The Propagation of a Gravity–Inertia Wave in a Positively Sheared Flow

Abstract

When a gravity?inertia wave in two dimensions is generated by flow over a stationary boundary above the critical level, its vertical propagation will depend on whether it encounters the singular level at which kU/f is equal to unity. If so, the wave is cellular below this level and vertically propagating above it, with drag and momentum flux oscillating in time between positive and negative, with no steady state approached. This is demonstrated by simulation and explained by analysis as the result of near resonance. When the disturbance is excited by flow over an isolated ridge, the flow will, or will not, oscillate depending on its Rossby number and on the width of the ridge as scaled by the wavelengths of the oscillatory portion of the spectrum. In particular, the quasigeostrophic solution is highly oscillatory.