves tend to have their largest amplitudesright at the boundary. If you subscribe to the idea thatsub-thermocline mixing occurs at water€arth boundaries(Gilbert and Garrett, 1989), then at middepth levels(2000m - 3000 m) in the ocean you have to be con-cemed about what motions exist along the -50,000 kmof mid-ocean ridge cress. Irrespective of a role in glo-bal mixing, the resonant oscillations definitely play arole in the redistribution of anthropogenic and hydroth-ermal effluents (e.g., Cannon et al., l99l), as will beclear from the following examples. It is also clear thatnon-linear advection can result in strong residualcurrents, as already demonstrated by observations (En&-sen, l99l) and numerical simulations (Haidvogel et al.,1993) of resonant waves at seamounts.

Killworth (1989a) has emphasized the importance oftopogpphic waves in extracting energy from coastalKelvin waves (when the ridge intersects a coast). A log-ical extension of this idea is that ridge waves may beimportant sinks for open ocean Rossby wave energy.The implications for general circulation models whicheither don't have the horizontal resolution to resolve thevarious topographic wave modes or incorporate generalLaplacian damping is that the shorter-scale topographicwaves will be under-represented resulting in under-damping of the Kelvin or Rossby type motions.

On the following pages I will present examples ofwhat appear to be resonant oscillations trapped tospecific topographic features, including especially theHawaiian Islands and the Juan de Fuca Ridge. Thematerial presented is from both a review of the litera-ture and ongoing research.

Considering that many topographic waves are physi-cally distant from the sea surface and hence apparentlyisolated from the action of surface winds, investigationof how the waves are forced has led to sorne especiallyintriguing observations and speculations of new energypathways or energy transfer mechanisms. Waves trappedto seamounts and ridges, for instance, that are evanes-cent upward still may be forced by atmospheric winds,either directly via the wind's establishment of forcedoscillations that are evanescent downward from the sur-face but still intersect the topography (producing a "tun-nelling" of energy from the surface to the topography),

Table 1. Examples of waves trapped to discrete topography

Characteristics References

Ridse Sesments

Iuan de Fuca Ridge (-46oN, 129'W) 4 days baroclinic; trapped to ridge cresthorizontally and venically

barotropic; uapped horizontally

barotropic; trapped horizontally

baroropic; rapped horizontally

baroclinic; bottom trapped;rectification observed

Thornson (1989)Chave et ar. (1989)

Cannon et al. (199L)Allen and Thomson (1993)

Miller et al. (1995)

Huthnance (1974)

Hunkins (1986)

Eriksen (1991)Noble et al. O99a)

Wunsch 11972a)Hoee 0980)Erilcsen (1982)

Luther (1985)hnpkin (1995)

Saint-Guily and Inmy (1988)

Faroe-Iceland Ridge (-63oN, lO'W)

Banks. Plateaus. Seamounts

Rockall Bank C57"N, l4'W)Yermak Plateau (-82'N, l0"E)Fieberling Guyot (-32oN, 128"W)

Islands

Bermuda Is. (-32oN, 65'W)

Hawaiian Is. (-2loN, 157"W)

Kerguelen Is. (-49oS, 70'E)

l0 hrs to 17 dys baroclinic; Kelvin Wave analogue

l7 hrs to 5 dys baroclinic; Kelvin Wave analogue

1.5 dys baroropic; shelf wave analogue

1.8 days

I dayI dayI day

WAVES TRAPPED TO DISCRETE TOPOGRAPHY 45

or indirectly through generation of free barotropicwaves which subsequently propagate into the region ofa ridge. That the surface atmospheric fields do generateboth evanescent and free barotropic waves at sub-inertial frequencies has been theoretically investigated(e.g., Frankignoul and Milller, 1979; Miiller and Fran-kignoul, 1981) and observationally confirmed (e.9.,Luther et al., 1990; Chave et al., 1992). The intermedi-ary oscillation could transmit the atmosphere's effectsover long distances before exciting the topographicwaves, as may occur with sprface gravity wave excita-tion of trapped waves around the Hawaiian Islands.Finally, resonances on neighboring topographic featuresmay co-oscillate after one or the other resonance hasbeen excited, as the trapped waves around the HawaiianIslands demonstrate. Examples of some of thesephenomena will be presented in the following pages.

Some Examples of Waves Trapped toDiscrete Topography

Table 1 summarizes characteristics of sonre oscilla-tions that have been observed at discrete topographicfeatures. This is not an exhaustive list, but it will give aflavor of the growing number of observations of such

| 30" 125"WFigure l. Line drawing of the Juan de Fuca Ridge and itssegments. Three open squares show approximate locationsof some of Cannon et al.'s (1991) moorings, including onebetween Axial and Brown Bear senmounts; the open circlesindicate locations of five of Chave et aL's instruments: and.the cross at the end of the Endeavor Segment locates theThomson (1989) aray. Circles with dots are seamounts: (A)axial; (B) Brown Bear; (C) Cobb; and, (V) Vance. Figuremodified from Cannon et al. (l9v^l).

waves, and will provide some information on theirsalient features. Note that seamount fapped waves aretreated in detail by other authors in this volume, and sowill not be discussed further here. In this section, obser-vations of waves trapped to the Juan de Fuca Ridge andto the Hawaiian Islands will be explored.

Ridge Waves

Cannon et al. (1991) describe several years of currentand temperature observations from instruments mooredat the southern end of the Juan de Fuca Ridge (JDFR)and at Axial Seamount in the middle of the ridge (Fig-ures I & 2). Instruments near the ridge crest are dom-inated by a -4-day oscillation that rotates predom-inantly clockwise (Figures 3 & 4). The oscillation isubiquitous in all records in all years (Figure 4). Theoscillation has maximum currents near the bottom in therift valley. Near-bottom amplitudes are not uncommonlylG15 cm/s (Figure 3). The currents decay upward andaway{ (ffrpendicularly) from the ridge axis. Near thebottom the 4day oscillation is more energetic than the

Figure 2. Chart of rhe southem end (ttre Cteft Segment) ofthe Juan de Fuca Ridge showing detailed locations of someof Cannon et al.'s (l9l) moorings. Moorings are shownby solid circles with identification (ID) numbers on theright (4, 12, and 19 are at the same central location;8 is onthe west side; ll is on the east side). Solid lines betweenopen circles arc conductivity-temperaturc-depth (CTD) sec-tions. The contour interval is lff) m, and 230G2400 m arestippled to bettsr outline the ridge. Figure modified fromCannon et al. (1991\.

