Vertical Profile of Wind Speed Over the Open Sea. By Toshio Fujita Meteorological Research Institute, Yatabe, Tsukuba, lbaraki 305, Japan

Transcription

1 100 Journal of the Meteorological Society of Japan Vol. 61, No. 1 Vertical Profile of Wind Speed Over the Open Sea By Toshio Fujita Meteorological Research Institute, Yatabe, Tsukuba, lbaraki 305, Japan Shigeru Nemoto Ochanomizu University, Bunkyo-ku, Tokyo 112, Japan Kiyohide Takeuchi Tokyo District Meteorological Observatory, Chiyoda-ku, Tokyo 100, Japan Masuo Tosha Meteorological Research Institute, Yatabe, Tsukuba, ibaraki 305, Japan (Manuscript received 11 November 1981, in revised form 19 November 1982) Abstract In the pre-garp experiments in 1969 and 1970, we measured mean profiles of wind speed, air temperature and humidity over the open sea. Many abnormal wind profiles were obtained under the conditions of high wind speeds and swell wave. The wind profiles did not have a logarithmic shape, but had a jet-like flow at about twice as high as wave height. All of the wind profiles were observed over the open sea about km away from the land by the use of R/V Hakuho-Maru. Wind speeds were measured by five small threecup anemometers installed along the pole 9.6m away from the bow, and wave heights were observed by the gyroscope, accelerometer and sonic wave gauge. Overspeeding of the cup anemometers, ship movements and thermal stratification of the air layer were taken into account for obtaining the wind profiles. Our conclusions are as follows: As a mean wind speed increases on the open sea with significant swell waves, a departure from a logarithmic wind profile becomes larger, and obvious two peaks in the profile are recognized corresponding to the wave height distribution with two maxima. 1. Introduction In July, 1969 and 1970, the preliminary observations of the GARP-AMTEX were conducted on the East China Sea and the western Pacific Ocean. We participated in the pre-garp cruises and measured, over the open sea, the mean profiles of wind speed, air temperature and humidity by using the vertical pole attached to the boom at the bow of the R/ V Hakuho-Maru. We often observed abnormal wind profiles under the conditions of high wind speeds and swell waves. The departures from a logarithmic wind profile are not likely to be caused by diabatic atmospheric stratifications or the errors of wind measurements. Now, we examined many wind profiles which had been so far observed over the water surface. A list of wind profile data over the marine surface reported upto 1962 can be found in the Table X of Roll's text-book (1965). A later survey of 17 wind profiles is presented on the Table 4.1 of Blanc (1981). Some researchers reported that the logarithmic wind profiles were observed even over the sea surface. Roll (1965), Hay (1955) and Kondo et al. (1972), for example, obtained logarithmic wind profiles. Miyake et al. (1970) reported that the vertical profiles of observed wind speed, U(Z)

