P8.3 Dynamics of the Surface Layer Over the Ocean As Revealed
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P8.3 DYNAMICS OF THE SURFACE LAYER OVER THE OCEAN AS REVEALED FROM FIELD MEASUREMENTS OF THE ATMOSPHERIC PRESSURE £ ¾ ¿ Tihomir Hristov½ , Kenneth Anderson , James Edson and Carl Friehe ½ Dept. of Earth and Planetary Sciences, Johns Hopkins University, Baltimore, Maryland ¾ SPAWARSYSCEN-SD, 2858, San Diego, California ¿ Woods Hole Oceanographic Institution, Woods Hole, Massachusetts Dept. of Mechanical and Aerospace Engineering, Univ. of California, Irvine, California 1. INTRODUCTION on the turbulent pressure fluctuations to provide a ran- dom (Langevin) force acting onto the water surface that The spatio-temporal structure of the pressure field in the ensures wind-to-wave energy transfer. Fields in the wind atmospheric boundary layer is a significant element in the correlated with the water surface motion are considered layer’s dynamics. Pressure affects the atmospheric re- negligible and are ignored. Within this model the wave fractive conditions, thus pressure statistics is required in amplitude increases linearly in time, thus evolving in a studies of electromagnetic propagation. Although indi- way similar to a Brownian particle driven by the random rect experimental estimates and models have suggested forcing from its surrounding particles. The most efficient important role for the pressure field both over land and wind-to-wave energy transfer is found to occur from a over the ocean, infrequent measurements have so far pressure component advected with the wave and hav- provided only scarce data (Wyngaard (1998)). ing the same wavenumber. Several theories for wind- In turbulent boundary layers, the kinetic energy (TKE) wave interaction (Miles (1957); Davis (1969); Belcher and ½ ÔÛ is balanced through the pressure transport Þ .A Hunt (1993)), although differing in their details, are built belief commonly shared before the Kansas experiment on the concept of fluid-mechanical instability. In that con- has been that the pressure transport term is small. How- cept the waves perturb the mean air flow and the turbu- ever, indirect estimates as well as direct pressure mea- lence in the wind, so the perturbation provides the feed- surements have indicated that over land the pressure back from wind to waves ensuring wave growth. Nu- transport can be a significant TKE gain if the surface layer merical models (Gent and Taylor (1976); Chalikov and is unstable (Wyngaard (1992, 1998)). Over the ocean Makin (1991); Meirink and Makin (2000)) have also em- the atmospheric surface layer is modified by the pres- ployed such a concept, while direct numerical simula- ence of ocean waves, as shown by wind velocity anal- tions have arrived to it (Sullivan et al. (2000); Sullivan and ysis of Hristov et al. (1998, 2003). The distribution of McWilliams (2002)). air pressure on the water surface determines the rate of Observations have so far provided limited information kinetic energy transfer from wind to the surface waves. on the physics of wind-wave interaction. Particularly, the Consequently, past experiments have conducted direct random force mechanism has never been addressed ex- measurements of the interfacial pressure (Shemdin and perimentally. Here the basic distinction between the way Hsu (1967); Dobson (1971); Elliott (1972); Snyder (1974); the random force and the instability mechanisms oper- Snyder et al. (1981)) or have considered extrapolated ate, is used to formulate an experimental criterion for estimates Papadimitrakis et al. (1986); Hasselmann and their relative efficiency. The random force mechanism Bosenberg¨ (1991); Hare et al. (1997); Donelan (1999). requires that the pressure field in the wind is predomi- However, the interfacial pressure distribution does not nantly turbulent, while, in contrast, the instability mecha- specify the spatio-temporal structure of the wave-induced nism relies on the organized wave-induced fields of ve- air flow, which uniquely selects the physical mechanism locity and pressure in the air. Therefore, to compare the of wind-wave coupling. Experimental determination of efficiency of the random force versus the instability mech- that structure requires measurements in the surface layer anism, we need to compare the intensities of the turbulent over the ocean. and wave-induced pressure in the air flow. On the other Broadly, the wind-wave interaction models and theo- hand, recognizing a particular instability mechanism in ries proposed so far have considered two categories of measured data requires finding an agreement between physical mechanisms. The Phillips (1957) theory relies the theoretically predicted and the observed structure of the wave-induced flow (Hristov et al. (2003)). £ Corresponding author