.Ylncouv:r \t

(c

a

(,zal

:

46 LurHsn

-?5

15

-15

15

0

-15

Figure 3. Currents (2.8-hour filtered) along 20o true in the rift valley of the Juan de Fuca Ridge(mooring 19, south; 18, north; see Figure 2) and across (l0o true) the Axial-Brown Bear sill (Figure l)for winter 1988, showing the 4-day signal dominating the tidal flows. Vertical line shows northwardpropagation of the 4-day oscillation. Figure taken from Cannon et al. (1991).

FUcoo\

-=U

FU

o\N=

UFUooo\

U

1 t0 ?0 1 t0 20 I 10 ?0 IJon Feb Mor Rpr88 88 88 88

tides and inertial oscillations (Figure 4), but a few hun-dred meters off the bottom it is not. The oscillation ismbst eneigetic in winter suggesting direct atmosphericforcing, which is borne out by coherence between localwind stress and cunents at mooring 19.

The oscillation is highly correlated along and acrossthe ridge. Cannon et al.'s (1991) experiment extendedabout halfway along the JDFR (Figure 1) for a distanceof approximately 150 km. Coherence phases among allthe Cannon et al. (1991) moorings, irrespective of loca-tion across the ridge, indicate a northward phase propa-gation of l-1.5 m/s. This phase speed range correspondsto a wavelength range of -350-500 km that brackets the-450 km length of the JDFR.

At the northern end of the JDFR. on the EndeavorSegment approximately 200 km north (Figure l) ofCannon et al's (1991) most northerly instruments,Thamson (1989) and Allen and Thomson (1993) reportobservations of a 4-day oscillation with the samecharacteristics (such as clockwise polarization,amplification near the ridge crest, and vertical trapping)as reported by Cannon et al. (1991).

Chave et al. (1989) report observations of the 4-dayoscillation in measurements of the horizqntal electricfield made on and near the JDFR. At periods greaterthan I day, the horizontal electric field is proportional

to the vertically-averaged horizontal water velocity, aneffect due to motional induction caused by the seawatermoving through the earth's stationary magnetic field.The array of electrometers was able to detect clearly adecay of the oscillation away from the ridge axis, aswell as the clockwise rotary character of the motion atthe ridge. They also find a factor of 3 decay of energyalong thg ridge, from south to north, over -150 km dis-tance. This last observation is consistent with the energylevels reported by Cannon et al. (1991) compared withthose shown by Allen and Thomson (1993). The Chaveet al. (1989) results deviate from Cannon et al's (1991)in their estimation of a southward propagation speed forthe wave on the eastem flank of the JDFR, whereasCannon et al. (1991) report northward propagation onboth sides of the crest.

The 4-day oscillation is certainly a type of stratified,topographic oscillation. Allen and Thomson (1993) havesimulated many of the characteristics (e.g., clockwisepolarization, bottom and ridge crest trapping) of theoscillation with a forced model under the assumption ofno along-ridge variability. Killwonh (1989a, 1989b)has performed the most complete analysis to date of thepotential suite of free oscillations trapped to a ridge, butnecessarily restricted his model to no more than twofluid layers to retain a certain amount of analytical trac-

Vl4 - Axiol Sill

Yt' - cteft (N)

Vt9 - Cteft (s)

WAVES TRAPPED TO DISCRETE TOPOGRAPHY 47

o'ot o ' l .y . t r r ldoy

t ' to 'o

Fi3urc 4. From top to bottom, auto-spectral densities fortemperature at 2000 m at mooring 12, currents at 2000 m atmooring 12, currents at 2000 m at mooring 19, and near-bottom currents at 2200 m at mooring 19. Mooring 12 wasdeployed in 1986-1987, while mooring 19 was deployed in1987-1988. For the currents, the solid curve is clockwise.Confidence limits of 95% are shown for 24 degrees of free-dom. Figrrre taken from Cannon et al. (l9l).

tability. Even so, Killworth's models provide enoughinformation on wave structure and dispersion to specu-late as to why the JDFR 4-day oscillation is resonant,and why there might be different phase propagationdirections at difTerent distances from the ridge.

Many of the solutions presented by Killworth havevery asymmetric structures. That is, they have verylarge amplitudes only at the crest and on one side of theridge, i.e., the side where the ridge crest is to the rightof the direction of propagation (northern hemispherecase). One can then readily imagine that oscillationscould propagate north along the west side of the JDFRand south along the east side. Reinforcement, that isresonance. occurs when the distance of a transit aroundthe ridge equals an integral number of along-isobathwavelengths of the oscillation. The gravest mode (model) would have a wavelength equal to twice the length ofthe JDFR. The second gravest resonant mode (mode 2)would have a wavelength equal to the length of theJDFR;i and so on. Cannon et al's (1991) phase speedmeasurements could correspond to a mode 2 wave,while Chave et al.'s (1989) measurements suggest model. (N.b., Chave et a/. (1989) point out that their phasespeed estimate is uncertain to about a factor of 2, sothat their 3 m/s speed is not significantly different fromCannon et al.'s (1991) 1.5 m/s speed; Chave et al.( I 989) defi nitely observe southward propagation.)

It is remarkable that such a resonance should occuralong the JDFR in the presence of that ridge's highlyinegular topography. Figures | & 2 only give a scantindication of the true complexity of the topography.Notice that the JDFR is not even a single continuousridge, but has several discontinuities (offsets) along itslength. As will be shown below, resonant waves existrapped to, and propagating around, highly inegularisland topo.geometries, as well.

An appealing way to reconcile the existence of aresonance with the complicated structure of the JDFR isto argue that, for a specific frequency and along-ridgewavenumber, zero group velocity along the ridge per-mits an accumulation of energy. In this case, one ima-gines the resonant character of the wave as being deter-mined not by whether a complele circuit of the topogra-phy can be circumnavigated by the wave, but by theexistence of a group velocity zero point on thefrequency-wavenumber dispersion curves that permitslocal accumulation of energy at a particular frequency.Then every small segment of the JDFR can have itsown zero group velocity point, and, since the cross-ridge profile of these segments is nearly the same, theycould all have resonances at approximately the samefrequency, and hence excitation of a resonance at onelocation could spread down the ridge.

