Spectra and gust factors for gale force marine winds

SPECTRA AND GUST FACTORS FOR GALE FORCE MARINE

WINDS

STUARTD.SMITH Department of Fisheries and Oceans, Bedford Institute of Oceanography, P.O. Box 1006, Dartmouth,

Nova Scotia, Canada B2 Y 4A2

and

PETERC.P.CHANDLER Martec Limited, 5670 Spring Garden Road, Hal&. Nova Scotia, Canada B3J IH6

(Received in final form 4 June, 1987)

Abstract. Wind turbulence measurements obtained at a stable floating platform 10 km off the coast of Nova Scotia are unique in the range of wind speeds covered, and in freedom from influences of platform motion and flow distortion. Spectra of wind velocity components are presented according to Monin-Obukbov similarity theory. Gust factors for downwind, lateral and vertical components are reported for a range of gust durations and sampling intervals. These results are compared with published values, continning the concept of similarity theory for spectra in gale force winds, and resolving a discrepancy among published gust factors.

1. Introduction

With the increasing complexity and sophistication in the design of vessels and marine structures, the variation of wind loading must be considered in addition to the mean forcing. Wind spectra allow an estimate to be made of the fluctuating wind force at any given frequency or over a given frequency band. The cospectrum of vertical and horizontal wind defines the frequency distribution of wind stress on the sea surface. Gust factors give the probable ratio of peak winds of a given duration to the mean wind over a specified interval: the gust duration relevant to a given structure depends on its size and dynamic response. The turbulence levels and the associated spectral levels and gust factors depend on the wind speed, and on the aerodynamic roughness of the underlying surface. The sea surface is smoother than all but the flattest of land surfaces, but its roughness increases with increasing sea state and hence with wind speed. The data reported here were obtained in the marine boundary layer at high wind speeds and so are directly relevant to the estimation of wind loading on marine structures.

1.1. GUST FACTOR

The gust factor G is an estimate of the extreme value of the wind velocity during a measuring interval, T

GO, T) = (4 ,,,/W + 1,

where ii, is the running mean of the downwind wind velocity fluctuation over a gust duration t and U is the mean wind velocity during a measuring interval T (T >> t). The

Boundary-Layer Meteorology 40 (1987) 393-406. 0 1987 by D. Reidel Publishing Company.

394 STUART D. SMITH AND PETER C. P. CHANDLER

duration of a gust which is of interest depends on the intended applications. The gust factor generally decreases with increasing gust duration and increases slightly with record length.

In the low turbulence levels characteristic of the marine boundary layer, G differs only negligibly from a gust factor defined using the absolute value [(U + z&)’ + ii; + ii:],!& of the wind velocity.

The gust factors of the wind components in the lateral and vertical directions are defined in terms of the difference between the minimum and maximum running mean values of the components,

Gi(t, T) = (aimax - fiim,,)/U, i = 2, 3 . (2)

As an example, suppose the mean wind speed (U) is 20 m s - ‘, and the lateral wind component (fi2) has a maximum value of 10 m s - ’ in one direction (say positive to the left of the mean wind speed direction) and 6 m s - i in the other (negative) direction. The maximum range of values in the lateral wind component is thus 16 m s - i, and given the mean wind speed of 20 m s - ‘, the gust factor G, is 0.8.

Gust factors for marine engineering applications are often derived from Bretschneider (1969) or Det Norske Veritas (1977). Wieringa (1973) presented gust factors for water and land surfaces, and listed comprehensive references to earlier work. Smith (1974) and Smith and Banke (1975) gave gust factors for wind components over water.

1.2. WIND SPECTRA AND COSPECTRA

The wind velocity vector

u = (U + %), 4, u3 (3)

is defined with the mean wind, U, during the sampling interval, directed along the hrst axis, the second axis crosswind, and the third axis vertically upward. In right-handed axes, the second component is directed to the left of the first; for example, if the frrst axis (mean wind direction) happens to point to the east, then the second axis points to the north. Each of the three components of the wind fluctuation vector ui, u2, u3 can be decomposed into a spectrum, where the integral of the spectrum over all positive frequencies, f, is equal to the variance; for example u

s Mf)W) = 2 0 (4)

Similarly, the integral of the cospectrum of two fluctuating quantities, say ui and u3, is equal to their covariance,

x-

s 43 3tfhKf) = u1u3 (5)

0

and the integral over any finite band of frequencies is the contribution to the variance or covariance from that particular frequency band.