2 February 1983 T. Fujita, S. Nemoto, K. Takeuchi and M. Tosha 101 were better expressed by In Z-*(Ri) (Z: height, Their experiments were carried out in the (Ri): a function of Richardson number). * Paulson trade wind region of the Atlantic Ocean where et al. (1972) showed that a composite wind the swell waves were predominant. They found profile of 141 observations was expressed by the that a characteristic feature of all observed wind log-linear law. profiles was the presence of a jet-like air flows at But these wind profiles, except Paulson et al., were taken on coastal sea or inland water. 2 or 3 times height of the average swell height. In order to obtain better data we need some On the other hand, many non-logarithmic wind examinations. In this paper, overspeeding of a profiles were reported, which were observed on cup anemometer and hull effect on the air flow the open sea or large lake surface. are checked. Effects of both thermal stratification Sheppard (1951) made wind profile observations and fetch on a wind profile are also ex- over a large lake and found that there amined. were marked kinks in the profiles at a height of 1.5m to 2m from a mean sea level (M.S.L.). Bogorodsky (1966) observed mean wind profiles 2. Observation Observation place, station over the sea swell waves in the low latitude Various observations concerning air-sea inter- of the Atlantic Ocean. He showed in his Table action during the pre-garp were made from 1 that a secondary maximum of mean wind speed the board of the R/V HakuhO-Maru on the East existed at a height of 2m to 3m from M.S.L. China Sea and the western Pacific Ocean. As Nan'niti et al. (1968) also found the distinctive kinks in their wind profiles which were seen in Fig. 1, the wind profiles were observed at St. 1, St. 2 and St. 3, km away from measured on the mast of a buoy over the open Kyushu Island. sea in the Pacific Ocean. They reported that As one of the observations, profiles of wind when the wind speeds at a height of 6.1m exceeded 6m/sec, departures from a logarithmic A bow boom was projected horizontally from speed, air temperature and humidity were studied. wind profile could be found at m heights, the top of the bow, 9.6m in length and 7.5m which were twice as high as swell height. According high above M.S.L. (See Fig. 2). to the report of Krugermeyer et al. A pole, 3cm in diameter and 6.5m in length (1978), the wind profiles over the wavy sea surface was vertically attached to an end of the boom are distorted by the waves especially in the and five sets of the instruments were installed vicinity of the sea surface. The wind profiles along the pole at the heights of 4, 5, 6.25, 8 are distorted to lower wind speeds compared with and 10.25m respectively, above M.S.L. the flow above a rigid surface. Takeda and Misawa (1971) investigated air Dimensionless slope of a profile was larger in the lower part of the profile and increased with significant wave height. flows near the bow top of the R/V which was moving to the windward with a dead slow speed, and a horizontal velocity gradients were scarecely Yefimov and Sizov (1969) measured the wind profiles by using a buoy which did not vertically move due to waves. observed at the neighborhood of the boom Fig. 1 Observational stations of wind profile in the pre-garp cruises, 1969, Fig. 2 Relative position of a boom and an observational pole to the hull and the sea.

3 102 Journal of the Meteorological Society of Japan Vol. 61, No. l end. In the wind tunnel experiments using a model vessel (1/50), Takeda and Ishikawa (1971) also confirmed that any anomalies from a mean wind speed in the tunnel were not found on a vertical wind profile 10m apart from the bow top (see Fig. 3). Therefore it may be regarded that the observation of the wind profiles was not influenced by the hull. Fig. 3 An anomaly distribution of mean wind speed on the vertical section. (After Takeda and Ishikawa) Instrumentation Measurements of the mean profiles of wind speed, air temperature and humidity were made by the following instruments. (1) 10min mean wind speed: Five small three-cup anemometers (Makino Type AF750P) were used, whose distance constants were in the range of m for starting and m for setting down. The number of rotation of the cup corresponding to the wind run was printed out on a paper chart every 10min. Starting velocities of the anemometers were only about 20-30cm/sec, because they were designed to minimize the mechanical friction by using lamp-photocell devices. (2) Air temperature and humidity: Aspirated psychrometers with thermister sensors were used, a pair of bead-thermisters, 1mm in diameter was put in the double shelter coated with glitter stainless steel. One of thermisters was covered with a thin Japanese paper which was always wet with distilled water from a small water tank. The sensors were always exposed to the air were suitable to measure 10-min mean air temperatures and humilities. The output voltages were recorded on the chart of the pen recorders every 30sec. (3) Angles of pitching, rolling and azimuth of the hull: A gyroscope mounted on the R/V was used and a vertical component of acceleration of the hull was utilized, which was observed by an accelerometer during the 1969 cruise. We got the wave data during the 1970 experiment, which were obtained from a sonic wave gauge by Ocean Research Institute, University of Tokyo. A summary of wind pfofile data and related statistics is indicated in Table Examination of observation errors The problem of overspeeding of the cup anemometer has been frequently reported by many authors. Izumi and Barad (1970) compared the threecup anemometers with the sonic anemometer as a reference sensor, and obtained the result that overspeeding of the cup anemometer was estimated to be about 10% of the reference wind speed. But the measurements were made on land where roughness height is two order larger in magnitude than that of the sea surface. Kondo et al. (1971) numerically investigated a dynamic response of cup anemometers to the stepwise and sinusoidal wind changes and turbulent air flows. In the turbulent flows, horizontal and vertical variances of instantaneous wind direction effect on the rotations of the cup anemometers. They synthetically estimated the overestimation factor in mean wind measurement over the sea to be %. Bush and Kristensen (1976) reported that the overspeeding of the cup anemometer depended on the ratio of a distance constant of the anemometer to a roughness height, and also the ratio of a measurement height to a roughness. Inferring from their diagram, the overspeeding factors of our anemometers would be less than 0.1% due to small values of roughness heights. Francey and Sahashi (1982) investigated a overspeeding of a six-cup anemometer and obtained overestimation factor of about 3.7%. Kondo and Sato (1982) derived the empirical formula to the u-error, Eu as flows (about 5m/sec) sucked into the shelters by aspirators. The time constants of the thermisters were Eu=(Ucup-U/U)U=C((*u)6*/U)2 2-3sec (dry-bulb) and 4-5sec (wet-bulb), respectively. These sensors were so sensitive that they where Ucup and U are the mean values of ucup