The dispersion characteristics of the waves exploredby Killwonh (1989a, 1989b) have particular frequencies

19 - 2200 m

48 LUTHER

and along-ridge wavenumbers where the along-ridgegroup velocities are zero, which would then permit theaccumulation of energy, as for instance is the case forequatorially-trapped internal gravity waves (Wunsch andGill, 1976). There would still be phase propagation, andgiven the sructures calculated by Killwonh, there couldeasily be two oscillations at the same ridge segmentwith exactly the same frequency and exactly the samealong-ridge wavelength, but which have phase propaga-tion in opposite directions and are therefore relativelyisolated from each other because their amplitudes arestrongest on opposite sides of the ridge. This scenario,then, could also explain the observations of northwardpropagation on the west side of the JDFR and south-ward propagation on the east side.

What is not explained by either scenario above is theapparent dominance of northward propagation at the topof the ridge in Cannon et al.'s (1991) observations. Ofcourse, for the zero group velocity resonance, one couldargue that the wave with northward phase propagationis stronger for some reason than the southward pro-pagating wave.

The difference between the two scenarios of reso-nance above is more than an esoteric thought experi-ment. Whether energy propagates readily along theridge directly relates to the major introductory pointabout whether the effects of forcing at one location on amid-ocean ridge can travel far from the source. If theresonance on the JDFR is due to a wave propagatingenergy along the JDFR, then we can conclude that thesubstantial topographic inegularities do not impedepropagation of these mesoscale waves along the ridge,hence we could expect to see disturbances propagatereasonably rapidly for thousands of kilometers alongridge crests. If, however, the resonance on the JDFR isdue to zero group velocity, then the question of whetherany ridge waves can propagate very far along a ridge isleft unanswered, although diffusion of the energy of theresonance along the ridge is still possible through leak-age to resonant waves on neighboring ridge segments.

Irrespective of this issue of whether or not the wavespropagate energy along the ridges, the JDFR resonancedemonstrates the existence of non-trivial ridge-trappedoscillations, which has a number of important localimplications as outlined in the introduction.

Island-Trapped Waves (ITW)

Using sea level data, Luther (1985) showed that bothsub-inertial and super-inertial waves are trapped to indi-vidual islands of the Hawaiian group. A few of themodes identified by Luther (1985) are indicated in sealevel power spectra in Figu.re 5. That these oscillationscan be associated with substantial current amplitudes isdemonstrated in Figure 7. Luther (1985) established thatthe sub-inertial trapped oscillations were baroclinic,

rol l l(days)

30 20 15 r08 05 4 g 2 1 15

10 -3 10-2

E-ra^rr ' / 'a \r r vY*ency (cpnl

Figure 5. Energy density spectra of adjusted sea level (theisostatic effect of air pressure has been removed) from Hilo,Honolulu and Nawiliwili (see Figure 6 for locations),employing 24, 18 and 13 years of data, respectively.Suspected ITW are indicated with arrows. The inenial fre-quency for the mean latitude of each island is indicatedwith /. For ease of comparison, each spectrum is displacedfrom its neighbors by one decade along the ordinate. Thediurnal and semi-diurnal tidal peaks in the Honolulu andNawiliwili sp€ctra have been clipped to simplify the figure.The fortnightly and monthly tides are clearly evident. The95% confidence intervals at the bottom of the figure areexact for Nawiliwili but are slightly large for the other.spectra. An increasing averaging bandwidth rcsults in adecreasing confidence interval as frequency increases. Theconfidence intervals apply to each independent point. Everyother point plotted is independent. The ordinate is in unitsof (cm)zlcph.

10'

1o+

103

tn2

10r

Nawiliwili

WAVES TRAPPED TO DISCRETE TOPOGRAPHY 49

Kelvinlike trapped waves as first described by Wunsch(1972a) at Bermuda. The dynamics of the super-inertialniodes arc still unknown.

The potential impact of ITV/ on horizontal dispersionnear Hawaii is suggested by Figure 8; band-passedcurrents (integrated over time) are shown in four fre-quency bands, including the sub-inertial band encom-passing the gravest ITW mode around the island ofHawaii. Assuming the integrated currents emulate theLagrangian drift of fluid particles, trapped waves wereresponsible for advection over 6 km compared to 2 kmfor inertial, diumal and semi-diumal motions.

Since baroclinic modes other than the first have littlesea level deflection (unless the higher modes are sub-stantially more energetic than the first), Luther (1985)necessarily only found clear evidence for first baroclinic.modes, with a hint of a couple of second baroclinicmodes. At Oahu, for instance, power spectral peaks at1.5 days and 2 days (Figure 5) correspond to peaks incoherence amplitude between sea level stations onopposite sides of the island (Figure 9). The coherencephase at these periods is not significantly different (atthe 95Vo level) from what would be expected (- 105')for an azimuthal mode I wave propagating clockwisearound the island as appropriate for Kelvin waves.Luther (1985) concluded that the 1.5 day oscillation wasthe lst baroclinic, lst azimuthal ITW mode for Oahuand that the 2 day oscillation was the 2nd baroclinic,lst azimuthal mode.

At Bermuda, where sea level deflections of the modesare not at all robust (compare Wunsch's, 1972b, Figure2 with Figure 5 here), HoSS 0980) observed modes ashigh as the 4th baroclinic in current meter data. For theisland of Hawaii, the 4th baroclinic, lst azimuthal modewould have a period of approximately 8 days, assumingthe validity of the cylindrical model for computing theresonant periods. Hogg (1980) also speculated thatstrong coherence among current meter records at -17days may be due to an island or topographically trappedoscillation. This information is presented simply to indi-cate the potential range of periods for which trappedwaves may provide a significant amount of thenearshore variability.

Figure,l0 shows power spectra of azimuthal velocitytaken from a mooring (C10 in Figure 6) near the islandof Hawaii. A clear peak at 2.7 days period is seen at 54m and 363 m. This is probably the lst baroclinic, lstazimuthal mode identified by Luther (1985) and seen inFigure.r5 (top). At the deepest depth available (771 m),tbe 2.7-day peak is no longer evident, but a peak at 4.5days is seen. Whether this longer period peak representsa higher baroclinic trapped mode(s) is the subject ofcurrent research. At lhe moment, the cause of the 4-5day peak at 771 m in Figure 10 is suspected to be that,at this depth, the graver baroclinic/radial modes withsmaller periods are relatively weaker than the higherbaroclinic/radial modes with longer periods. Our intui-tion on this point comes from the results of Bink

r59. 156.

Figure 6. Map of the Hawaiian Islands showing locations of sea level and meteorologi-

cal stations and current meter mooring sites, not all of which are mentioned in the text.