SPECTRA AND GUST FACTORS FOR GALE FORCE MARINE WINDS 395

Monin-Obukhov similarity theory predicts that wind spectra and cospectra at a height z in the atmospheric surface layer, when compared using a nondimensional frequency

L =fw

and normalized by dividing by the square of the friction velocity,

(6)

u2 = * - qu3 9

should be universal functions of the atmospheric stability,

(7)

- z/L = -gKz(t,u,)/T,u: , (8)

where L is the Monin-Obukhov length, K = 0.4 is the von K&man constant, T, is the virtual temperature with fluctuations t,, and g = 9.8 m s - 2 is the acceleration of gravity.

We note in passing that in the context of similarity, it is possible to define gust factors using Id * rather than U, which are functions of height and stability only. For practical applications, however, it is usually more convenient to measure the mean wind speed, and as such we shall not pursue this alternative.

Kolmogorov’s theory of inertial subrange turbulence argues that there is an energy cascade from generation of turbulence at scales comparable to the scale of the mean flow (e.g., the height) to viscous dissipation by shear at much smaller scales. On dimensional grounds, over an ‘inertial subrange’ of frequencies between generation and dissipation, the velocity spectra should be proportional tof - 5/3 and should be related by

(9)

The inertial subrange generally commences near the highest frequencies of the spectra reported here and extends to substantially higher frequencies.

Miyake et al. (1970) and Smith and Anderson (1984) have published spectra from wind turbulence measurements taken at shallow, near-shore sites in light and moderate winds. At high wind speeds, the aerodynamic roughness, the wavelength, and the wave breaking activity of the sea state increase. Spectra over land surfaces (e.g., Kaimal et al., 1972) are influenced by diurnal surface heating and convection and so may not necessarily be identical to those over the sea, even when scaled by similarity theory to account for differences in surface roughness (Smith and Anderson, 1984). Although the roughness of land surfaces generally does not change with wind speed, it depends strongly on the type of terrain.

2. Data

Wind speed data were collected using a thrust anemometer positioned 13.4 m above mean sea level on a stable platform moored in 55 m of water, approximately 20 km southeast of Halifax, Nova Scotia and 10 km from the nearest shore. The platform (Fletcher et al., 1985) was designed to have minimal response to waves and to offer


minimal blockage to the wind. A thrust anemometer (Dessureault and Knox, 1980; Smith, 1980a) sensed the wind thrust vector on a 3.8 cm diameter perforated sphere, and velocity components were computed from the thrust vector. Data runs consisted of about 40 to 45 min of wind data recorded in analog frequency-modulated form on magnetic tape. The fetch ranged from 10 km for winds from northnorthwest, to unlimited for winds from the south and east.

Ten data runs from Smith (1980b), taken at mean wind speeds from 18.5 to 22 m s - ‘, were selected for spectral analysis as being representative of gale force winds and actively breaking surface waves (Table 1). During all of these data runs, the atmospheric stability, as determined from simultaneous surface heat flux measurement, was nearly neutral, - 0.059 < z/L ZG 0.042; this is expected, since for a given sea-air temperature difference, the stability depends approximately on the inverse square of the wind speed. The mean drag coefficient, C,, = 1.8 x 10W3, is about twice as large as that for light winds (U < 10 m s- ‘) at the same site (Smith, 1980b, Figure 6b).

An additional 14 runs (Table II) were selected to extend the above data base for gust factor analysis, giving a wind speed range from 6.5 to 22 m s - ’ and a stability range - 0.24 I z/L I 0.042. Strip chart records of the input signals were checked for all of the above data runs, and none of the selected data contained ‘spikes’ due to momentary interruption of the original analog signals in the transmission or recording process. Smith (1980b) did not find significant differences between drag coefficients and other statistics for offshore (fetch 2 10 km) and onshore winds (unlimited fetch).