4 February 1983 T. Fujita, S. Nemoto, K. Takeuchi and M. Tosha 103 Table 1 A summary of wind profile data and related statistics.

5 104 Journal of the Meteorological Society of Japan Vol. 61, No. 1 and u respectively; *=*/U is the response time constant; C is the empirical constant (*1.0 for our cup anemometers) and (**)6* is the standard deviation of u when the sampling duration is 6*. It was estimated from their Fig. 3, using the values of u* in Table 1 and the average distance constants in starting and setting down of our anemometer, 7.7m. The maximum u-error of the wind speeds in Table 1 was only 0.52% of the true wind speed. Since the pitching angles in the pre-garp cruises were within *2* at most and wind directions were in almost steady state, the range of the standard deviations of wind direction might be assumed to be less than 5*. Then, the *-, and w-errors are estimated to be nearly zero from the Fig. 4 of Kondo and Sato. The mean wind speeds in Table 1 are corrected by the values of Eu. On the other hand, Meshal (1977) carried out the measurements of wind fluctuations as well as wind profiles in the marine surface layer in Bedford Basin, N. S., Canada. He reported that there was no overspeeding of the cup anemometers comparing with a sonic anemometer at the same height. In the observation runs adopted here, the thermal stratifications were nearly neutral as shown in Table 1 except Run A, so that an influence of the stratifications may be negligible. In the Run A, on the other hand, assuming the log-linear wind profile, a diabatic wind profile is expressed by a broken line in Fig. 4. On account of a weak wind speed, it can be well explained by the diabatic profile rather than by a wave effect. Finally, the pitching and rolling effect of the hull on the measurements of mean wind profiles are examined. Deacon (1962) showed that the effects of harmonic rolling motion of a ship on the mean wind speed measured on the ship board are expressed by a following formula, where where Ur : true mean wind speed U : apparent mean wind speed h : height of anemometer from M.S.L. a : rolling angle T : rolling period In the present case, representative values of h,, T and U were 10m, 2*, 8sec and 5m/sec * respectively. Then the value of b2/4 is equal to 7.5*10-4. Therefore it is seen that a rolling motion of the hull scarecely influence on the measurements of mean wind speed. Next, we consider an error due to a vertical displacement of an observation pole. We assume that a profile of mean wind speed is expressed by a following formula, for instance, The wind profile has a maximum wind speed like a `jet' flow at a height of 6.5m above M.S.L. The wind profile is illustrated by a solid line in Fig. 5(a). We further assume that vertical displacement of the pole is sinusoidal, with a period of 8sec and an amplitude of 3m. Using the model wind profile, under the above assumptions, the mean wind speeds to be measured for a cycle by the small cup anemometers at the heights of 10, 8, 6.5, and 4m were calculated. Table 2 Apparent wind profiles measured by vertically moving anemometers. (a) indicates the case in the wind profile with a jet-like air flow (see Fig. 5(a)). (b) the case in the Log wind profile (Fig. 5(b)). In both cases, anemometers make vertically sinusoidal motion with a period, 8 sec and an amplitude, 3m.