Dark shading is land; light shading defines the 100 m ircbath. The 1000 m isobath is

also shown. Figure taken trom btntpkin (195)'

JU LUTHER

q1n9n

Erooo

ATMOSPHERIC PRESSURE

. . . , i . . . . . ' . . . . i . . . .

i"*q"+,,ygr'\ i

Trappod mve bard (55-55 h period)

:3-z-rorz3Estwsrd displ&€msn Gm)

OurEl band (22-26 h Friod)

-g

o

-gaE

ts6

'Ez

I

=o

9l

*!

E3

z

1

:3-2-10r23E6lwad disCe6m6nt (km)

Ssmjdiumal b3nd (11-13 h porbd)

10

SIGNIFICANT WAVE HEIGHT

- :buoy1 : i - lbuoy3 : !' ' ' '1 ; . , i t

; ; ; "" ,'' , f-' n' i.^.r.*lN 'rl^il'4;-r' i: x -JV

SEA LEVEL

: ;- ;Hi lo ;

F

9

RxiiIE Q

E

F

o.ElgEcE

ts-1,a

z-20

CURRENTS

DAYS IN JANUARY 'I 985

Figure 7. Sea level from Hilo and Kahului (neitheradjusted for the isostatic effect of air pressure), and currentsfrom the Alenuihaha Channel mooring (Figure 6), for atime period when the ITW mode around the island ofHawaii (-2.5 day period) was particularly strong. Thesedata have been low-pass filtered to remove energetic tidalfluctuations. Also shown are atmospheric "pressure, windsand significant wave height from two NOAA buoys to thewest of the islands (-23'N, 162"w, and -19"N, 161'W).Figure courtesy of M. Merrifield.

(1989), whose calculations show that the higher

baroclinic/radial, seamount-trapped modes occur atlonger periods than the gravest modes and are more bot-tom trapped. [The term "baroclinic/radial" modes is nowused to emphasize that with significant topography theclassic definition of baroclinic modes is usually notvalid. Higher modes have more nodes offshore thangraver modes, but the nodes tend to be neither verticallynor horizontally oriented.l

Identification of as many normal modes as possible isan important tool for discriminating the dynamicalappropriateness of models of variability around theislands, akin to the discrimination of earth. structuremodels by the enumeration of normal modes of theearth (e.g., Gilbert and Dziewons&i, 1975). For instance,

:3-2 ' , -4or2gE6tda|ri disphcement (km]

-3-2-10123Estward disdacgmtrt (km)

Figure 8. Progressive vector plots of the currents at 54 mat the Keahole Pt. OTEC-I site, off the leeward coast of theisland of Hawaii (Figure 6). Band-passing has isolated themotion at 55-65 h period (top left), 32-39 h period (topnght),22-26 h period (bottom left) and ll-13 h period (bot-tom right). The 55-65 h band encompasses the gravest ITWmode around the island of Hawaii. Fisure taken fromLumpkin (1995).

iloSg (1980) showed how an ad hoc incorporation of asloping bottom will significantly alter the expectedequivalent depths for each baroclinic mode and thusalter the expected resonant mode periods.

One of the important results from Luther (1985) wasthe realization that good agreement between tbeobserved periods of the first baroclinic sub-inertialITWs and the theoretical periods of simple baroclinicKelvin-like modes trapped to a cylindrical island(Wunsch, 1972a) could be achieved by matching the cir-cumference of the real island (at the 20m isobath) to thecircumference of the hypothetical cylindrical island.Previously (Wunsclt, 1972a; Hogg, 1980), arbitraryidealized geometric figures (i.e., ellipses) were fit to thereal island geometry and employed to estimate an

effective cylindrical island radius. But, the cylindricalisland is not expected to yield very useful predictions ofhigher baroclinic mode sub-.inertial IT1W frequencies(e.g., Hogg, 1980), which can also be deduced from thefact that the Burger number (the ratio of the intemalRossby radius of deformation to the radial scale of thetopography) for the higher modes is relatively small. Inother words, based on Hogg's (1980) work and Brink's(1989) study of searnount-trapped waves, it is certainthat the dynamics of the ITW is non-trivially dependentupon topography, especially for the higher

100

E0

-1 00

Ns-.insrtial band (32-39 h penod)

ffiwrNDs (BUOY 3)

NEAR-SURFACE

WAVES TRAPPED TO DISCRETE TOPOGRAPHY 5r

a5

-J-------

t l l

at each of the islands. Luther (1985) concluded, on thebasis of coherence between sea level stations (Honoluluand Moku o Loe) on opposite sides of Oahu, that theinter+idal peaks at the Oahu stations were due to oscil-lations propagating around the island that were probablytrapped. He suggested that Wnnsch's (1972a) theory ofpseudo-resonant trapped waves might explain the peaks,as it did for super-inertial peaks at Bermuda. Wunsch(1972a) studied the reflection of an intemal plane wavefrom a cylindrical island and found that at certain fre-quencies nearshore amplification occurred; he called thisamplification a pseudo-resonance since there is not atrue trapping of the wave around the island, i.e., freeinternal gravity waves exist at all frequencies to carrythe energy away from the island. Lumpkin (1995) hasevaluated the full Wunsch (1972^) solution with param-eters appropriate for the Hawaiian Islands and has foundthat, for any reasonable choice of baroclinic and azimu-thal mode numbers (i.e., less than 25 for each), thepseudg-resonances always occur closer to the inertialfrequency / than 1.25l, whereas the inter-tidal peaks inFigure 5 occur at approximately twice the inertial fre-quency (at about l7 hours period). [N.b., the phase lagsfound by Luther, 1985, suggest by Occam's razor anazimuthal mode number less than 4.1

rd

E t0 'F

N

oIa. .

o

P'd

Eo

Fr€qu€ncy (@h)

Figure 10. Azimuthal velocity spectra for 109-day longcurrent rccords flom the Keahole PL OTEC-I site: 54 m(top), 363 m (middle) and 771m Oottom). The 54 m (771m) spectrum has been displaced up (down) one decade forviewing convenience. The sub-inertial peaks in the 54 mspectrum are at 2.8, 2.2 and 1.6 d4ys period. Peaks in the363 m spectrum arc at 4.0, 2.8, 2.2 and 1.9 days period.The 771 m spectrum peaks at 4.4, 2.2 and 1.6 days period.The vertical dashed lines mark the inertial' diurnal andsemi-diurnal pcriods. Figurc taken from Lr t,n (1995).

