Pulse-To-Pulse Coherent Doppler Measurements of Waves and Turbulence

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Pulse-To-Pulse Coherent Doppler Measurements of Waves and Turbulence 1580 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 16 Pulse-to-Pulse Coherent Doppler Measurements of Waves and Turbulence FABRICE VERON AND W. K ENDALL MELVILLE Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California (Manuscript received 7 August 1997, in ®nal form 12 September 1998) ABSTRACT This paper presents laboratory and ®eld testing of a pulse-to-pulse coherent acoustic Doppler pro®ler for the measurement of turbulence in the ocean. In the laboratory, velocities and wavenumber spectra collected from Doppler and digital particle image velocimeter measurements compare very well. Turbulent velocities are obtained by identifying and ®ltering out deep water gravity waves in Fourier space and inverting the result. Spectra of the velocity pro®les then reveal the presence of an inertial subrange in the turbulence generated by unsteady breaking waves. In the ®eld, comparison of the pro®ler velocity records with a single-point current measurement is satisfactory. Again wavenumber spectra are directly measured and exhibit an approximate 25/3 slope. It is concluded that the instrument is capable of directly resolving the wavenumber spectral levels in the inertial subrange under breaking waves, and therefore is capable of measuring dissipation and other turbulence parameters in the upper mixed layer or surface-wave zone. 1. Introduction ence on the measurement technique. For example, pro- ®ling instruments have been very successful in mea- The surface-wave zone or upper surface mixed layer suring microstructure at greater depth (Oakey and Elliot of the ocean has received considerable attention in re- 1982; Gregg et al. 1993), but unless the turnaround time cent years. This is partly a result of the realization that of the pro®ler is small compared to the time between wave breaking (Thorpe 1993; Melville 1994; Anis and Moum 1995) and perhaps Langmuir circulations (Skyl- events, the probability of sampling an intermittent event lingstad and Denbo 1995; McWilliams et al. 1997; Mel- may be signi®cantly reduced when compared with an ville et al. 1998) may lead to enhanced dissipation and instrument at a ®xed depth. This may be dif®cult to signi®cant departures from the classical ``law-of-the- achieve in the upper mixed layer. On the other hand, wall'' description of the surface layer (Craig and Banner ``®xed'' instruments need to be mounted either on a 1994; Terray et al. 1996; Agrawal et al. 1992). The moving buoy or vessel (Osborn et al. 1992; Drennan et classical description would lead to the dissipation, «, al. 1996), and then the problem of transforming from a being proportional to z21, where z is the depth from the temporal signal to a spatial signal through some form surface, whereas recent observations show «}z22 to of Taylor's hypothesis can be dif®cult if not impossible. z24 (Gargett 1989; Drennan et al. 1992), or «}e2z (Anis From the work of Agrawal et al. (1992) and the mod- and Moum 1995), with values of the dimensionless dis- eling of Melville (1994), we assume that the maximum sipation «kz/u3 (where k is the von KaÂrmaÂn constant dissipation rate in the wave zone will be approximately *w 3 andu the friction velocity in water) up to two orders «5Au w/kz, where to be speci®c we take the numerical *w * of magnitude higher than the O(1) expected for the law factor to be A 5 100. Now if we assume that U10 is in of the wall (Melville 1996). the range 3±15 m s21 and z is in the range 1±10 m, then Measuring the dissipation in the surface wave zone with the further assumption that the air±sea drag co- 23 is made dif®cult by the wave motion, the relatively small ef®cient CD 5 O(10 ) (Komen et al. 1994), we ®nd 23 2 23 thickness of the layer, and the general dif®culty of mak- that « ranges from 10 m s (for z 5 1 m and U10 21 27 2 23 ing measurements near the air±sea interface. If breaking 5 15 m s )to93 10 m s (for z 5 10 m and U10 is the source of the high dissipation events, then the 5 3ms21). For these values of « the Kolmogorov length intermittency of breaking can have a signi®cant in¯u- h, time tk, and velocity scales y, are (in SI units) (1.7 3 1024,33 1022,63 1023) and (1023,1,1023), respectively. At large Reynolds numbers the k25/3 sub- range begins to roll off in the dissipation region at kh Corresponding author address: Prof. W. Kendall Melville, Scripps Institution of Oceanography, University of California, San Diego, La 5 0.1. For example, for a turbulent Reynolds number 21 5 Jolla, CA 92093-0213. Rt 5 uln of 2 3 10 , corresponding to a breaking E-mail: [email protected] wave of 2-s period (Rapp and Melville 1990), where u q 1999 American Meteorological Society NOVEMBER 1999 VERON AND MELVILLE 1581 and l are, respectively, the velocity and length scales of the energy containing eddies and n the kinematic vis- cosity of water, this subrange extends for two decades to lower wavenumbers before rolling off in the energy- containing range. For this particular conservative Rt we expect to have an inertial subrange over two decades of wavenumbers. Thus, for the largest « given above we would have an inertial subrange over length scales from 0.01 to 1 m, and for the smallest «, 0.06±6 m. In sum- mary, for breaking-induced near-surface turbulence we expect to have inertial subranges for scales in the range O(0.01±1 m). Since dissipation estimates are made from measure- ments over the inertial or dissipation subranges of the turbulent scales, it would be desirable to avoid any form FIG. 1. Photograph of the Dopbeam head, which includes transduc- of Taylor hypothesis and have an instrument that could er and analog electronics. make direct spatial (wavenumber) measurements over these ranges in the ®eld. To our knowledge, the only means of making dense spatial measurements of veloc- Q(t)I(t 1 t) 2 I(t)Q(t 1 t) C5tan21 , (2) ities are either optical or acoustical. Experience in the []I(t)I(t 1 t) 1 Q(t)Q(t 1 t) laboratory with laser Doppler velocimetry (Rapp and Melville 1990) and a digital particle imaging velocim- where l is the system wavelength, t is the delay between eter (DPIV) (Melville et al. 1998) led us to believe that adjacent pulses, and Q(t) and I(t) are, respectively, the optical techniques, while very attractive, may be less quadrature and in-phase components of the received sig- robust than acoustical systems in the active wave zone nal S(t), and S*(t) denotes the complex conjugate. Clear- of the ocean. Accordingly, we decided to pursue acous- ly, the direct velocity measurement is limited to zCz # tical techniques. p, giving a maximum velocity range of This paper describes our laboratory and ®eld tests of l the suitability of a pulse-to-pulse coherent acoustic Vmax 56 . (3) Doppler instrument (Dopbeam, Sontek, San Diego) for 4t measuring turbulence in the inertial subrange under The maximum achievable range is breaking waves. Direct comparisons are made with a ct DPIV system in the laboratory, and with a single-point R 5 , (4) acoustic velocimeter in the ®eld. max 2 where c is velocity of sound in water. This leads to the 2. Instrumentation well-known ``range±velocity'' ambiguity lc a. Coherent Doppler sonar RV 56 . (5) max max 8 As opposed to conventional incoherent Doppler sys- The Dopbeam is a 1.72-MHz, programmable, mono- tems, which extract the velocity from the frequency shift static, single-beam sonar system performing pulse-to- in the backscatter, coherent Doppler sonars transmit a pulse coherent Doppler measurements of the along- series of short pulses, allowing continuous recording of beam ¯uid velocity. Typically, it operates in the range the ¯uid velocity at densely spaced range bins. This 0.5±5 m with a direct unambiguous velocity measure- leads to the possibility of acquiring information on the ment between 0.3 and 0.03 m s21. The waterproof unit ¯uid turbulence (Lhermitte and Lemmin 1990, 1994; is 40 cm long and 6 cm in diameter (Fig. 1). It is Lohrmann et al. 1990; Gargett 1994). equipped with a single 2.5-cm-diameter transducer at For each pulse, the backscattered signal is range gat- one end, and an underwater connector for communi- ed. The radial velocities V are extracted using the pulse- cation with a controller at the other end. For a circular pair coherent technique (Miller and Rochwarger 1972) piston transducer, the directivity of the emitted acoustic by taking the time rate of change of the phase C of the intensity is given by the Rayleigh function complex signal autocorrelation X(t) 5 S(t)S*(t 1 t). Hence 2J (pD sinu/l) Ra(u) 5 1 , (6) pD sinu/l 1 l C V 5 , (1) 2p 2 t where J1 is the ®rst-order cylindrical Bessel function and D the diameter of the transducer. The spreading with angle of the main lobe is then given by Ra(u 0) 5 0, 1582 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 16 which leads to u 0 5 2.48, and the half-power beam angle is given by 20 log10[Ra(u3dB)] 523, which leads to u3dB 5 18. The Fresnel zone (near ®eld) boundary is located at D 2/4l 5 18 cm from the transducer. b. Digital particle image velocimeter A DPIV is a system that measures two components of velocity in a plane by measuring particle displace- ments between sequential images.
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