Unsteadiness and periodicity in gravity waves and lee waves forced by a fixed rigid boundary

It is shown that a vertically sheared, inviscid stratified flow over a sinusoid, starting from rest, results in one of two responses, both nonsteady: 1) resonance modes, in which the phase lines are vertical, and wave amplitude and drag grow linearly with time; or 2) oscillatory (in time) modes, with one or more frequencies, phase lines sloping alternately upwind and downwind, momentum flux alternately negative and positive, and drag alternately positive and negative. Flow over an isolated ridge will excite all of the foregoing modes. The resonant modes are the familiar trapped waves; oscillatory modes will tend to be evident or dominant only when the ridge is broad and/or the Richardson number low.