(days)30 20 15 108

t Bo o r

900

n\

U)^a

Oo

-3--9oo

C)-O 0.25

-* 0.50

-!< 0,2s

- 1800 l -10 -s

40 30

1 0-2

05 {

10 -r

t0 0

0.001o-3 1o-2 I

/ r \

. t , requency (cph)10-r

Figure 9. Coherence amplitude and phase between 8 years

of adjusted sea level (isostatic effect of air pressure hasbeen removed from the sea level) from Honolulu and Mokuo Loe on the island of Oahu (Figure 6). High coherenceamplitude is seen at the diumal and semi-diurnal tidal fre-quencies. The high coherence amplitude with zero phase atperiods grcater than 3 days is due to open ocean barotropicoscillations. High coherence amplitude at 1.5 and 2 days isdue to the lst and 2nd baroclinic ITW modes around Oahu.respectively, both of which have auto-spectral peaks in Fig-ure 5. The coherence phase at these periods is notsignificantly different from the -1059 expected for anazimuthal mode I clockwise-propagating wave. A possiblethird barorclinic mode at about 2.7 days is also highlightedin this figure and Figure 5. The inertial frequency for themean latitude of Oahu is indicated with / The 95% level ofno significance is indicated with a dotted line.

baroclinic/radial modes. However, given the success of

mapping a real island to a cylindrical one, it is likelythat a simple improvement of the model can yield rea-sonably good agreement with observations. That simpleimprovement is to include a radially{ependent, butazimuthally-invariant topography. The modal structuresand frequencies can be obtained by resonance iteration,in a straight-forward adaptation of Brink's (1989) calcu-lation of stratifi ed-topographic, seamount-trapped waves.Brink has recently modified his code for this purpose.

The power spectra in Figure 5 clearly. suggest theexistence of narrow-band, super-inertial oscillations atfrequencies between the diurnal and semidiurnal tides

1.00

52 LUTHER

Furthermore, if it is assumed that the inter-tidalwaves that are showing up in the sea level observationsat each island have the same horizontal phase speed, itis hard to imagine how they could produce nearly thesame resonant frequency at islands like Kauai andHawaii whose circumferences differ by a factor of three.(The resonant frequencies of the sub-inertial trappedwaves after all - Wunsch, 1972a - are directly related toisland size.) With similar periods of the super-inertialmodes at each island, the differing island sizes alsoseem to rule out a refractively-trapped explanation, asmight occur due to the sloping topography around theislands. However, if the oscillation is baroclinic it ishard to imagine that the topography doesn't pldy a role.

A relationship has been sought between the frequen-'cies of the inter-tidal oscillations and sum or differencefrequencies of the prominent tidal and inertial frequen-cies. The inter-tidal oscillations have a strong seasonaldependence (e.g., Figure 1l and Luther,1985) and so aconnection with the tides is unlikely. Despite the sea-sonal dependence, no coherence with atmospheric vari-ables has been detected. Interannual dependence of thewave's amplitude rules out a connection to the sub-inertial trapped waves, since the super-inertial waves are

196't 1968 1969 1970 l97l 1972 1973 197'1 1975

Figure 11. Variance of adjusted sea level from Hilo,1966-1974, obtained from a complex demodulation using aS-point Butterworth IIR filter with a cutoff frequency yield-ing the equivalent bandpasses of 52-76 h (top) & 17-19 h.Note the seasonal dependence (highest variance in winter)for both the sub-inertial and super-inenial motions, but notethat they do not have the same interannual dependence ofvariance, and are therefore not likely to be dynamicallylinked to each other. Figure taken from ltmpkin (1995).

found to be stronger in years when the subinertialwaves are weakest and vice versa (Figure l1).

For now, there are a couple of pieces of informationsuggesting a connection between the inter-tidal oscilla-tions and near-inertial oscillations. First, the most prom-inent inter-tidal spectral peaks (at Hilo, Hawaii, andNawiliwili, Kauai; Figure 5) are at approximately halfthe inertial period. Second, a comparison by Lumpkin(1995) of cotemporal sea level data from Hilo andKawaihae on opposite sides of the island of Hawaiiyields the startling result (Figure 12) that Kawaihaedisplays a strong near-inertial peak (and Hilo doesn't)while Hilo shows a strong ff peak (and Kawaihaedoesn't). Inter-tidal coherence between the two stationsis high only at periods slightly longer than the Hilopeak. At Oahu at least, Luther (1985) showed that theinter-tidal auto-spectral peaks for stations on oppositesides of the island coincided with coherence amplitude

Frequency (cph)

Figure 12. Adjusted sea level spectra for Hilo (solid) andKawaihae, both on the island of Hawaii, for tbe same 3.5year time period. The major tidal constituents have beenanalyzed and subtracted. Arrows indicare the theoreticalperiods of the first baroclinic, first azimuthal (center) andsecond baroclinic, first azimuthal (left) and second azimu-thal (righ$ ITW modes. The vertical dashed lines mark theinertial, diurnal and semi-diurnal periods. Both spectra havean impressive sub-inertial peak centercd at 2.5 days period,corresponding to the gravest ITW mode. The Kawaihaerecord has a near-inertial (super-inertial) peak at 1.4 daysperiod which is not prcsent at Hilo; an inter-tidal peak inthe Hilo spectrum reaches its maximum at -17.9 hours, butis not seen at Kawaihae. Figure from hmpkin (195).

8qur.d rnpllixb rl Hllo, 5a-75 lu6 p.,bd

t r l- - t - - - - - - '1 --__r__J__J__

t l l- - r - - - t - - - l t - -

Sqund rmplitrdr rt Hilo, 17-19 lnE Fdod

t l t l- - r - - - t - - - - l * - -T - -T - - T- - *- -t- -

-- - -1 - - -i - - -f - - r- - -

_ _r-L _ _t_ _ I _ _ _L _ _l_ _ _ L_ _--l+ - -l- --l - - + - - r - -r--- -llT - --1- - -n - - -T - - -rr- - r - -

WAVES TRAPPED TO DISCRETE TOPOGRAPHY 53

peaks with significantly non-zero phase lags that indi-cated propagation around the island.

The present state of our knowledge of the dynarnicsof the narrow-band, super-inertial oscillations observedat the Hawaiian Islands is quite unsatisfactory. Further-more, unlike the sub-inertial ITW which have beenshown to be associated with significant cunents, nosuch correspondence has yet been found for the super-inertial waves. They remain a curiosity, but whetherthey are more than that is not known.