6 February 1983 T. Fujita, S. Nemoto, K. Takeuchi and M. Tosha 105 Wind Velocity Temperature Fig. 4 Representative profiles of mean wind speed and air temperature in the pre-garp experiments. Bars indicate standard deviations of some 10-min averaged wind speeds and air temperatures. Fig. 5 Apparent wind profile measured by vertically moving anemometers. Solid lines show true wind profiles and broken lines, apparent profiles. The results are listed at Table 2 and shown by a broken line in Fig. 5(a). Overestimating factors at the height of 8m and 5m are 2.9% and 2.9% respectively and at 6.5m height a mean wind speed is underestimated by 6.5%. It may, then be seen that the vertical displacement of the anemometers apparently tends to smooth a jet-like flow. That is, a wind speed at the height of near a jet core becomes weaker, and stronger winds appear at the upper and lower levels than the jet core. If a logarithmic wind profile shown in the following was assumed U(Z)= ln the vertical displacement of the cup anemometers would hardly change the measured values from an original wind profile (Fig. 5(b)). The results correspond to the conclusion which Deacon et at. (1957) derived theoretically. Accordingly, if the wind profile over the sea was expressed by the logarithmic law, it never make a jet-like flow by the vertical displacement Z

7 106 Journal of the Meteorological Society of Japan Vol. 61, No. 1 Fig. 6 Frequency distributions of pitch angle for the Runs in the cruise in of the anemometers. At the time of observations, following close attentions were paid to the instrumentation. (1) The anemometers on a pole were sometimes interchanged and carefully checked before and after observations. (2) In the cruises, the heights of anemometers from M.S.L. varied to some extent of several tenth centimeters but these variations were corrected. 4. Results The distinctive wind profiles were frequently observed over the open sea where swell waves prevailed and winds were relatively strong. The representative mean profiles of the winds and temperatures are illustrated in Fig. 4. In all observation runs, a bow boom was always faced against windward. In 1969, because of the bad weathers and high waves, the observations were limited only to the afternoon of 7th, July. On that day, mean wind speed gradually increased from about 1m/sec to about 8m/sec for several hours, then the mean wind profile for each 10min was studied separately (Run A to E in Table 1). Sampling durations of the other runs covered through 30 to 180min, because we had steady winds and also almost steady air temperature. The horizontal bars in Fig. 4 indicate standard deviations of some 10min means. They were less than 10% of the total mean except Run G, in which the wind speed was very low. The profiles in Run A, G and H are approximately expressed by the logarithmic law; in the case of Run A, a thermal stratification was stable in the layer between 10m above M.S.L. and sea surface, so a log-linear wind profile was expected. It was represented by a broken line in the Figure. Fig. 7 Frequency distributions of relative wave height in the cruise in Run G had a neutral stratification as shown in Table 1, and so the mean wind profile was almost logarithmic one. Since a thermal stability in Run H was somewhat unstable (Ri =-0.022), the wind indicated an unstable profile which was concave upwards as is observed in the surface layer on, the land in summer. These runs are characterized by the fact that the mean wind speeds are less than 3m/sec, especially weak in Run A and G (*2.5m/sec). The wave heights in these Runs were 2.7m, 1.5m and 2m respectively. On the other hand,

