On the energetics of mean-flow interactions with thermally dissipating gravity waves

This study was stimulated by the need to describe the vertical heat transfer by thermally dissipating gravity waves within the well-known Doppler-spread parameterization (DSP) by C. O. Hines. It is noted that the exact description of the effect, otherwise widely known as “dynamical cooling”, depends on detailed assumptions about the nature of the thermal dissipation. Since the DSP does not distinguish between the thermal and mechanical (frictional) dissipation, certain assumptions have to be made. The resulting expressions are then in general agreement with other studies using similar assumptions. As a more general result, it is observed that thermal dissipation of waves is an example of a process leading to an increase of both the energy and entropy of the background stratification while conserving the column integral of mass-weighted potential temperature. This particular process may thus be put within the context of a recent discussion on maximum-entropy temperature profiles where such processes have been hypothesized but, to our knowledge, not actually identified. It is noted finally that since, on balance, energy is deposited into the mean stratification, the familiar term “dynamical cooling” may be somewhat misleading. Since estimates of wave heat fluxes are available from observations, the corresponding energy deposition rates may also be evaluated.