TABLE I

Thrust anemometer data used in spectral and gust factor analysis

Run number

Start time/date (GMT)

Fetch

04

Wind direction

(deg T)

1977

Wind Drag Stability speed coefficient 4L Udm s - ‘1 10s c,,

67 0451 Apr. 4 13 293 19.6 1.05 0.013 107 1234 Nov. 26 074 18.5 2.10 - 0.016 108 1338 Nov. 26 080 18.9 1.50 -0.017 117 1604 Nov. 27 70 251 20.0 1.76 - 0.041 119 1800 Nov. 27 13 259 18.7 1.66 - 0.059

1978

141 2331 Jan. 9 146 19.0 1.61 0.042 143 0138 Jan. 10 150 22.0 1.79 0.032 190A 0946 Feb. 7 075 19.4 2.20 - 0.002 190B 1027 Feb. 7 076 19.2 2.23 - 0.014 19oc 1108 Feb. 7 079 19.3 1.99 - 0.015

Note: The wind speeds shown have been adjusted from the instrument height of 13.4 m to a 10 m elevation using a neutral logarithmic formula.

Indicates unlimited fetch.


TABLE II

Supplemental thrust anemometer data used in wind gust analysis

Run Start time/date Fetch number (GMT) (km)

Wind Wind Drag Stability direction speed coefficient z/L (deg T) U,dm s - ‘) lo3 c,,

20 1348 Nov. 12 11 283 11.1 1.59 - 0.240 32 1708 Dec. 7 160 12.3 1.21 -0.005 33 1804 Dec. 7 152 13.6 1.16 0.002 34 1937 Dec. 7 156 15.0 1.32 0.020 35 0000 Dec. 8 166 17.2 1.82 0.030

84 1546 Nov.1 83 246 6.5 0.69 -0.225 86 1311 Nov.7 17 010 10.5 1.41 -0.126 87 1958 Nov. 7 17 025 9.5 1.95 -0.115

112 1110 Nov. 27 83 247 18.6 1.65 -0.021 113 1207 Nov.27 83 247 19.4 1.79 -0.026 11.5 1403 Nov.27 83 246 19.0 1.88 -0.044 116 1459 Nov.27 83 246 19.8 1.54 -0.054 126 0129 Nov.28 10 273 13.1 1.41 -0.213

160 1952 Jan. 12 11 284

1976

1977

1978

11.2 1.91 -0.217

- Indicates unlimited fetch.

2.1. ANALYSIS

The time series data were low-pass filtered, with a sharp cutoff at 11 Hz (half-power point), and digitized at a rate of 20 samples per second. Wind thrust signals were converted to velocity components (Smith, 1980a). At this stage, the mean and the trend were removed from each wind component, leaving a time series of fluctuations. The trend was determined by fitting a linear regression to the data. The difference in the trend line between the beginning and end of the run was generally small, in comparison to the rms turbulence level, and so did not substantially affect the gust factor analysis. The trend represents longer-term variability in the wind which is not relevant to gusts or to turbulence spectra.

Spectra and cospectra of the wind velocity components were computed using the programs of Dobson et al. (1974) adapted to the Cyber computer of the BIO Computing Centre. Choice of a block length of 819.2 s allowed spectral analysis over a frequency band from 0.0012 to 10 Hz, with standard errors among several blocks available as a measure of the variability of the spectral estimates for each run.

For the gust factor analysis, the rnns were subdivided into time intervals of T = 600,


1200, and 2400 s. For example, a run of 2600 s duration was divided into four 600 s time intervals, two 1200 s time intervals, and one 2400 s time interval. The last 200 s of the record was not used. During each interval, the maximum and minimum running mean values of each velocity component were determined for gust duration intervals oft = 1, 3, 6, 15, 60, and 240 s. This information was then used to calculate the gust factors G, G,, and G, (t, T).

