Internal waves in a continuously stratified atmosphere or ocean

Abstract

A stably stratified shear flow has the velocity profile V(1 - e−y/h) and the density profile log(ρ/ρ) = σ(1 − e−y/h) in 0 < y < ∞ and is bounded by the rigid plane y = 0. It is proved that small disturbances with respect to this basic flow are stable for all wavelengths and Richardson numbers. The eigenvalues for neutral disturbances (internal gravity waves) are enumerated. The results are applicable to the atmosphere and to an infinitely deep ocean.