8 February 1983 T. Fujita, S. Nemoto, K. Takeuchi and M. Tosha 107 in Run F, in spite of almost the same wave height (1.5m), double kinks appeared in the wind profile. It seemed that the kinks arose from a stronger wind which was about two times higher than that in the previous Runs. Generally speaking, the departure from a logarithmic wind profile becomes larger as the mean wind speed increases; namely the wind profile is bent and has obvious kink when a mean wind speed is over 5m/sec. Fig. 6 shows the frequency distributions of pitch angles obtained from the output of gyroscope and also Fig. 7 shows the same of relative wave heights from a sonic wave gauge. In Fig. 6, under the weak winds, a peak frequency is inconspicuous but as the wind speed becomes wind observation errors, under the high wind speeds and swell waves, the distinctive wind profiles are observed and it is deduced that a jet-like flow existed at the height of about twice a wave height. 5. Discussions The present authors suggested indirectly that a jet-like flow existed in the marine surface layer over the open sea with significant swell waves. It corresponds to the maximum wind speeds in the profiles observed by Yefimov and Sizov. They measured them by use of the buoy-mast which did not move with wave. Accordingly, in their time-height cross section, a sharp jet flow was illustrated. larger than about 5m/sec, the two peaks clearly The distinctive wind profiles observed in the appear on the frequency distributions. open sea and the water-wave tunnel by other For example, in Run E, a wave height was researchers support our wind profiles. about 3.3m, so we supposed that the anemometers which were moving up and down by er the swell waves We convince that the wind profiles with a `jet' will be directly observed ov pitching and heaving of the R/V, frequently in future. passed across the zone of maximum wind speed At present, the mechanism for the formation over the sea. of the jet-like flow in the marine surface layer In the run, the frequency distribution of pitch is not yet clear, but the relation between wind angle has two peaks in -0.9* and +0.7*. The speed and swell speed may be a key to solve the peak angles displace the anemometers about problem. 1.5m upward and about 1.4m downward respectively. That is, many authors including Stewart (1961) Therefore, if there was a maximum assert that there are organized wave-like flows wind speed at 6.5m height as Schooley (1963) and not turbulence in the layer near the sea observed in the water-wave tunnel, the anemometers surface. at 5m and 8m heights would apparently Volkov (1969, 1970) found that the velocity measure higher wind as shown by the model fluctuations u and w induced by the waves could calculation in the last section. be intercorrelated, and in the case of wind wave, In Run F, the anemometers at 4.4m, and (z), the stress due to wave-induced flows ** had 6.6m heights measured higher wind, a wave the same sign as *t(z), turbulent stress, on the height observed by the eye was about 2m. Accordingly, other hand, in the case of surge wave, **(z) in Run F, it is estimated that there could reverse its sign. These discussions on a existed a maximum wind speed at a 2.5 times momentum transfer over the water waves suggested height of a wave height. that in the higher wind speed over the In Run I, J, K, in the level from 4.5m to swell wave, a momentum could be transferred 5.5m above M.S.L. the jet-like air flows might from the waves to the air flows under the critical exist, but unfortunately an anemometer at 4m level (U=c). If this mechanism is valid, there height was broken down. The lower peaks in may be found a jet-like air flow in the wind the wind profiles were not able to observe. profile over the open sea with significant swell The turbulence characteristics showed in Table waves. 1 were obtained from a bulk method which had been developed by Fujita (1978). Since the atmospheric 6. Conclusions thermal stabilities except Run A were (1) Since the anemometers move up and nearly neutral, it is considered that the departures downward with wave motion, a jet-like air flow from the logarithmic wind profile were not due to them. on the wind profile was apparently the two peaks on it. observed as Taking considerations into various kinds of A numerical simulation of a wind profile by

