TURBULENT

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OF

MOMENTUM,

VAPOR IN THE ATMOSPHERIC DURING M. DUNCKEL, Meteorologisches

Institut

HEAT

AND

WATER

SURFACE LAYER AT SEA ATEX*

L. HASSE, L. KRUGERMEYER, and J. WUCKNITZ

D. SCHRIEVER,

der Universitiit Hamburg and Institut fiir Radiometeorologie Meteorologic an der Universitiit Hamburg, F.R.G.

und Maritime

(Received 11 June, 1973) Abstract. The vertical turbulent fluxes have been determined during the Atlantic Trade Wind Experiment (ATEX) both by direct and profile methods. The drag coefficient obtained from direct measurements was CD= 1.39 x 10m3.A distortion of the wind profile due to wave action could be demonstrated, this produced an increased drag coefficient estimated by the profile method. The dissipation technique using the downwind spectrum gave a lower drag coefficient of 1.26 x 10-3, probably due to nonisotropic conditions (the ratio of vertical to downwind spectrum at high frequencies scattered considerably with an average of 1 instead of 4). From direct measurements, the sensible heat flux showed a poor correlation with the bulk parameter product UAB, contrary to the heat flux obtained from profiles. It is shown that this is due to the higher frequency part of the cospectrum, say above 0.25 Hz, which contributes more than 50 % of the total flux. Determination of the heat flux from temperature fluctuations by the dissipation method would be in agreement with the direct determination only if thecorresponding Kolmogoroff constant were 2.1 instead of 0.8. For the vertical flux of water vapor obtained from profiles, the bulk transfer coefficient was 1.28 x 10-3.

1. Introduction In 1969, R.V. ‘Meteor’ participated in the Atlantic Trade Wind Experiment ATEX, which was initiated and coordinated by the late Prof. Brocks. The purpose of ATEX was to investigate comprehensively the energy, momentum, and water vapor balances in the Trade Wind branch of the global circulation of the atmosphere (Brocks et al., 1972). The upper layers were investigated by detailed serological observations (Augstein et al., 1973)while the surface layer was probed with aid of meteorological buoys. Concurrent observations give the possibility of checking and improving methods for bulk parameterization of turbulent transfer, which is an important tool for large-scale air-sea interaction studies. As most determinations of the bulk aerodynamic transfer coefficients originate from observations in the temperate zones, the opportunity was welcomed to use R.V. ‘Meteor’ which worked in fairly low latitudes with a Coriolis parameter of 4 of that of temperate zonesand with high temperatures and water vapor pressure. ‘Meteor’ was drifting between 9”N, 33” W and YN, 41”W. The meteorological conditions were as follows: mean wind speedfrom 4.5 to 11m s-l, mean temperature difference air-sea - 1.9 to -0.2”C, estimated wave heights 1 to 3 m. During the dates * This work was supported by the Deutsche Forschungsgemeinschaft, Schwerpunktprogramm Meeresforschung and later the Sonderforschungsbereich Meeresforschung Hamburg. Boundary-Layer Meteorology 6 (1974) 81-106. AN Righrs Reserved Copyright o 1974 by D. Reidel Publishing Company, Dordrecht-Holland

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3 through 13, and 19 through 22, February 69, ‘Meteor’ was in the undisturbed trades, while from 14 through 18, the ship was near or within the ITCZ. The profile measurements reported here extended with short breaks for servicing over the period from 3 to 22 February. The eddy-correlation measurements are from the period 15 through 21 February only, mainly during disturbed conditions. 2. Experimental Set-up To obtain the vertical fluxes of heat and momentum, two systemswere used: one buoy for measurements of the vertical profiles of dry- and wet-bulb temperatures and of wind speed(Figure l), and a second buoy for measurementsof wind (horizontal and vertical components) and temperature fluctuations (Figure 2). Connected by floating cables, the two buoys lay 300 and 450 m, respectively, windward from the drifting researchvessel‘Meteor’, free of its disturbances. All the electronic units for processing, recording and quick inspection were on board the ship (Figure 3). For profiles, the instruments were mounted at heights between 1 and 8 m on a surface-following buoy. The tilt angle of this buoy was within a range of about 10 deg. Wind velocities were obtained at 7 heights by small light-weight cup anemometers. Two additional heights on the lower part of the buoy mast were not used during most of the time becauseof the high waves, which after a short time destroyed the instruments. The responsedistance of the cup anemometerswas 2.6 m. The rotation of the anemometers was measured by the aid of an opto-electronic pick-up module. The frequency of the voltage pulses was proportional to wind speed. For averaging, the pulses were counted; each 10 min the output of the counters was printed. Simultaneously the pulses were recorded on a hi-fi tape recorder with the aid of a frequency multiplex technique. The water temperature and the dry- and wet-bulb temperatures of aspirated psychrometers were obtained by meansof glass-moulded platinum resistancethermometers. Considerable care was taken to avoid radiation errors. To this end the psychrometer was made of synthetic material and each thermometer was shielded with two concentric chromium-plated tubes. The 11 resistancethermometers in three-conductor mode were switched in turn to a Wheatstone bridge coupled with a 12-channel stripchart recorder. The sample period of each channel was 72 s. One of the channels used a constant value resistance as reference. The overall accuracy of the system was 0.01“C for relative measurements(Dunckel, 1967). The sensorsfor measurementsof wind and temperature fluctuations were mounted on a tilt-stabilized mast on a surface-following buoy. The tilt-stabilizing system was a gyro-controlled servo-motor unit, which kept the mast always vertical within rfr 1 deg (Brocks and Hasse, 1969). Connected to the stabilized mast was a three-axis accelerometer unit to obtain the translational motions of the buoy in all three directions. The immersion depth of the buoy was measured by two pressure gaugesmounted on the buoy body near the seasurface. The measurement of wind fluctuations was made by means of a constant-current-

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Fig. 1. Profile buoy during ATEX with R.V. ‘Meteor’.