3. Spectral results

The spectra of horizontal and vertical wind components for data run 141 are plotted in the form f+(f) on a logarithmic frequency scale in Figure 1. The vertical axis has dimensions of velocity squared, and in this form the contribution to the variance, or to the turbulent kinetic energy, is proportional to the area under the spectrum in any frequency band. The area enclosed by the cospectrum of horizontal and vertical wind components (Figure 2) similarly gives the frequency distribution of wind stress at the 13 m level. The quadrature spectrum represents wavelike (out-of-phase) air motions, and is smaller than the cospectrum, except at the surface wave frequency of 0.1 Hz. However, small rocking motions of the platform may have contributed to a substantial part of the observed quadrature spectrum.

Fig. 1. Downwind spectrum f+l(f), a, and vertical spectrum f&(f), + , for run 141. Width of symbol shows bandwidth of spectral estimates, and height shows k standard error among blocks into which data

run has been subdivided. Area under spectra is proportional to kinetic energy.

SPKTRAAND GUSTFACTORS FOR GALEFORCEMARINEWINDS 399

Fig. 2. Cospectrum, + , and quadrature spectrum, 0, of downwind and vertical wind turbulence for run 141. Area between cospectrum and axis is proportional to frequency distribution of sea surface wind stress

at 13 m elevation.

In Figure 3, all ten spectra for the three velocity components have been normalized to the dimensionless form f,&(f,)/u ‘, . It follows from Equation (4) that

If the turbulence is entirely generated by shear stress in the surface layer, these spectra should, according to similarity theory, be universal functions of the stability, z/L. However, the variability of wind in the overlying boundary layer may depend on larger-scale processes, and may influence the low-frequency part of the spectra. Spectra for the three runs in slightly stable stratification (0.013 < z/L I 0.042) are displaced toward higher frequencies in contrast to the remaining spectra, although all of the runs could be classified as near-neutral. The displacement in frequency of the stable spectra is, of course, much less than for the stable group (0.35 I z/L < 0.58) reported by Smith and Anderson (1984).

A smooth line drawn through the middle of the group of normalized downwind spectra (Figure 4) agrees closely with the similarly grouped neutral downwind spectra of Smith and Anderson (1984), and with our interpretation of the downwind spectra of Miyake et al. (1970) normalized with u ‘, . The spectra of Miyake et al. (1970), as summarized by Smith and Anderson (1984, Figure 7), were normalized by 03’ rather than ~2. In the present Figure 4, we show the neutral spectra normalized with ~1 (Smith


NORMALIZED FREOUENCY ft.)

Fig. 3. Normalized downwind, crosswind and vertical spectra for the group of 10 runs, plotted on log-log axes. Broad dashed lines are for runs in stable stratification. Note that & has been multiplied by a factor

of 10 and +, by a factor of 1000.

and Anderson, 1984, Figure 4) and place the Miyake et al. (1970) spectra in the appropriate relative positions. At the high-frequency end, the spectra follow a power law s,wi) Kf,-2’3 as predicted by theory. Extension of the spectral analysis to lower frequencies clearly shows a broad peak at f, = 1 to 2 x 10 2, as previously seen at much lower wind speeds (4 to 9 m s - ‘) in the spectra of Miyake et al. (1970). Although our wind speed range (18 to 22 m s - ‘) does not extend to the maximum design winds commonly used in offshore engineering, the success of similarity theory over a wide range is very encouraging, and suggests that some extrapolation of spectra to even higher wind speeds may be justified.

The normalized lateral spectra again agree with Smith and Anderson (1984), with an f,- 2/3 power law at the high frequency end. However, the lower values of Miyake et al. (1970) are attributed to rolloff in the response of their sonic anemometer. At surface wave frequencies, f, z 0.1, the higher values from the present data may reflect a tendency of the stable platform to rotate slightly about its vertical axis in response to wave loading, introducing additional apparent variations in wind direction. At lower frequencies, the lateral spectra are close to the low edge of the range of values reported


. . .,..,” . . ,,,.,” , , ,,.,,” , , ,,,,,,, r lo-’ 10-g 10-a 100 161

NORYALIZED FREOUENCY (fn 1

Fig. 4. Typical spectra from Figure 3, solid lines, compared with spectra published by Smith and Anderson (1984), dotted lines, and by Miyake et al. (1970), dashed lines.

by Miyake et al. (1970), and confirm the existence of a spectral peak which was not clearly shown by Smith and Anderson (1984).