Forcing Mechanisms

Ridge Waves

The generation of bottom trapped oscillations, such asthe seamount trapped waves and the ridge waves dis-cussed earlier. has been considered in some sense to beindependent of the winds. For instance, regarding theforcing of seamount trapped waves, Brin& (1990) hasstated that it seems unlikely that such bottom+rappedfeatures could be forced by surface wind stress effects.Rather, he suggests resonant excitation by ambient oce-anic currents. Of course, this sidesteps the issue of whatcauses the "ambient oceanic currents." In fact, atperiods from the inertial to l0 days in which the JDFRwave resonance occurs, the atmosphere readily forcesoceanic currents (e.g., Frankignoul and Miller, 1979;Miiller and Frankignoul, 1981) that are evanescent fromthe sea surface (at the shorter periods in this band) orbarotropic. free waves (at the longer periods). Theevanescent oscillations tend to have large vertical decayscales so that they have non-negligible velocities at theseafloor. Therefore. the "ambient oceanic currents"needed to force waves trapped over bottom topographicfeatures could be directly forced by the fluctuatingwinds (as opposed to being the result of mean currentinstability, for instance).

A potential flaw in this sequence of events is that the(barotropic or evanescent) curents forced by thefluctuating winds are not very energetic. Luther et al.(1991) and Chave et al. (1992) observed amplitudes ofonly O(1 cm/s) for barotropic cunents directly forcedby the atmosphere in the midlatitude North Pacific. Butthis simply emphasizes one of our points, that is, theexistence of free waves trapped to topography, espe-cially if the dynamics impose a resonance, permits localnear-topography enhancement of the initial forcingamplitude. Chapman (1989) and Haidvogel et al. (1993)find amplification factors up to O(100) times thestrength of the incident barotropic current in analyticaland numerical models of forcing of waves trapped toisolated topographic features.

Cannon et al. (1991) detected significant coherencebetween local wind stress and the 4-diry oscillating

currents over the southern JDFR. In conjunction withthe winter-time enhancement of the energy in this bandthat they and Allen and Thomson (1993) report, directatmospheric forcing of the JDFR waves appears certain.

Island-Trapped Waves

Direct forcing by the wind is clearly capable of excit-ing at least the gravest suFinertial ITW. Figure I Iexhibits a seasonal cycle in the energy of the gravestITW mode around the island of Hawaii, which charac-teristic is generally interpreted as resulting from directforcing by the atmosphere (Wunsch, 197?.a; Hogg,1980). Furthermore, Figure l3 shows significant coher-ence amplitude between adjusted sea level and northwind stresS at the period of the gravest ITW around theisland of Hawaii. The phase associated with this highcoberence rapidly changes nearly 180' at the ITrrI/period as expected for a forced resonance. This type ofevidence of excitation of resonant ITW modes was alsofound by Hpgg (198q at Bermuda.

The simplest model of the wind forcing is to considera flat-topped, cylindrical island with an imposed

(days)-40 30 20 15 t08 €5 4 3 2 I l5

360 "

zToo

a)U)5 r8oo(-i

0.90o

0-3

1.00

a)15 0.75-l

-+J

+ 0.50

-)-..< 0.?5

0.00l 1o-2

Frequency (cph)

Figure 13. Coherence amplitude and phase between 24

years of adjusted sea level and north wind stress from Hilo.

The period of the gravest sub-inertial ITW mode around the

island of Hawaii is indicated by the short venical lines in

the amplitude and pha^se plos. Due to the highly significant

coherence amplitude and the nearly l80o phase shift' the

gravest ITW around Hawaii can be considered to be

resonantly forced by the local wind 6eld.

<A LUTHER

homogeneous, unidirectional, oscillating wind stress.Under these conditions it is easy to imagine that anazimuthal mode one ITW could be excited by the diver-gence of the wind-produced Ekman flux as it encountersthe island. On one side of the island the horizontal fluxdivergence causes a set-down of the thermocline, and ontbe other side a set-up. Half a period later the set-down/set-up pattern is reversed, thus potentially rein-forcing an azimuthal mode I wave that has propagatedhalfway round the island. The dynamics of this scenariohas been qualitatively confirmed by Lumpkin (1995)with a simple analytical model that examines the modelresponse as the forcing frequency varies. The normal-ized energy spectrum from this model is presented inFigure 14. The figure clearly displays the lower frequen-cies and shorter offshore decay scales of successivelytiigher baroclinic modes. All the modes have an azimu-thal wavenumber of l, since the choice of forcing pro-jects only onto that mode. Model parameters werechosen so that the maximum sea level energy densityand frequency bandwidth of the gravest ITW modematches the sea level spectrum at Hilo in Figure 5.With this choice of parameters, the second mode (at@ lf s = .35) is a factor of 2 too energetic, while theenergy of the mode I currents is actually under-predicted by a factor of 2 compared with the availablemoored current meter observations.

Insofar as the model is unable to match observedspectral energy levels or explain other significantcharacteristics of the observations, such as the sea levelvs. wind stress coherence functions at specific locationsaround the islands, successively more sophisticatedmodels need to be investigated, first incorporating radialtopographic variations following Brink's (1990) analysisof forced searnount-trapped waves, then modelling thenear-island amplification of the winds due to islandorography, and so on. It is also probable that at times atemporally-confined model of the wind-forcing (see tli'ewind data in Figure 5) is the appropriate paradigm forthe forcing function. Azimuthal variations in the topog-raphy (Figure 6) are also likely to contribute to thespecific character of the ITW modes around each island.