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Fig. 2. Eddy flux sensors at 3.5-m height on servo-stabilized mast. The mast can be retracted; operating height for the measurement reported in this paper was 2.4 m.

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SHIP -.... PROFILE

BUOY

TEMPERATURE STRIPCHART RECORDER

HIFI

TAPE

RECORDER WIND+ TEMPERATURE

PRINTER IOMIN.

EDDY CORRELATION ON TILT STABILIZED

2.4 m

BUOY MAST

1 u’, i’, T’

1.7 m

450m FLOATING

CABLE

b,. ON BUOY BODY QUlC% LOOK ZllZ2 GYRO CONTROLLED TILT STABILIZING SERVO SYSTEM

HIGH SPEED RECORDER

Fig. 3. Scheme of flux determination, indicating levels of measurement for profiles of wind, temperature, and humidity, and for fluctuation measurements of horizontal wind component, inclination and temperature.

mode hot-wire device, the measurement of temperature fluctuations by means of a free mounted platinum-wire resistance thermometer. The system was insensitive to a &- 20-deg variation of azimuth angle around the mean wind direction. For greater wind direction changes,the systemwas rotated by a vane-controlled servomechanism, whereby the position in eachcasewas recorded. The hot-wire anemometer consisted of two independent systems.For measurement of the total horizontal component of wind velocity, two platinum wires of 0.015-mm diam were vertically mounted. The two wires of 10and 20-mm lengths were operated at different wire temperatures in two arms of a Wheatstone bridge. Using this bridge, output becomes independent of air temperature changes. After amplification, the signal was linearized and then fed through an automatic range selector before recording on an FM magnetic tape recorder. In this way a signal-to-noise ratio of better than 500: 1 was achieved, i.e., the range of O-16 m SC* has a resolution of about 3 cm s-l. The second hot-wire system consisted of two inclined hot wires of 0.015-mm diam and lo-mm length. The vertical angle between the two wires was 140 deg; both were

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mounted symmetrically to the horizontal line. The wires were electrically connected as two arms of a Wheatstone bridge. Becausehot wires to the first order are sensitive only to the wind component perpendicular to the wire axis, the output of this sensor configuration is nearly proportional to the wind inclination. The signal of this configuration is also sensitive to changes of wind direction. To overcome this effect, the wire system was shunted by a second wire system of the same configuration as the first one, which was adjacently mounted with an azimuth angle of 40 deg to the other. Using this unit, the signal was nearly independent of the shift of wind direction within a range of + 20 deg. The bridge output was amplified and then recorded on an FM magnetic tape recorder. The range of wind inclination that could be measured was + 20 deg; the resolution was about 1%. The measuring device for fluctuations of air temperature was a platinum wire of 0.015-mm diam and about 150-mm length, which was wound around small isolated supports. This resistancethermometer was one arm of a Wheatstone bridge. The output was amplified and recorded on an FM magnetic tape recorder. The temperature range was 2 “C and the resolution was about 1%. Before eachrecord, the bridge output was centred, so that the range was sufficient. The main problem of the sensor system for measuring fluctuations was the calibration instability of hot wires. The most important reason for this is contamination of the wires by salt spray. The heat transfer from the wires to the air is noticeably changed and also the surface of the wires is affected under such conditions. Becauseof this, the sensor units were used only for time periods of no more than 5-6 h. After that, a new sensor was mounted. During the runs, the wind velocity was also obtained by means of nearby cup anemometers, which are very much more stable in calibration. This allows a continous check of the calibration during data reduction. The calibration of inclination can be checked by calculating mean vertical velocities. 3. Data Reduction

Profile measurementswere averaged over periods of half an hour by counting anemometer output pulses over this time for wind and by taking means over data sampled every 70 s for dry- and wet-bulb temperatures. Vertical differences were computed from a log-linear least-squarefit of the profile. Turbulence records (horizontal wind velocity, wind inclination, temperature, and buoy accelerations) were digitized with a sampling rate of 100 s-l by an analogue-todigital converter with eleven-bit resolution. To account for the remaining nonlinearities in the hot-wire output, the relevant calibration curves for each sensor had been carefully obtained in a wind tunnel in steps of about 0.2 m s-r. These calibration curves were interpolated by a quadratic formula between given points to correct the individual values in the data-reduction program. To compensate for drifts of the hot-wire sensors,the horizontal wind was adjusted to cup anemometer readings. The wind inclination was readjusted to give zero mean vertical wind over the runs, which were mostly of l-h duration. Buoy accelerations were numerically integrated in the