The normalized vertical spectra agree with those of Smith and Anderson (1984) at the high-frequency end. The response of the anemometer used by Miyake et al. (1970) rolled off at high frequencies and showed somewhat lower values at the higher frequencies. Small peaks in the individual spectra at surface wave frequencies, f, z 0.1, are again attributed to a small amount of wave-induced rocking of the platform, rather than to the wind itself.

Nicholls and Readings (198 1) measured wind spectra over the sea from an aircraft flying at elevations of 25 to 230 m. They normalized their spectra by matching their highest frequency decade, a form from which it is not quite as easy to recover dimensional spectral values given an estimate of u *. For flight tracks along the wind direction, their non-dimensional wave number is equivalent to f,. For neutral stability, their spectral shapes and peak frequencies are similar to those reported here, but for highly unstable stratification, z/L < - 0.15, they find larger lower frequency spectral peaks which are particularly pronounced in thef”&(f”) spectrum. These low-frequency peaks approach the values reported by Kaimal et al. (1972) over land surfaces in


unstable conditions, which are generally believed to represent the influence of convective processes. For a given air-sea temperature difference, z/L has an inverse-square depen- dence on the friction velocity (Equation (8)); at high wind speeds we have always found near-neutral stability at z = 13.4 m, jz/L I < 0.06 (Table I), At higher elevations the influence of stability on the spectra becomes progressively more important.

3.1. PROCEDUREFORUSINGTHENORMALIZED SPECTRA

To estimate the wind spectrum above the sea surface at agiven elevation and wind speed from the normalized spectral plots, the vertical axis must be multiplied by

u’, = C,U’, (11) where Smith (1980) gives a drag coefficient for the 10 m level

C D,. = 0.61 x 10e3 + O.O63U,, (m s-i) (12)

in near-neutral conditions, for wind speeds at 10 m height of from 6 to 22 m s - ‘. Alternatively, Smith (1981) has tabulated drag coefficients CD for a number of anemometer heights, wind speeds, and sea-air temperature differences.

The normalized frequency can be multiplied by a factor

f u -=- “fn z

(13)

Since the graphs are in log-log form, both multiplications (Equations (11) and (13)) have the effect of sliding the scales along the axes, but do not change the shape of the spectra. Caution must be used in estimating spectra beyond the range of the experimental data. In particular, the similarity theory applies to the atmospheric surface layer, and other factors may determine the spectra at higher elevations.

4. Gust Factor Results

In Figure 5, the gust factors are presented as a function of gust duration t and record 1engthT. Halving the record length is seen to reduce G by about 0.02, and we infer that increasing the record length by SO%, from 2400 to 3600 s, would increase G by about 0.01.

The gust factor ranges from 1.38 for a gust duration of 0.05 s (one sample of the data) to 1.04 for a duration of 240 s. Error bars show plus and minus the root-mean-square variability among the data runs.

In comparison with the gust factors determined in this study, Wieringa (1972, Table IV) reported slightly lower gust factors from data taken at the shoreline of Lake Flevo in near-neutral conditions at 10 m height, at wind speeds in the vicinity of 10 m s- I. A slightly lower gust factor G(0.05,2400) = 1.30 & 0.07, was reported by Smith (1974) for 28 runs of sonic anemometer data over Lake Ontario at wind speeds from 4 to 10 m s - ’ ; the drag coefficients and turbulence levels were also lower than in


THIS STUDY SMITH (1974)

0 Wieringa.1972. Gk6W) d- G(24OOl :

0 HandboOk 0‘ axan and underwater - G,(2400) n Error bars * rrns

Engineering, 1669. Ott, 36001 - G,(2400) b variability amang runs

@ oet ~orske Writas. 1977. G(t, 3600) -- GWOOI

--- GWOI

Fig. 5. Gust factors G(t, T) and Gi(t, T) as a function of gust duration t from this study, and from Smith (1974) and Wieringa (1972).

the present experiment because of the difference in wind speed and associated sea surface roughness. The lateral gust factor G,(0.05,2400) = 0.62 f 0.17 again falls just below the bottom of the error bar of the present data, while the vertical gust factor G,(0.05,2400) = 0.43 k 0.07 agrees well with the present data.