address: Tihomir Hristov, Depart- ment of Earth and Planetary Sciences, Johns Hopkins Uni- In this work, from experimental perspective, we ad- versity, 3400 North Charles Str., Baltimore, MD 21218, dress the relative intensity of random force and instability e-mail: [email protected] mechanisms. We also discuss the issue of TKE balance 1 1 11 (a) (b) (c) 0.8 10 ) η 0 9 10 0.6 uu 8 S −1 0.4 10 7 Coherence (u, 0.2 6 −2 Along−wind velocity [m/s] 10 0 −2 −1 0 −1 0 0 20 40 60 80 100 10 10 10 10 10 1 (d) (e) (f) 5 0.8 −2 ) 10 η 0 0.6 pp S −3 −5 10 0.4 Pressure [Pa] Coherence (p, 0.2 −10 −4 10 0 −2 −1 0 −1 0 0 20 40 60 80 100 10 10 10 10 10 0 (g) 10 (h) (i) 0.4 2.5 −1 10 0.2 2 −2 10 ηη 1.5ηη 0 S S −3 10 1 Wave Height [m] −0.2 −4 10 0.5 0 −2 −1 0 −1 0 0 20 40 60 80 100 10 10 10 10 10 Time [s] Frequency [Hz] Frequency [Hz] Figure 1: A flow regime frequently observed during CBLAST. (a) Timeseries of along-wind air velocities from the four ultrasonic anemometers over 100s; (b) Power spectra of along-wind air velocities calculated from 1 hour of data; (c) coherence between the along-wind air velocities and the surface elevation; (d) timeseries of the atmospheric pressure fluctuations at 2 levels; (e) pressure fluctuations power spectra calculated from 1 hour of data; (f) coherence between the pressure fluctuations and the surface elevation; (g) timeseries of the water surface elevation; (h) and (i) power spectra of the water surface elevation. over the ocean in the context of our experimental data. 3m. Instances of flow distortion from the tower are rel- atively rare, although very clear in the data. Rain occa- 2. EXPERIMENTAL SETTING sionally disrupted the sonic anemometers work. The data analyzed here were collected at the WHOI- 3. DATA INTERPRETATION operated Air-Sea Interaction Tower (ASIT) off the coast of Massachusetts. Four sonic anemometers sampled the Figure 1 summarizes the features of a flow regime fre- wind velocity at 20Hz at levels of 7.2m, 9m, 11m, 13.4m quently observed during the experiment. The data show above the ocean surface. Two pressure sensors were that the along-wind velocity is mostly turbulent, as indi- positioned at heights of 9m and 11m. A TSK instrument cated by the timeseries and the power spectra, with some measured remotely the water surface elevation beneath suggestion of small wave influence in the coherence func- the sonic anemometers and pressure sensors. Data tion. In contrast, the pressure appears almost entirely or- were collected continuously from late June through early ganized and modulated by the waves. Comparing the November of 2003. For most of that period winds ranged pressure and the wave height signals, it is clearly no- between 1 and 12 m/s and significant wave heights were ticeable that the wave crests approximately coincide in below 1.5m, except for short storm periods when winds time with the minima and the troughs with the maxima reached 20m/s and significant wave heights exceeded of the pressure. A distinct peak at the wave frequency 2 2 10 is present over the turbulent background in the pressure. 360 25 19 The wave-pressure coherence, which here compares the 0 12 ] 10 270 5 intensities of the wave-induced and the turbulent pres- −1 [s −2 [deg] 180 u sure, approaches 1 and is significant over a broad fre- 10 25 u A 19 Φ 90 quency range even for low-energy wave modes. Clearly, −4 12 10 5 the data demonstrate that in the wind the organized wave- 0 −4 −2 0 2 −4 −2 0 2 10 10 10 10 10 10 10 10 induced pressure dominates and therefore in this flow z/z z/z regime the instability mechanism of wind-wave interac- c c tion is favored to the mechanism of random (Langevin) 25 ] 19 0 force. Two circumstances discussed below offer a likely 10 12 −1 270 5 m explanation. Also, predominantly wave-modulated pres- ⋅ [deg] −2 p sure suggests an analytic estimate for the pressure trans- 10 25 Φ [Pa p 19 port term in the TKE equation. A 12 180 5 −4 10 −4 −2 0 2 −4 −2 0 2 10 10 10 10 10 10 10 10 4. DISCUSSION z/z z/z c c If a flow allows to ignore the fluid’s compressibility, the Vertical profiles of the wave-induced along- static pressure in that flow satisfies the Poisson equation: Figure 2: wind and pressure fluctuations obtained from numerical ¾ solutions of the Rayleigh equation, according to the crit- Ö Ô Ö ¡ ´Ú ¡ÖµÚ ical layer theory of Miles (1957). Different curves corre- Ù From here, extending Kolmogorov’s arguments regard- spond to specific values of the wave age parameter £ , Ù ing the spectral scaling of the turbulent velocity to the as indicated in the symbol list. The amplitude of the ¨ Ù turbulent pressure leads to the conclusion that turbu- along-wind velocity fluctuations (upper left), the phase ´ µ lent pressure spectrum decays with scale as Ô of the along-wind velocity fluctuations (upper right), the ¿ ´ µ Ô , i.e.