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time domain with a step of 0.1 s to give velocities. To avoid drifts due to this process, a fifth-degree polynomial was first subtracted from the acceleration data to extract very low frequency components. This procedure, combined with digital high-pass filtering, gives far better low-frequency values than integration of spectra. The computation of spectra and cospectra was done by the method of time-averaging over short, modified periodograms (Welch, 1967), applied to two overlapping frequency bands (0.2 to 50 Hz and 0.004 to 0.5 Hz). Frequency components outside these bands were suppressedby digital filtering. For the high-frequency band, only every hundredth periodogram was evaluated in order to save computing time and to give comparable statistical reliability in both bands. Corrections for buoy movements in the wind data were done by adding periodograms of horizontal or vertical buoy velocities to the wind periodograms. All eddy-flux values given in this paper are computed by means of corrected cospectra. 4. Momentum Flux 4.1. EDDY-CORRELATION TECHNIQUE The fluctuation measurementsof horizontal and vertical wind components and temperature were made on the smaller buoy. The sensor was installed on the verticallystabilized mast at a height of 2.4050.15 m above the instantaneous water surface during sea waves of 1 to 3-m height. 26 runs could be used for stress determination. The first step for determination of the eddy-correlation products z was a crossspectral analysis. The measured wind data (u,, NJ,,,)were corrected by adding the buoy motion (ub, wb): u=u,+u*,

w=w,+wb.

The uncorrected values u,w, were found to be smaller than the corrected values by around 40x, in contrast to Pond’s (1968) optimistic assumption, that correction for buoy motions might be neglected because of the quasi-elliptical path of a floating buoy. One has to consider that the horizontal motion of our buoy is influenced by the mooring cable inhibiting truly wavelike motion. Besidesthis, the matter is more complicated due to the correlation between the wind field and buoy motion, because both are influenced by the waves(seebelow). The tilt of the mast compared to a truly vertical axis was smaller than l”, the deviations being nearly uncorrelated with wave motions. Errors in the stressestimates are therefore small. The effect of a small mean tilt of the sensor, which cannot be avoided, is eliminated by shifting the calibration curve of wind inclination so that the vertical wind velocity equals zero in the mean for each record. In Figure 4 the resulting vertical fluxes of momentum are plotted as a function of UT,. Thecorrespondingmean drag coefficient cD, defined as is customary by u:/UI,, is 1.39 x 10e3. Obviously there is no dependency on mean wind velocity. This value of cD agreeswell with results for the ocean by many other groups (e.g., seeHasse, 1970;

M. DUNCKEL

0.00

0

ET AL.

I

I

I

I

I

I

I

10

20

30

40

50

60

70

[ 1

u:, g$

Fig. 4. Vertical flux of specific momentum versus mean wind speed squared. Full line is best-fitting line by method of least squares; broken lines indicate residual standard deviation from the best fitting line.

Pond et al., 1971)but there is still a considerable scatter of individual points about the fitted line. 4.2. PROFILE TECHNIQUE

From the profiles, the stresshas been obtained using the KEYPS diabatic flux-gradient relationship (Panofsky, 1963)

with

For a stability index, z/L= (&/qH)Riv was used, where Ri, was determined from the profiles. The deviation from the original formulation by Panofsky (1963), who used z/L’= (cp,/cp,) *z/L, is immaterial, (P” was taken as a function of stability from Dyer (1967): qPH=(l-15z/L)- o.55. Fortunately in most cases the deviation from neutral conditions was small, so that the choice of the stability function and of the accompanying constant is not important. Profiles with Ri, < 0.1 are not considered here. The results are shown in Figure 5, where of determined from half-hour mean profiles is plotted against U:,. Additionally, the results of the direct determination of the stressare shown in the samefigure. It is evident that the stressesfrom the profiles are significantly higher than those from direct measurements,cD= 1.90x 10m3.On the other hand, it is evident that the scatter itself is small, the unexplained variance of U; from the best-fitting line being 0.01 m2 sm2,for r.4:=0.13 m2 s-‘, i.e., lessthan 10%. The systematic difference between direct and profile determinations came as a surprise, since profile and direct measurementswith the sameequipment in the North Sea and the Baltic both resulted in a drag coefficient near 1.3 x 10m3(Brocks and

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u:[&] 0.2-

0.1 -

0.0 1 0

I 20

I 20

I 60

I 80

I 100

I

120

u :o [$$]

Fig. 5. Friction velocity squared versus mean wind speed squared. Dots are from wind profiles between 1.2 and 8 m; circles are from direct measurements.

Krugermeyer, 1972; Hasse, 1970).It is reasonable to assumethat the difference might be due to the different wave conditions encountered. Observations were therefore divided according to estimated wave height h”. Figure 6 shows that in fact the drag coefficient increaseswith wave height, while for comparable wave heights, differences in drag coefficients for the North Sea, the Baltic and the Atlantic are small. Since mean wind speedswere about the same,the difference cannot reasonably be explained by an increaseof cDwith wind speed. As the lowest usable level of wind measurements (1.20 m) was right within the height of the wave crests, the apparent drag coefficient may be easily in error due to a small distortion of the wind field near the wavy surface. This also is evident on inspection of the original profiles (Krugermeyer, 1974). The stressestherefore were reevaluated using 2.33 m as the lowest anemometer level (Figure 7). Although(due to the use of fewer levels) the uncertainty of the profile increases,as is evident from the increasedscatter, the drag coefficient* changesto cD= 1.56x 10m3in fair agreement with the direct results. The agreement is even (somewhat) better if only simultaneous profile and direct measurements are compared; the drag coefficients are 1.50 x 10e3, and 1.39 x 10m3,respectively. The same effect seemsto be present in the wind profile data of the 1965 Atlantic Expedition, but cannot be shown in such detail, as the number of anemometer levels was smaller and the lowest level was higher above the water (i.e., 1.7 to 3.1 m depending on wave conditions) (Hoeber, 1969). 4.3.

