Acoustic measurements of breaking wave turbulence

An improved understanding of turbulence and mixing due to wave breaking is essential for progress in a number of areas of air-sea interaction. For surface waves, breaking is normally considered to be a sink of energy (and action); although, like any disturbance, it may also be a source. Breaking, as a dissipative mechanism when momentum is conserved, leads to the generation of currents. The details of the near-surface currents depend on the fact that breaking is a source of turbulence for the upper mixed layer, and may lead to departures from classical law-of-the-wall velocity profiles. Fluxes of heat and gas across the air-sea interface, which are so important for weather and climate up to global scales, depend on the levels of surface turbulence, which are due in part to breaking. Bubbles entrained by breaking may also contribute to gas transfer, and their contribution depends on the depths to which they are mixed by the surface currents and turbulence. Breaking provides strong signatures in remote sensing of the ocean surface; signatures that depend on processes of wave-current interaction associated with wave breaking. For these reasons and more, an improved knowledge of the fluid dynamics of breaking is vital to a better understanding of air-sea interactions from micro- to global scales (Banner and Peregrine, 1993; Melville, 1996).

The surface-wave zone or upper surface mixed layer of the ocean has received considerable attention in recent years. This is partly a result of the realization that wave breaking (Thorpe 1993, Melville 1994, Anis and Moum 1995) and perhaps Langmuir circulations (Skyllingstad and Denbo 1995, McWilliams et al. 1997, Melville et al. 1998) may lead to enhanced dissipation and significant departures from the classical ``law-of-the-wall'' description of the surface layer (Agrawal et al. 1992, Craig and Banner 1994, Terray et al. 1996). The classical description would lead to the dissipation, ε, being proportional to z-1, where z is the depth from the surface, whereas recent observations show (Gargett 1989, Drennan et al. 1992), or (Anis and Moum 1995), with values of the dimensionless dissipation (where κ is Von Karman constant and u*w the friction velocity in water) up to two orders of magnitude higher than the O(1) expected for the law of the wall (Melville 1996).

Figure 1 A) Example of velocity data recorded by the Dopbeam a) and the DPIV b) for a breaker with a slope of S=0.656. The color code is the downstream velocity in cm/s. The horizontal axis represents the downstream distance from the location of the breaker xb, and the vertical axis is the time elapsed from tb, the time of the breaking event. B) Wavenumber spectra computed from the data of figure II.4b and figure II.8. The solid line has a -5/3 slope.

Since dissipation estimates are made from measurements over the inertial or dissipation subranges of the turbulent scales, it would be desirable to avoid any form of Taylor's hypothesis and have an instrument that could make direct spatial (wavenumber) measurements over these ranges in the field. To our knowledge, the only means of making dense spatial measurements of velocities are either optical or acoustical. Experience in the laboratory with Laser Doppler Velocimetry (LDV) (Rapp and Melville 1990) and Digital Particle Imaging Velocimetry (DPIV) (Melville et al. 1998) led us to believe that optical techniques, while very attractive, may be less robust than acoustical systems in the active wave zone of the ocean. Accordingly, we decided to pursue acoustical techniques.

The experiments were performed in the 28.7 m-long glass-walled wave channel at the Scripps Institution of Oceanography. The tank is 0.5 m wide and was filled with fresh water to a depth of 0.6 m. Waves were generated by a hydraulic paddle that sent a packet consisting of high frequency waves followed by low frequency waves so that constructive interference leads to breaking at a time tb at a predetermined location xb along the channel (see Rapp and Melville 1990, Loewen and Melville 1991 for details). The velocity under breaking waves was measured using a pulse coherent Doppler sonar with a range resolution of 1 cm. Figure 1 shows the velocity under a typical breaking event measured with the Doppler and a PIV system. It appears that most of the velocity field can be identified as either orbital motion due to surface waves or turbulence. Using two dimentional Fourier techniques, it is possible to decouple the turbulence from the wave motion. It is then possible to use common statistical tools to analyze the turbulence created by the breaker (Tennekes and Lumley 1972). We consider the one dimensional wavenumber spectrum defined as:

Within the inertial subrange of the turbulence, the spectrum takes the form (Hinze 1975)

where α is Heisenberg's constant ( for high Reynolds number flows).
Figure 2 show the wavenumber spectrum calculated on the velocity of figure 1 and shows a well define inertial subrange in the turbulence. We have then used equation 1.2 to determine ε by fitting a k-5/3 constant slope curve through the inertial subrange part of the spectrum.

Figure 2 A) Example of the vertical velocity recorded by the Dopbeam in the surf zone. Note that the bottom is apparent at a range of approximately 1 m. B) Wavenumber spectra for both orientation of the Dopbeam in the surf zone. The solid line has a -5/3 slope.
This acoustical technique was also extended to the field where we have measured the velocity wavenumber spectra in the upper 40 cm of the ocean under various wind and wave conditions. It was found that the kinetic energy dissipation levels were consistaat with a layer of enhanced turbulence levels near the surface.

The Doppler was subsequently deployed in the surf zone were it demonstrated its ability to resolve fluid velocity in extreme conditions and showed that it could be potentially employed in a wide range of applications.

We have presented tests of a pulse-to-pulse coherent acoustic Doppler profiler in both the laboratory and the field. It has been stated that the main advantage of the Dopbeam over conventional single point velocity measurements is the ability to acquire profiles of the fluid velocity with a high sampling rate which leads to two-dimensional data where the fluid velocity is a function of range and time. We have seen that this permits the study of turbulence in great detail and the collection of flow statistics as a function of time In the laboratory, direct comparisons of velocity and wavenumber spectra from the Dopbeam and DPIV measurements are very good. A two-dimensional Fourier transform of the data shows a fairly clear separation of the turbulence and the wave field, allowing for appropriate filtering. Spectrograms of the turbulence generated by breaking waves show the accelerating propagation of the spectral peak with time toward higher wavenumbers (i.e. the breakdown of energy containing eddies into smaller scales). Averaging the wavenumber spectrogram of a breaking event over time yields a single wavenumber spectrum. Breaking waves of varying strength were studied and the spectra obtained exhibit a -5/3 spectral slope, the signature of the inertial subrange in the turbulence. Identifying the inertial subrange, and measuring the spectral level permits direct estimates of the turbulent kinetic energy dissipation ε under breaking waves. In the field, analysis of the data shows that the instrument can measure wavenumber spectra and resolve the inertial subrange over wavelengths in the range O(0.01-1) m, demonstrating its use for measuring turbulent dissipation in the upper mixed layer/surface-wave zone. Since, any form of Taylor's hypothesis is avoided by the direct spatial measurement, the instrument is not limited to wave conditions which satisfy the requirements of a frequency-wavenumber transformation. One limitation of the instrument, however, is that it requires the presence of an inertial subrange in the turbulence in order to be able to measure the dissipation rate. We conclude that the instrument may prove useful for direct field measurements of turbulent wavenumber spectra.