Despite the clear relationship between the gravestITW mode around Hawaii Is. and the wind in Figure13, Luther (1985) has already noted that it is easy tofind time periods, including whole years, when the sealevel signatures of the ITW around many of the islandsare not significantly coherent with the local winds.Luther (1985) has postulated two additional mechanismsof ITW forcing to account for this. First, due to the nar-rowness of the inter-island channels, it is possible thatsignificant energy in an ITW mode around one islandwill leak (scatter, if you prefer) to a neighboring island,exciting a co-oscillation of that island's ITW modes.Lumpkin (1995) found, using time-dependeirt coherencefunctions (Figure l5), a number of time periods which

Figure 14. Total mean specific energy divided by meanbackground specific kinetic energy for the forced island-trapped wave model of Lumpkin (1995), with a dissipationtime scale lr-' =

-f o / 0.015 (=15.8 days). Frequencies from@ lf n = 0.1 to ol lf o = 1 (inertial) are shown; tick marksare at the inertial frequency and at the baroclinic eigenfre-quencies. The energy ratio is given for radial dislance r

ranging from the island radius a ro 3a. Note thar the trap-ping scale decreases for increasing baroclinic mode(decreasing frequency). Figure taken from Lumpkin (1995).

appear to clearly show such co.excitation of the Maui

group's gravest ITW by. Hawaii's gravest ITW, while

also showing time periods when the gravest HawaiiIsland ITW was strong and the Maui Island ITW wasweak (e.g., winter of 1974), and vice versa (summer-fall

of l97l). In both the latter cases, there is no coherencebetween the islands indicating that the individual islandsdo have separate resonances, although just why theleakage should not always occur is not immediatelyapparent. A multiple regression analysis of the Hilo andKahului sea levels and local winds has confirmed thatleakage from the island of Hawaii to Maui is moreimportant than local wind forcing at Maui, although thelatter does occur.

This is perhaps the first time such a co-oscillationphenomenon has been identified in the ocean.

Quantification of this process, and the extent to which it

occurs between other islands in the group is the subject

of current research. This process may explain theexistence of the 4-day oscillation all along the JDFR,despite the discontinuous nature of that ridge (Figure l).

That is. if the JDFR resonance is due to the excitation

of waves that have zero along-ridge group velocity' the

(er+er)

(er)1 000\

I

r .00

125

1.9

1.75

2.00

l lozzs

i v tf'= 0'oI5 i

2s 35

@lf"

2.50

2.7\

3.00

WAVES TRAPPED TO DISCRETE TOPOGRAPHY

produce tlrc huge surf for which Hawaii is famous (note

. the significant wave height in Figure 7).It is only in the last ten years that ade4uate time

series of surface gravity wave energy have becomeavailable to permit a better testing of the gravity waveexcitation mechanism. And there is certainly sufficientwind data now to be able to isolate those time periods

when local wind forcing could not be responsible forthe ITW generation. Investigations with these data arein progress. If the surface gravity wave forcing of ITWis found to actually occur it will represent a new addi-tion to the suite of mechanisms by which the atmo-sphere generates intemal motions in the ocean.

In summary, it is easy to imagine that at times abroad-scale oscillating wind (possibly rotating anti-cyclonically) is responsible for significant sub-inertialITW excitation, while at other times short-lived stormevents, or surface gravity wave set-up/set-down, contri-bute significantly to the wave excitation. And then atother ti$es wave energy at one island may be due toleakage from ITW modes around a neighboring island.

Final Remarks

There is sufficient observational evidence to concludethat energetic, resonant, baroclinic oscillations existtrapped to islands and mid-ocean ridges. The lowestorder dynamics of these waves is known, but significantdetails remain un-determined, such as the specific roleof topography for the IT\i/ and the cause of the reso-nance of the JDFR waves. For the super-inertial oscilla-tions at the Hawaiian Islands, even the lowest orderdynamics is not known.

Direct atnrospheric forcing of both ITW and ridgewaves has been demonstrated. The former is most likelvvia divergence of the Ekman transport as it impinges onthe island, and the latter may involve a "tunnelling" ofenergy from the surface to the topography if thefrequency-wavenumber characteristics of the forcing donot permit the generation of free open-ocean Rossbywaves. Indirect atmospheric forcing is postulated forridge waves through the intermediary of Rossby or Kel-vin waves, and for ITW through the intermediary ofsurface gravity waves.

The existence of resonant ridge waves engenders thenotion of a whole class of waves capable of propagatinginformation long distances along the mid-ocean's ridges.Their extraction of energy from non-topographic Rossbyor Kelvin waves may be a significant sink of energythat, for instance, is poorly modeled in GCM's.

Both the ITW and ridge waves imply the existence ofenhanced current amplitudes in the immediate vicinityof the topography. This variability may be important tooceanic mixing by intensifying boundary layer shears orimproving the efficiency of removal of boundary-mixedwater. The waves must certainly enhance the dispersal

55

Hilo ASL. 60-58 h6. Frbd

r l l l l t t l- - t - - r - - -1-- Tu- -r - - r - - [ - -F

1972 197.1 1975

Figure 15. Bottom two frames, running coherence ampli,tude and phase between band-passed adjusted sea levelrecords from Kahului and Hilo for the 2.5 ro 2.83 daysperiod band.. The complex demodulated variance in thisband for each station is presented in ttre top two frames,The coherence was calculated from the phase-bearingband-passed signals and not from the variance envelopes.The horizontal line at coherence amplitude 0.75 indicatesthe 95% confidence level. Figure from Lumpkin (1995).

similarity of the cross-ridge topographies for each smallsbgment ensures that the resonant modes will all havelhe same frequencies. Then excitation of a resonantmode on one small ridge segment could result in co-oscillation of neighboring segments' resonant modes,and so on down the length of the JDFR. If one postu-laties a small amount of energy loss as this processoccurs, the observation of south to north decay -ofenergy in the 4-day oscillation discussed earlier couldbe explained.

Continuing in a speculative vane, as appropriate forthis workshop presentation, note that Luther (1985)found a reasonable correspondence between theincidence of large tsunamis and ITW excitation atHawaii. He postulated that the divergence of the radia-tion stress associated with a tsunami as it shoals wouldbe sufficient to produce a substantial set-up/set-downprofile of the thermocline (as well as of the sea surface),since ttre thermocline is relatively shallow and is rela-tively close to shore due to the steepness of the islandtopography. After the passage of the tsunami, when thestress divergence which maintained the thermocline set-up/setdown is gone, the thermocline profile will try torelax to its former position and this relaxation processshould generate ITW. Such a sequence of.events couldalso occur when large ocean swells hit the islands to

trv,x'

1957 1968 1969 1970 1971 1972 197ts 1971 1975

56 LUTHER

of anthropogenic effluents at islands and hydrothermaleffluents at mid-ocean ridges. In addition, both wavetypes may result in substantial rectified flows.

The concept of energy leakage, or forcing of oneresonant trapped oscillation by a resonant oscillationtrapped to a neighboring topographic feature, has goodsupporl from the observations of ITW at the HawaiianIslands, and may be responsible for the diffusion ofenergy down the JDFR. However, this problem hasmany non-intuitive aspects (e.g., Jansons and Johnson,1988; Hendershott, this volume). Most importantly,energy propagation through, for instance, an array ofseamounts may not necessarily proceed in the straight-forward rnanner that previous discussions would sug-gest; that is, even if the seamounts have identicalresonant frequencies, a resonance excited at oneseamount need not spread equally to all the others, evenif they are in close proximity.