COMPARISON

OF EDDY-CORRELATION

AND PROFILE TECHNIQUES

AND SOME ASPECTS

OF THE WIND FIELD OVER WAVES

The discrepancy between eddy-correlation stress at 2.4 m and stressfrom wind gra* Using ~=0.4 as throughout the paper.

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2.0 1.5 1.0 0.5 0

2.0 1.5 1.0 0.5 0

2.0

00 --*- y-o --

i

----__0

1.5

oo,-o-,---o--

a8 -~o~-,-----o---

---_-_8-:"_0 ---O---P-o_o~ 0 -__---

-2.0

----_

0 -1.5

-1.0

IOAtlantic 0.5-

0 -0.12

Ii-

-0.5

0.8 m

u,,= 5.7& I -0.10

I

I

I

I

-0.08

-0.06

-0.04

-0.02

0

0 0.02 Riv3,,6

Fig. 6. Influence of wave height on the apparentdrag coefficientdeterminedfrom profiles. Full line is the best fitting KEYPS flux gradient relationship.

dients within the Iowest few meters of the atmosphere has been discussed for some time (e.g., Stewart, 1961). Our observations may be a contribution to the solution of this problem, although effects of buoy motion cannot be excluded a priori. Some numerical calculations were performed in order to check how buoy motions may affect the measured mean wind profile. This investigation was somewhat extended compared to Pond’s (1968) analysis in order to account for the characteristics of our profile equipment. Rotational motions relative to a vertical axis become especially important becauseof the long beams carrying the cup anemometers sideways from

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Fig. 7. As Figure 5, but excluding wind speed measurements at levels below 2.3 m.

the mast. We found that the velocity caused by the motion of the buoy itself does not affect the measured mean wind profile enough to explain the observed discrepancy. On the other hand, the vertical displacement of the sensors within the wind field caused by the vertical motion of the floating buoy due to waves must be further considered. The effect depends on the way the wind field responds to the wave profile. Assuming a logarithmic wind profile without any wave-induced streamline bending, we obtained a reduction in the measured mean wind speed at the1owest 1 or 2n that was nearly as great as observed. In contrast to the above assumption, the fluctuation measurementsobtained from the other buoy indicate streamline bending that follows approximately potential flow theory, at least at the 2- or 3-m height (Wucknitz, 1974). Other investigators also observed streamline bending, appearing at a fixed height in the form of downwind maxima above the wave troughs and minima above the crests, during conditions with wave components moving faster than the mean wind at a height of some meters (Yefimov et al., 1971; Byshev and Kuznetsov, 1969; Volkov, 1969; Kondo et al., 1972). Earlier observations by Pond et al. (1963) Pond et al. (1966), Weiler and Burling (1967), Smith (1967) and others as well as our own measurements over the Baltic Sea,which showed no wave-coherent wind fluctuations, do not contradict the abovementioned results. During this time, relatively small wind waves (not fully developed) were prevailing. During ATEX we have to presume that streamlines were nearly parallel to the waves. The profile buoy almost follows the water surface, and therefore yields estimates of wind profiles following the wavy surface. For an explanation of the observed curvature of the profiles, let us divide the total Reynolds stress into two parts, as usual : z = 7, + T,

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r,,, being wave-induced, rt purely turbulent (seee.g., Phillips, 1966).The sum r can be taken as constant with height. Within the layer above say 3 m, the total stress is purely turbulent, though there are wave-induced wind undulations but without covariance. The mean wind gradient can be used to estimate the true drag coefficient. In the lowest meters, the fast propagating waves are feeding momentum upwards into the air stream. This positive stressis balanced by additional negative turbulent stress in the near-water layer, enhancing the turbulent stress there. So the wind profile, which is determined solely by turbulent fluctuations, yields a higher stressestimate, if the levels below 3 m are included. Wave-induced stress,which might begin to appear at the height of our flux sensor (2.4 m) should be seenin the (negative) cospectrum of stress as a positive peak near frequencies of the dominating swell. Some authors (Davidson, 1970; Volkov and Mordukhovich, 1971) found distinct positive peaks corresponding to waves in their stresscospectra in some cases.In our cospectra it is difficult to show such peaks, becausesmall errors in buoy-motion measurementcan obscure these phenomena. The averaged cospectrum (Figure 8) does not show signif-

n.4”M -u,’ I

0.4

/’ I

!’

/

.-‘\ ‘\. ‘.

\ i

0.3

0.2

0.1

Fig. 8. Normalized cospectra of momentum flux. Full line: average of 25 runs during ATEX; dotted line: cospectra over sea adapted from Miyake ef al. (1970); dash-dotted line: from Panofsky and Mares (1968); broken line: from Kaimal et al. (1972). In the inset the simultaneous wave spectrum is shown for the corresponding frequencies.

