Radiation damping of inertial oscillations in the upper ocean

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Abstract
Turbulent motions within the wind-mixed layer, which is advected by near-surface inertial oscillations, excite internal gravity waves in the underlying ocean layers. Momentum transport in the radiated wave field results in a drag force on the inertial currents. Because the magnitude of the inertial currents is large compared with the turbulence intensity, the resultant rate of dissipation of inertial oscillation energy is approximately equal to the energy flux in the radiated wave field. Using linear internal wave theory, asymptotic results are derived for the energy flux in terms of the Brunt-Väisälä frequency N below the mixed layer, the magnitude U0 of the inertial current, the integral length scale l of the mixed-layer turbulence and the mean-square displacement 〈ζ20〉 of the base of the mixed layer. For representative conditions, we estimate an energy flux of 1-10 erg/cm2 s into relatively short (wavelength of order 2πU0/N) high frequency (of order, but less than, N) internal waves. The resultant decay times for inertial oscillation energy range from a day to a week or so, in agreement with reported observations on the decay of inertial oscillations in the upper ocean. The estimated energy flux is comparable in magnitude to estimates for other internal wave generation mechanisms, indicating that, in addition to being a significant sink of inertial energy, this process may locally represent a significant source of internal wave energy in the open ocean.

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