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J. L. Lumley and E. A. Terray


Turbulent velocity spectra measured beneath wind waves show a large enhancement about the central wave frequency. A “5/3" frequency dependence can be seen both above and below the central peak, but with an apparent increase in spectral density at high Frequencies.

We show that these features can be understood via a generation of Taylor's hypothesis to the case in which frozen, isotropic, homogeneous turbulence is bodily convected past a fixed probe by a combination of drift and wave orbital motions. In a monochromatic wave field turbulent energy is aliased into harmonics of the wave frequency fp. We show qualitatively how drift currents or a random wave field broaden these lines into a continuous spectrum, and present the results of direct calculations which demonstrate clearly the transition from “line-like” to a smooth “5/3" spectrum. We calculate the leading asymptotic behavior in the limit of large and small frequencies for an arbitrary wave-height spectrum. For wave orbital velocities larger than the mean drift (in the direction of wave propagation) we findwhen U denotes an rms velocity. This result provides a possible explanation for the observed increase in spectral densities for frequencies above the peak.

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S. A. Kitaigorodskii and J. L. Lumley


We analyze in detail the budget of total and fluctuating energy in the surface layer of the ocean. We suggest a rational scheme for separating the budget of turbulence from that of random wind-generated surface waves, and suggest in particular a form for the interaction term appearing in the turbulent energy equation. This is derived from an analysis of the potential velocity field excited by surface motion, and its interaction with the turbulence. Finally, we explore some implications of the proposed interaction both for the surface wave energetics, as well as for the turbulence structure.

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S. A. Kitaigorodskii, M. A. Donelan, J. L. Lumley, and E. A. Terray


We present the results of an analysis of field data collected by Donelan who used a miniature drag sphere to measure velocities beneath wind waves on Lake Ontario. Linear statistical techniques are used to separate the velocity into wave and turbulent parts. While we mostly aim at demonstrating the effects of surface wind waves on the statistical characteristics of the turbulent field in the upper mixed layer, we also interpret several features of the data on the hags of recent theoretical results.

One of the most intriguing features of the turbulent velocity spectra so obtained is a large peak near the dominant wave frequency. We review various possible explanation for this behavior although we prefer a model in which the turbulence is assumed frozen on the timescale of the Waves. This model requires no new dynamics and gives explicit formulae relating the dissipation rate to the magnitude of the spectral densities for high and low frequencies. On this basis we have determined a dissipation length from the data. The dependence of this quantity on depth is inconsistent with pure shear produced turbulence. Moreover the observed turbulent velocities shows a strong dependence on wave energy,. which cannot be explained solely within the framework of similarity theory for the inner (constant flux) layer.

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