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icant breaks although the wave spectrum exhibits distinct peaks. Compared with normalized cospectra suggestedby Panofsky and Mares (1968), Miyake et al. (1970) as well as Kaimal et al. (1972), the ATEX cospectra show a flatter behaviour in the frequency range of seawaves. 4.4. DISSIPATION TECHNIQUE Assuming horizontal homogeneity, the budget of turbulent kinetic energy near the surface can be written as follows :

(1) E

P

-0

B

-0

The last two terms have not been determined during our measurements. They can be assumedto be zero as a good approximation (e.g., Wyngaard and Cott, 1971). From Kolmogoroff’s similarity hypothesis, the energy dissipation E can be estimated from the downwind spectrum I$,, (n) within the inertial subrange: &,,,(n) = Ae213(a>“’

K513,

(2)

where use has been made of Taylor’s hypothesis to transform wave-number spectra into frequency spectra. For local isotropy, dhvw= 49Lu*

(3)

Replacing &,, by j&,,, in Equation (2), we have another way of computing the energy dissipation. For all runs under consideration, the ratio B/P of the buoyancy to the shear production was estimated from gradient measurementsof wind speedand virtual temperature, utilizing diabatic flux-gradient relationships. During the present measurements, the density stratification was only slightly unstable with z/L being between -0.027 and - 0.001 so that B amounts to less than 3% of P. For 7 runs, the sensibleheat flux was measured additionally by the eddy-correlation method; for these runs, B is of the order of 1% of P. Thus B was considered negligible so that P-E=o.

(1’)

In the shearproduction term P, the gradient aU/az was approximated by

au

u*

- - CPM(z/L) 3 i?i - kz

(4)

where cpusignifies the stability function in the KEYPS formula. The dissipation was estimated from the downwind spectrum. Combining (I’), (2)

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and (4) we get 142= A-l&,(n)

n5’3

2mcz

u (4 (PM(z/J3 >

213

’

A = 0.48 (Pond et al., 1963, 1966), z =2.4m. The term c#~~~(n)n~/~ was obtained from the high-frequency part of the spectrum between 3 and 20 Hz. This frequency band corresponds to normalized wave numbers kaz-4.5 to 30; k*z-4.5 is taken as the lower limit of the inertial subrange (Pond et al., 1963).

The results which are plotted as ~2 vs UfO in Figure 9, indicate a fairly high scatter of

Fig. 9.

Usederived by the dissipation method from the downwind spectrum.Full line is the linear regression,broken lines indicate standard error of estimate.

points. The mean drag coefficient cD= 1.26x 10V3 is similar to that obtained from eddy-correlation technique, yielding cD= 1.39x 10e3. In Figure 10 the results of the eddy-correlation and dissipation method are compared. The correlation coefficient is 0.71; Paquin (1972) found a value of 0.76 in his comparison. Moreover, Paquin could demonstrate a very good agreement of methods on the average. In our case, the shear stressesobtained by the dissipation technique are lower than those from the eddy-correlation technique by about 10%. This difference would increase to about 30% if we were to use A = 0.57 as Paquin did. For comparison, E was derived from the vertical velocity spectrum. From (l’), (2), (3) and (4)

4wwwas obtained as described for +,,. Figure 11 shows remarkably less scatter of points compared to Figure 9 but the mean drag coefficient is small: c,=O.83 x IO- 3. This corresponds to the fact that the ratio c$,,,~/c#+,~ was found to be about 1, in contrast to Equation (3).

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I-

IJ: (Diss.’ ) m2 set 2

[ 1

0 0

0.05

0.10

u’w’

0.15

Fig. 10. Comparison of momentum fluxes from eddy-correlation technique (abscissa) and dissipation technique (ordinate). Full line is the one-to-one relation.

0.15U:[gJ O.lO.

0

10

20

30

50

60

Fig. 11. As Figure 9, but from spectrum of vertical velocity.

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M.DUNCKELETAL.

The main conclusions are : The Kolmogoroff constant of 0.48 seemsto fit the data better in contrast to more recently published values near 0.55 (Hicks and Dyer, 1972; Paquin and Pond, 1971; Pond et al., 1971). The ratio +,,,,+,/A,rangesfrom 1.6to 0.4 for individual runs and is near 1 in the mean. Some other authors found similar ratios (Davidson, 1970; Weiler and Burling, 1967), while Garratt (1972), for example, supports the theoretically predicted value 4. Our results might be expectedto differ from other measurementsfor the following reasons: The position of our probe was wave-following at a constant height of 2.4 m above the water level, where wave heights amounted to as much as 3 m. The spectra, even their high-frequency part, may depart from those obtained at a fixed height of 2.4m above the mean water surface. There is a lack of information about modification of the near-water turbulence field by waves at frequencies higher than the dominant gravitywave frequency. Additionally the ‘$-law’ was not obeyed and the divergence terms in Equation (1) might be more important in the presenceof waves. 5. Sensible Heat Flux 5.1. PROFILE TECHNIQUE

The flux of sensible heat has been determined from the temperature and wind pro.. files by aid of

The results are shown in Figure 12. Again, as detailed above, the 2.33-m level was taken as the lowest one for the wind profile. Even though this increases the scatter somewhat, there is still a very good correlation between the heat flux H and the bulk parameter product Cr.At?. The mean heat transport coefficient cH= H/(c,QUAO) = 1.46x 10m3.This is slightly greater than the heat transport coefficients estimated earlier, which were nearer to 1.0 x 10e3 (Hasse, 1970; Kruspe 1972). This difference is not very important since the bulk parameter product UAO was small during ATEX and cH therefore is determined as a ratio between small numbers. There was a small upwards heat flux for UAtl = 0 of the same magnitude as observed earlier (Hasse, 1970). This may be explained by the argument that temperature fluctuations can be interpreted as horizontal temperature differences which tend to induce upward heat transport. Even during vanishing gradients of potential temperature in the surface layer, temperature fluctuations do not vanish fully. In the same way, the buoyancy caused by water vapor will transport sensible heat upward if there is a positive correlation betweentemperature and humidity fluctuations. 5.2. EDDY-CORRELATION

