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.