Acknowledgments. This work benefited from discus-sions with R. Lumpkin, M. Menifield and S. Allen. Iam grateful to G. Cannon and R. Lumpkin for permit-ting the use of many of their figures.

References

Allen, S.E., and R.E. Thomson, 1993: Bottom-uapped subiner-tial motions over midocean ridges in a stratified rotatingfluid, "L Phys. Ocean.,23, 566-581.

Brink, K.H., 1989: The effect of stratification on seamounr-trapped waves, Deep-,Sea Res., 36, 825-8M

Brink, K.H., 1990: On the generation of seamount-trappedwaves, Deep-Sea Res., 37, 1569-1582.

Brink, K. H., 1991: Coastal-trapped waves and wind-drivencurrents over the continental shelf, Ann. Rev. Fluid Mech,,23,389-412

Cannon, G.A., D.I. Pashinski, and M.R. [rmon, 1991: Mid-depth flow near hydrothermal venting sites on the southernJuan de Fuca Ridge, J. Geophys. Res.,96, 12,815-12,831.

Chapman, D.C., 1989: Enhanced subinertial diumal tides overisolated topographic features, De ep-Sea Res., 36, 8 I 5-824.

Chave, A.D.. J.H. Filloux. D.S. Luther. L.K. Law. and A.White, 1989: Observations of motional electromagneticfields during EMSLAB, J. Geophys. Res., 94, 14,153-14,166.

Chave, A.D., D.S. Luther, and J.H. Filloux, 1992: The Baro-tropic Electromagnetic and Pressure Expe riment, l.Atmospherically-forced barotropic cunents, J. Geophys.Res., 9'l,9565-9593.

Eriksen, C.C., 1982: An upper ocean moorcd current and den-sity profiler applied to winter conditions near Bermuda, .LGeophys. Res., 87, 7879-7m2.

Eriksen, C.C., l99l: Observations of amplified flows atop alarge seamount, J. Geophys. Res.,96, 15,227-15,236.

Frankignoul, C., and P. Miiller, 1979: Quasi-geosuophicresponseof an infinite p-plane ocean to stochastic forcing bytheatmosphere, J. Phys. Ocean.,9, 105-127.

Gilbert, D. and C. Garrett, 1989: Implications. for mixing ofinternal wave scattering off irrcgular topography. J. Phys.Ocean.. 19. 1716-1729.

Gilbert, F and A.M. Dziewonski, 1975: An Application of nor-mal mode theory to the retrieval of structural parametersand source mechanisms from seismic spectra, Phil, Trans.Roy. Soc. Innd., A278, 187-269.

Haidvogel, D.8., A. Beckmann, D.C. Chapman, and R.-Q.Lin, 1993: Numerical simulation of flow around a tall iso-lated seamount. Part II: Resonant generation of trappedwaves, .L Phys. Ocean., 23, 2373-2391.

Hogg, N., 1980: Observations of internal Kelvin wavestrapped round Bermnuda, J. Phys. Ocean.,20, 1353-1376

Hunkins. K.. 1986: Anomalous diurnal tidal currents on theYermak Plateau, J. Mar. Res., 44, 5l-69.

Huthnance. J.M.. 1974: On the diumal tidal currents overRockall Bank, Deep-Sea Res., 21, 23-35.

Jansons, K.M., and E.R. Johnson, 1988: Topographic Rossbywaves above a random array of seamountains, J. FluidMech., 191.373-388.

Killworth. P.D.. 1989a: How much of a baroclinic coastal Kel-vin wave gets over a ridge?, J. Phys. Ocean., 19,321-341.

Killworth, P.D., 1989b: Transmission of a two-layer coastalKelvin wave over a ridge, J. Phys. Ocean.,19, l l3l-1148.

Lumpkirq R., 1995: Resonant coastal waves and superinertialoscillations, M.S. Thesis, U. Hawaii, Honolulu, HI, lt)6 pp.

Luther, D.S., 1985: Trapped waves around the HawaiianIslands, Proceedings of the 3rd Hawaiian Winter Workshop,L. Magaard (ed.), U. of Hawaii, Honolulu, HI, pp. 261-301.

Luther, D.S., Chave, A.D., J.H. Filloux, and P.F. Spain, 1990:Evidence for local and nonlocal barotropic responses toatmospheric forcing during BEMPEX, Geophys. Res. l*u.,r7, 949-952.

Luther, D.S., Filloux, J.H., and A.D. Chave, l99l: Low-frequency, motionally induced eiectromagnetic fields in theocean: 2, Electric field and Eulerian current comparison, J.Geophys. Res., 96, 12,797 -12,814.

Miller, A.J., P.F.J.G. lcrmusiaux, and P.-M. Poulain, 1995: A1.8-day topographic Rossby mode resonance traplrd to theIceland-Faroe Ridge, Proc. 10th Conf. Atmas. Oc. Wavesand Stabiliry, Big Sky, Montana, 5-9 June, 1995.

Miiller, P., and C. Frankignoul, l98l: Direct atmospheric forc-ing of geosrophic eddies, J. Phys. Ocean., ll, 287-308.

Noble, M.A., K.H. Brink, and C.C. Eriksen, 1994: Diurnal-period currenrs rapped above Fieberling Guyou observedcharacteristics and model comparisons. Deep-Sea Res., 41,643-658.

Philander, S.G., 1990: El Nifio, Ia Nifia, and the SouthernOscillation, Academic Press, New York, 289 pp.

Saint-Guily, B., and A. Lamy, 1988: Waves trapped by theKerguelen Island escarpement, C. R. Acad. Sci. Paris.307,II, 573-578.

Thomson, R., 1989: Effects of topography and buoyant plumeson near-bottom currents over a mid-ocean ridge, IEEE Oce-ans '89: The Global Ocean, 1,73-76.

Wunsch, C., 1972a: The spectrum from two years to twominutes of temperature fluctuations in the main thermoclineat Bermuda, Deep-Sea Res., 19, 577-593.

Wunsch, C., 1972b: Bermuda .sea level in relation to tides,wealher and baroclinic fluctuations, Rev. Geophys. Sp.Phys.,10, l -49.

Wunsch, C., and A.E. Gill, 1976: Observations of equatoriallytrapped waves in Pacific sea level variations, Deep-SeaRes.. 23. 37 l -390.