TECHNIQUE

In addition to the heat fluxes determined from profiles, there were 17 runs where the

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54 1

-12

-10

-6

-6

-4

-2

U,oA&

0

[& q

Fig. 12. Vertical flux of sensible heat from profiles as function of the bulk parameter product U&3

sensible heat flux could be determined directly from temperature and vertical velocity fluctuations. Calculation of sensible heat flux by the eddy-correlation method was carried out without regard to the buoy motion effects. For 7 runs, it was possible to calculate wT’ bothcorrected for buoy motions and uncorrected. The difference amounted to at most 10% but was almost 0 on the average. Thus the sensible heat flux could be determined without correction for buoy motion. In Figure 13, the eddy-correlation fluxes together with the sensible heat fluxes from simultaneous profile measurementsare shown. The profile fluxes are well related to the bulk parameter product UaA0 (correlation coefficient, cc=O.87), whereas the directly determined fluxes show a poor dependency. This is in rough agreement with results from BOMEX (Pond et al., 1971; Paulson et al., 1972). The mean coefficient c,=wT’/(UA8) is 1.5x 10m3 for the profile method and 2.1 x 10m3 for the direct method. It should be noted that lJ*Atl and the heat fluxes are rather small, SO that this value of cn cannot be considered as a reliable coefficient. From an inspection of the wT’-cospectra, it can be seenthat the vertical heat flux within a frequency range from about 0.005 Hz to 0.25 Hz depends rather strongly on UAtJ(cc=O.87). However, this part of the cospectrum contributes only 25% of the entire heat flux on the average. The remaining 75% is nearly independent of UA9 (Figure 14). The correlation coefficient between heat-flux portions of limited frequency bands and the bulk product l.JAB as a function of frequency is plotted in Figure 15. As might be expected, the lowest frequency part of the cospectrum is uncorrelated with UAf3; here about $ of the heat Aux takes place. More surprisingly, more than one half of the heat flux is found at frequencies higher than 0.25 Hz without considerable correlation with UA8.

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[1

HKmz

.15

0

0 0.: 0

0

0

0 l 00

0

.lO

l

2 0:

00

.5

00

0 0

-0

-4

-2

t 0

u,,*ne,&q Fig. 13. Comparison of vertical fluxes of sensible heat from simultaneous profiles (circles) and direct measurements (dots).

Although this behaviour cannot yet be explained fully, it may be presumed to be typical for tropical regions with high humidity. The shape of our cospectra - after normalizing and averaging - approaches that of Phelps and Pond (1971) during BOMEX; seeFigure 16. Holland (1972) found a variation of the sensibleflux with the bulk parameter product UAq rather than UAO. In our case,the variation both of the sensible heat flux and of UAq was small, which at least does not contradict Holland’s findings. 5.3. DISSIPATION TECHNIQUE

In addition, the sensibleheat flux was determined by the ‘dissipation’ method. Analogously to (l), a balance equation for temperature fluctuations +T’2 can be written as: -~~~~-N-:~~(wr’“)=&(:~). PO

N

-0

-0

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99

VAPOR

H[I W ii7

0

.lO

0

00

0 0

0

0 0

-0 ,8

-6 40.Af%o

-2

-4

0

[ml set s”q Fig. 14. Sensible heat flux from eddy-correlation measurements for different frequency bands. Dots are for 0.005 $ n < 0.25 Hz, circles are for the remaining frequencies.

+‘;“I +0.5 -0

O’ - 015

0.001

+22%++-

25 % -I-

0.01

53 % =

0.10

1.00

n Ls-I]

I 10.0

Fig. 15. Correlation coefficient r between the sensible heat flux in different frequency bands and the bulk parameter product UAO. Percentages indicate the contribution to the total heat flux.

Assuming steady-state conditions and neglecting the divergence term (see Garrett, 1972) we equate the production term P, with the dissipation N. N can be determined from the temperature spectrum using the Komolgoroff law which may be written with

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ET AL.

loo

lo*

I 10-l

I lo-*

1o-3

I 10'

f zn.6

'

Fig. 16. Averaged normalized cospectra of sensible heat flux. Full line from 17 runs during ATEX, broken line average taken from 16 runs during BOMEX by Phelps and Pond (1971).

the aid of Taylor’s hypothesis : 213 (#),(n)

=

$.&pI3

!g (

,-J/3* >

As shown earlier, the effect of stability on the mean wind profile is small, so E was calculated according to U*= (ICEZ) Ii3 . U, was replaced by jcOU,, with cn= 1.4 x 10m3. Finally we get for the heat flux:

Bk was taken as 0.8, as suggestedby Garratt (1972) and Paquin and Pond (1971),

summarizing most of the existing values. The resulting sensibleheat fluxes are remarkably higher than the eddy-correlation fluxes (Figure 17). In addition, the correlation UAO is negative (cc= -0.4). But again we have similarity with the above mentioned BOMEX results: Pond et al. (1971) found extremely high heat fluxes by the dissipation method under conditions similar to the ATEX conditions. For our measurements,we must insert B& = 2.1 to reduce the heat fluxes obtained from the dissipation technique in order to get agreement with the direct method, at least on the average. Higher values of Bk were derived by Boston (1971): B> = 1.6; and by Gibson et al. (1970): Bk=2.3. As Stegenet al. (1973) showed, the heat fluxes of Pond et al. (1971), based on two different methods, are close for B>=2 instead of 0.8. Obviously, this method must be tested further. Concerning our results, it has to be remembered that our probe was on a wave-following buoy in a wave-disturbed wind field, making the interpretation more complicated.