The vertical gust factor, G,, increases with height (Bretschneider, 1969) eventually approaching values of the lateral gust factor, G,. The data collected during this study, taken at a single elevation of 13 m, do not provide any information on the variation of G, with height.

Also shown in Figure 5 are gust factors G(t, 3600) published by Bretschneider (1969) and by Det Norske Veritas (1977). As noted above, we expect G(t, 3600) to be about 1 y0 higher than our values of G (f, 2400). The latter values and those determined from this study are in good agreement, within error bars. Bretschneider’s values, however, are significantly (4-20%) higher. This discrepancy can be resolved by noting that Bretschneider reported gust factors over land surfaces, compiled by the Australian


Bureau of Meteorology. The generally higher roughness of land surfaces generates stronger boundary-layer turbulence and higher gust factors than are observed in the marine boundary layer.

The influence of wind speed on G(0.05,2400) and G,(O.OS, 2400) is not as great as the variability among runs in any given speed range (Figure 6) but the trend is toward an increase with wind speed in keeping with the variation of the drag coefficient and turbulence levels (Smith, 1980b). The gust factors G(0.05, 7’) tabulated by Smith and Banke (1975) for T = 1320 to 2640 s, from data with onshore winds at Sable Island, N. S., are indistinguishable from the present results, and all of the points lie in the shaded area

G(0.05,2400) = 1.29 + O.O06U,,(ms-‘) kO.1, (14)

for U,, = 6 to 22 m s - ‘. The slightly lower mean gust factors from the earlier results of Wieringa (1972) and Smith (1974), shown in Figure 5, are seen to be entirely compatible with the present results for breezes of 5 to 10 m s - ‘. No difference is seen

G 1.0 7

0 =2

: :

-i--:-

iL-u

.x ” ,-:,b +l--

: .f gq

+ ‘. ‘..W : .‘. . ,. :+ -.. 0 G3

‘.f ” 4. : ‘: T+ + ,. ,_: - ..+:,, . . . .

Fig. 6. Gust factors G, G,, and G, (0.05, 2400) as a function of wind speed. Values of G from Smith and Banke (1975) are also shown, and stippled area for G is given by Equation (14). Beaufort wind scale is shown at top. Onshore wind; G 0, Gz 0, G, 0: Offshore wind; G *, G, x , G, + : Smith and Banke,

1975; G A.

SPECXRA AND GUST FAmORS FOR GALE FORCE MARINE WINDS 405

between onshore (unlimited fetch) and offshore (limited fetch) for G and G,. However, G, appears to be slightly greater for offshore winds, possibly due to persistence of the higher variability of wind direction typical of the upstream boundary layer over land.

Dividing the data runs into stable (z/L > O.O), near-neutral ( - 0.1~ z/L I 0.0) and unstable (z/L I 0.1) categories (Figure 7), we find relatively small differences in G(t, 2400) among stability classes, except that G(t, 2400) is higher in unstable conditions for t 2 3 s.

ts- G

Q + Q +

9 10 o!l 1 1 10 I I

mo

t (KC.,

Fig. ‘7. Gust factor G(t, 2400) as a function of atmospheric stability. Stable (z/L > 0) x , Neutral (-O.l<z/L<O)O,UnstabIe(z/L~ -O.l)+.

5. Conclusions

Gust factors for the marine atmospheric surface layer have been presented as a function of gust duration t, measuring interval i”, and wind speed and atmospheric stability. Our results conform and extend the gust factor values of Det Norske Veritas (1977), and Wieringa (1973) and Smith (1974), provided that comparisons are made for similar durations and wind speeds. The gust factors recommended by Bretschneider (1969) are higher than those which we have observed, probably due to their being derived from data over land surfaces.

