Damping of internal gravity waves by small-scale turbulence

Abstract

The interaction between turbulence and internal waves in a stratified fluid with a shear flow is considered on the basis of perturbation theory permitting a description of internal wave damping by turbulence. The results show that the behavior of the damping rate for internal waves is rather anomalous for the long-wave range: it remains finite for such waves but may decrease to very small quantities in a restricted range of wavenumbers, depending on the mode structure. Detailed computations are made for the first three modes of the internal waves. The effects of anisotropy of the turbulent fluxes are also considered. For the case of constant buoyancy frequency an exact solution is obtained of the linearized semiempirical equations valid even for a strong wave damping. Estimates show that the damping by the upper turbulent layer may be an effective energy sink for long internal waves in the ocean.