Lee waves in stratified flows with simple harmonic time dependence

TLDR

The study investigates internal gravity wave generation by a simple harmonic flow over an obstacle in a stably stratified fluid. The authors analyze limiting cases and estimate the energy flux into the internal wave field. They find that waves are generated at the fundamental frequency and its harmonics, with the fundamental dominating when ω₀/N > 0.5, the quasi‑static approximation accurately estimating the field when ω₀/N < 0.5, and the general solution agreeing with experimental data.

Abstract

The process of internal gravity wave generation by the simple harmonic flow ( U = U 0 , cos ω 0 t) of a stably stratified fluid (Brunt–Väisälä frequency N ) over an obstacle is investigated in some detail. Attention is primarily directed to the behaviour of the solution in various limiting cases, and to estimating the flux of energy into the internal wave field. In general, waves are generated not only at the fundamental frequency ω 0 , but also at all of its harmonics. But, for values of ω 0 / N greater than about one half, the waves of fundamental frequency are dominant. For values of ω 0 / N , less than about one half, the quasi-static approximation, in which the problem is considered as a slowly-varying version of the classical lee wave problem, is found to provide a viable estimate for the wave field. The general solution is found to compare favourably with the limited available experimental data.