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101

25 d iss.

20 0 0

0

15

10

5

0

Fig. 17. Comparison of vertical flux of sensible heat by eddy-correlation (abscissa) and dissipation technique (ordinate).

6. Latent Heat Flux from Profiles

The latent heat flux was calculated from the profiles of dry- and wet-bulb temperature and wind speedby auaq I E =lQK2z2 _-.-.-.i

az az (I)~(Pi'

where 1is the heat of vaporisation. Again, wind speedmeasurementsbelow the 2-m level have been discarded.

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The results are plotted vs the bulk parameter product U,,*de,, in Figure 18. deiO was determined from the water vapor at the 10-mheight at the buoy and the saturation water vapor pressure at the water temperature. No correction has been applied to account for the fact that the water temperature was measured at about 0.3-m depth and the relevant surface temperature deviates systematically therefrom (e.g., Hasse, 1971). For comparison, in Figure 18 the direct measurementsof the water vapor flux from Phelps and Pond (1971) during BOMEX have been added. There is excellent agreement. The average c,=E/(&UAq) is 1.28x 10m3.

LOO +$ 300

200

100

0 -1

, I

-120

I

-100

-60

II

-60

-40

-20

U,. Ae,, [&mbl

Fig. 18. Vertical flux of latent heat from profiles (circles). Triangles are values from the direct determination of latent heat flux by Phelps and Pond (1971).

It may be noted that this is in very good agreement with the early determination of c, by Brocks (1963) in the North Seaand Baltic, using a profile buoy. Brocks reported adiabatic profile coefficients for water vapor of 0.08 to 0.10 (for the 4-m height) which yield an adiabatic value for c,(lO m) of 0.9 to 1.35x 10e3. The agreement is even better considering that under slightly unstable conditions as occurred during ATEX, the transfer coefficients are increasedcompared with those in neutral conditions. 7. Conclusions

The turbulent transports of momentum, sensible and latent heat have been obtained by different methods and discussed with the aid of the bulk parameter products in order to compare observations under different conditions. For the momentum and water vapor fluxes the results are consistent to within 10%with other results from the tropics and moreover, from the temperate zones. In terms of Planetary Boundary Layer theories, the surface-layer bulk parameter products are dependent variables.

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103

It is therefore a useful result that parameterisation in terms of surface-layer parameters is reasonably independent of latitude both for momentum and water vapor, although the Coriolis parameter and the water vapor content, which influences buoyancy, vary considerably. For the flux of sensibleheat the processesare more complicated. It is hoped that the differing degree of correlation of &,,T with the bulk parameter product, in various spectral bands, may help to clarify the mechanism of sensibleheat transfer. Acknowledgement

The work reported here stemsfrom 20 years of active work in air-seainteractions by the late Prof. Karl Brocks. We are all indebted to him. Notations A BiB = (g/T,). wT; cD~

cH,

cE

c,=O.24 cal g-l K-’ E Ae, ho

f=n*z[U g=9.81 m s-’ H h k=2m/U L

Z=583 cal g-l N n P= -,w(au/az) PO= - wT’ (iM/az) P 4 q*&+~+~

Ri, T, T’

Kolmogoroff constant for downwind spectrum Kolmogoroff constant for temperature spectrum buoyancy production of turbulent kinetic energy turbulent transfer coefficients of momentum, sensible heat and latent heat, respectively specific heat of air at constant pressure latent heat flux mean difference between water vapor pressure (at 10-m height) and saturation water vapor pressure due to water temperature normalized frequency acceleration due to gravity sensibleheat flux estimated wave height wave number Monin-Obukhov length heat of vaporisation dissipation of temperature fluctuations frequency (Hz) shear production of turbulent kinetic energy shearproduction of temperature fluctuations fluctuation of air pressure specific humidity turbulent kinetic energy Richardson number, including buoyancy of moisture mean virtual temperature fluctuation of temperature (with subscript v: virtual)

104

M. DUNCKEL

u9 UIO u U* W Z

E A&

Aho

lc=o.4

Q= 1.18x lo-” (g cm-“)

ET AL.

mean horizontal wind velocity (at 10-m height) fluctuation of horizontal wind component shearvelocity fluctuation of vertical wind component vertical coordinate (distance from mean water surface level) dissipation of turbulent kinetic energy mean air-water difference of potential temperature (at 1O-mheight) von Karman constant mean air density during ATEX total Reynolds stress wave induced Reynolds stress turbulent Reynolds stress power spectrum of x cospectrum betweenx and y stability functions for heat and momentum, respectively References

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Byshev, V. I. and Kuznetsov, 0. A.: 1969, ‘Structural Characteristics of Atmospheric Turbulence in the Near-Water Over the Open Sea’, Zzv. Atm. Oc. Ph. 5,327-332. Davidson, K. L. : 1970, ‘An Investigation of the Intluence of Water Waves on the Adjacent Airflow’, ORA Rept. 08849-2-T, Dept. of Meteorol. and Oceanography, University of Michigan, 259 pp. Dunckel, M.: 1967, ‘Eine Apparatur zur Messung des vertikalen Wind-, Temperatur-und Feuchteprofils tiber dem Ozean’, ‘Meteor’ Forsch.-Ergebn. B.l, 45-53. Dyer, A. J.: 1967, ‘The Turbulent Transport of Heat and Water Vapour in an Unstable Atmosphere’, Quart. J. Roy. Meteoroi.