9 108 Journal of the Meteorological Society of Japan Vol. 61, No. 1 the vertically moving anemometers suggested that a jet-like air flow was also apparently dispersed up and downward to the jet-core height. (2) The total errors due to overspeeding of the small cup amemometer were less than 0.52% of the true mean wind speed and the rolling, pitching effects of the hull on the measurements of mean wind profile were negligible. (3) The atmospheric thermal stabilities were nearly neutral except Run A, then it was considered that they hardly influence on the observed wind profiles. (4) Considering the measurement errors, above mentioned, due to various causes, on the open sea, as a mean wind speed increases, a departure of wind profile from a logarithmic profiles becomes larger and two obvious peaks in the profile were recognized corresponding to the wave height distribution with separate two maxima. Acknowledgment The authors wish to express their thanks to the research group of the Ocean Research Institute, University of Tokyo, including Dr. A. Takeda for offering the wave data. Thanks are also extended to Mr. H. Uozu and crew men of the Hakuho-Mare for their kind helps to the observations and to Mr. N. Honda for drawing figures. References Blanc, T. V., 1981: Report and analysis of the May 1979 Marine surface layer micrometeorological experiment at San Nicolas Island, California, NRL Report 8363, Washington, D.C. p.8. Bogorodsky, M. M., (1966): Some peculiarities of the sea surface roughness. Okeanologir, 6, Bush, N. E. and L. Kristensen 1976: Cup anemometer overspeeding. Ris* Report No. 339, Danish Atomic Energy Commission Research Establishment, Ris* Physics Department. Deacon, E. L., P. A. Shepard and E. K. Webb, 1957: Wind profiles over the sea and the drag at the sea surface. Australian Jour. Phys., 9, Deacon, E. L., 1962: Aerodynamic roughness of the sea. Jour. Geophys. Res., 67, Fujita, T., 1978: Determination of turbulent flux by the bulk method using measurements at two levels. Papers in Meteorol. Geophys., 29, Francey, R. J. and K. Sahashi, 1982: The overestimation of wind speed from cup anemometers. Jour. Meteor. Soc. Japan, 60, Hay, J. S., 1955: Some observations of air flow over the sea Q. J. Roy. Meteor. Sco., 81, Izumi, Y. and M. L. Barad, 1970: Wind speeds as measured by cup and sonic anemometers and influence by tower structure. J. Appl. Meteor., 9, Kondo, J., G. Naito and Y. Fujinawa, 1971: Response of cup anemometer in turbulence. J. Meteor. Soc. Japan, 49, Kondo, J., F. Fujinawa and G. Naito, 1972: Waveinduced wind fluctuation over the sea. J. Fluid Mech., 51, Kondo, J. and T. Sato, 1982: The determination of the von Karman Constant. J. Meteor. Soc. Japan, 60, Krugermeyer, L. and M. Grunewald and M. Dunkel, 1978: The influence of sea wave on the wind profile. Boundary Layer Meteor., 14, Makino Applied Measuring Instruments Inc., 1973: On the characteristics of wind sensors. Tokyo, Japan (in Japanese). Meshal, A. H., 1977: Comparison of drag coefficients over water measured directly and determined by wind profile. Atmosphere, 15, Miyake, M., M. Donelan, G. McBean, 1970: Comparison of turbulent fluxes over water determined by profile and eddy correlation techniques. Q. Jour. Roy. Meteor. Soc., 96, Nan'niti, T., A. Fujiki and H. Akamatsu, 1968: Micrometeorological observations over the sea (1). Jour. Ocean. Soc. Japan, 24, Paulson, C. A., E. Leavitt and R. G. Fleagle, 1972: Air-sea transfer of momentum, heat and water determined from profile measurements during BOMEX (1972), Jour. Phys. Oceano., 2, Roll, H. U., 1965: Physics of marine atmosphere. Academic Press, New York and London, p Schooley, A. H., 1963: Simple tools for measuring wind fields above wind-generated water waves. Jour. Geophys. Res., 68, Shepard, P. A., 1951: Current research at imperial college, London, on the effects of turbulent flow -Eddy fluxes. Imperial College of Science and Technology, London. Stewart, R. W., 1961: The wave drag of wind over water. J. Fluid Mech., 10, Takeda, A. and H. Ishikawa, 1971: Measurements of turbulent fluxes over the open sea. Preliminary report at the autumn general meeting of the Meteorological Society of Japan (in Japanese). Takeda, A. and N. Misawa, 1971: On perturbations in the air flows due to the hull. Preliminary report at the spring general meeting of the Oceanographical Society of Japan (in Japanese). Volkov, Yu. A., 1969: The spectra of velocity and temperature fluctuations on air flow above the agitated sea surface. Izv. Atmospheric and Oceanic Physics, 5,

10 February 1983 T. Fujita, S. Nemoto, K. Takeuchi and M. Tosha 109 Volkov, Yu. A., 1970: Turbulent flux of momentum Yefimov, V. V. and A. A. Sizov, 1969: Experimenand heat in the atmospheric surface layer over tal study of the field of wind velocity over waves. a disturbed sea surface. Izv. Atmospheric and Izv. Atmospheric and Oceanic Physics, 5, 930- Oceanic Physics, 6,