Spectra of wind turbulence in gale force winds, scaled by Monin-Obukhov similarity theory, confirm and extend those of Smith and Anderson (1984) for near-neutral stability. There is a noticeable shift toward higher dimensionless frequencies even for very slightly stable stratification. The existence of a broad maximum in the downwind spectrum at a dimensionless frequency of 10 - 2, as reported by Miyake et al. (1970) for light winds, is confirmed.


Acknowledgements

We thank R. J. Anderson and D. L. Hendsbee for their role in the field work, and D. R. Chang of Evans Computer Applications for computer programming. The analysis was partially funded by Exxon Production Research Company, Houston, Texas.

References

Bretschneider, C. L.: 1969, ‘Overwater Wind and Wind Forces’, J. J. Meyers (ed.), Handbook of Ocean and Underwater Engineering, McGraw-Hill, New York, pp. 12-2 to 12-13.

Dessureault, J.-G. and Knox, D. F.: 1980, ‘Design of a Tri-Axial Thrust Anemometer for Measurement of Atmospheric Turbulence over Water’, Ocean Engineering 7, 521-537.

Det Norske Veritas: 1971, Rulesfor the Design, Construction and Inspection of Offshore Structures, Appendix A, Environmental Conditions, Oslo, pp. Al.

Dobson, F. W., Brown, R. F., and Chang, D. R.: 1974, A Set of Programs for Analysis of Time Series Data Including Fasr Fourier Transform Spectral Analysis, Computer note B l-C-74-2, Bedford Institute ofoceano- graphy, Dartmouth, N.S., 177 p.

Fletcher, J., Mills, R. G., and Smith, S. D.: 1985, Design, Construction, and Performance of a Moored Stable Platform, Can. Tech. Rep. Hydrogr. Ocean Sci. 62: iv + 41 p.

Kaimal, J. C., Wyngaard, J. C., Izumi, Y., and Cot&, 0. R.: 1972, ‘Spectral Characteristics of Surface-Layer Turbulence’, Quart. J. R. Meteorol. Sot. 98, 563-598.

Miyake, M., Stewart, R. W., and Burling, R. W.: 1970, ‘Spectra and Cospectra of Turbulence over Water’, Quart. J. R. Meteorol. Sot. 96, 138-143.

Nicholls, S. and Readings, C. J.: 1981, ‘Spectral Characteristics of Surface Layer Turbulence over the Sea’, Quart. J. Roy. Meteorol. Sot. 107, 591-614.

Smith, S. D.: 1974, ‘Eddy Flux Measurements over Lake Ontario’, Boundary-Layer Meteorol. 6,235-255. Smith, S. D. and Banke, E. G.: 1975, ‘Variation ofthe Sea Surface Drag Coefficient with Wind Speed’, Quart.

J. R. Meteorol. Sot. 101, 665-673. Smith, S. D.: 1980a, ‘Evaluation of the Mark 8 Thrust Anemometer for Measurement of Boundary Layer

Turbulence’, Boundary-Layer Meteorol. 19, 213-292. Smith, S. D.: 1980b, ‘Wind Stress and Heat Flux over the Ocean in Gale Force Winds’, J. Phys. Oceanogr.

10,709-726. Smith, S. D.: 1981, Coefffcientsfor Sea Surface Wind Stress and Heat Exchange, Rep. BI-R-81-19, Bedford

Inst. of Oceanography, Dartmouth, N.S., Canada, 31 pp. Smith, S. D. and Anderson, R. J.: 1984, ‘Spectra of Humidity, Temperature, and Wind over the Sea at Sable

Island, Nova Scotia’, J. Geophys. Res. 89, 2029-2040. Wieringa, J.: 1973, ‘Gust Factors over Water and Built-Up Country’, Boundary-Layer Meteorol. 3,424-441.

Spectra and gust factors for gale force marine winds

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