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Garratt, J. R.: 1972, ‘Studies of Turbulence in the Surface Layer Over Water (LoughNeagh). Part II: Production and Dissipation of Velocity and Temperature Fluctuations’, Quart. J. Roy. Meteorol. Sot. 98,642-657. Gibson, C. H., Stegen, G. R., and Williams, R. B.: 1970, ‘Statistics of the Fine Structure of Turbulent Velocity and Temperature Fields Measured at High Reynolds Number’, J. Fluid Mech. 41,153-167. Hasse, L.: 1970, ‘On the Determination of the Vertical Transports of Momentum and Heat in the Atmospheric Boundary Layer at Sea’, Tech. Rept. No. 188, Dept. of Oceanography, Oregon State

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University, 55 pp. (Translation of a German article of same title, in Geophysihalische Einzelschrifren 11, Hamburg.)

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Kriigermeyer, L. : 1974, ‘Vertical Transports of Momentum, Sensible and Latent Heat from Profiles at the Tropical Atlantic during ATEX’, in preparation for ‘Meteor’ Forsch.-Ergebn. Kruspe, G.: 1972 ‘Autocovarianzspektren von Brechnungsindex, vertikaler Windgeschwindigkeit, Lufttemperatur und -feuchte, Co-spektren des vertikalen Warme- und Feuchteflusses tiber See’, Berichte des Znstituts fur Radiometeorologie und Maritime Meteorologic, Univ. Hamburg, Nr. 20. Miyake, M., Stewart, R. W., and Burling, R. W.: 1970, ‘Spectra and Cospectra of Turbulence Over Water’, Quart. J. Roy. Meteorol. Sot. 96,138-143. Panofsky, H. A.: 1963, ‘Determinations of Stress from Wind and Temperature Measurements’, Quart. J. Roy. Meteorol.

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Panofsky, H. A. and Mares, E. : 1968, ‘Recent Measurements of Cospectra for Heat Flux and Stress’, Quart. J. Roy. Meteorol.

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Paquin, J. E. and Pond, S.: 1971, ‘The Determination of the Kolmogoroff Constants for Velocity, Temperature and Humidity Fluctuations from Second- and Third-order Structure Functions’, J. Fluid Mech. 50,257-269.

Paquin, J. E.: 1972, ‘A Comparison of Eddy Correlation and Dissipation Techniques for Computing the Fluxes of Momentum, Heat and Moisture in the Marine Boundary Layer’, Ph. D. Tesis, Dept. of Oceanography, Oregon State University, 71 pp. Paulson, C. A., Leavitte, E., and Fleagle, R. G.: 1972, ‘Air-Sea Transfer of Momentum, Heat and Water Determined from Profile Measurements During BOMEX’, J. Phys. Oceanography 2, 487-49. Phelps, G. T. and Pond, S. : 1971, ‘Spectra of Temperature and Humidity Fluctuations and of the Fluxes of Moisture and Sensible Heat in the Marine Boundary Layer’, J. Atmospheric Sci. 28,918-928. Phillips, 0. M.: 1966, The Dynamics ofthe Upper Ocean, Cambridge University Press, 261 pp. Pond, S.: 1968, ‘Some Effects of Buoy Motion on Measurements of Wind Speed and Stress’, J. Geophys. Res. 73,507-512.

Pond, S., Stewart, R. W., and Burling, R. W.: 1963, ‘Turbulence Spectra in the Wind Over Waves’, J. Atmospheric Sci. 20,319-324.

Pond, S., Smith, S. D., Hamblin, P. E., and Burling, R. W.: 1966, ‘Spectra of Velocity and Temperature Fluctuations in the Atmospheric Boundary Layer Over the Sea’, J. Atmospheric Sci. 23, 376-386. Pond, S., Phelps, G. T., Paquin, J. E., McBean, G., and Stewart, R. W. : 1971,‘Measurements of the Turbulent Fluxes of Momentum, Moisture and Sensible Heat Over the Ocean’, J. Atmospheric Sci. 28,901-917.

Smith, S. D.: 1967, ‘Thrust-Anemometer Measurements of Wind-velocity Spectra and of Reynolds Stress Over a Coastal Inlet’, J. Marine Res. 25,239-262. Stegen, G. R., Gibson, C. H., and Friehe, C. A.: 1973, ‘Measurements of Momentum and Sensible Heat Fluxes Over the Open Ocean’, J. Phys. Oceanography 3,8692. Stewart, R. W. : 1961, ‘The Wave Drag of Wind Over Water’, J. Fluid Mech. 10,189-194. Volkov, Yu, A. : 1969, ‘The Spectra of Velocity and Temperature Fluctuations in Airflow Above the Agitated Sea Surface’, Zzv. Atm. Oc. Ph. 5,723-730. Volkov, Yu, A. and Mordukhovich, M. I.: 1971, ‘Spectra of Turbulent Fluxes of Momentum and Heat Over a Wavy Sea Surface’, Zzv. Atm. Oc. Ph. 7,11-16. Weiler, H. S. and Burling, R. W. : 1967, ‘Direct Measurements of Stress and Spectra of Turbulence in the Boundary Layer Over the Sea’, J. Atmos. Sci. 24,653-664.

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