Topographic wave radiation and modon decay

The effect of topographic wave radiation on isolated eddies is modelled by an f-plane modon propagating parallel to an infinitely long escarpment. It is assumed that the lengthscale of the modon is much smaller than the lengthscale on which the topographic waves evolve. This enables the linearised equations of motion to be solved and the asymptotic (far-field, large-time) behaviour of the topographic wave field is subsequently described. A steady wave-like response is found when the modon moves within the range of possible topographic wave phase speeds. An anomalous case exists when the modon speed is the same as the long topographic wave group speed. This implies that energy cannot escape from the vicinity of the modon and consequently the response eventually becomes nonlinear. It is shown that the appropriate equation to describe the evolution of topographic waves in this case is a forced KdV equation.In the cases of the steady linear response and the nonlinear response (for positive forcing), the energy flux carried by the topographic waves is calculated. Conservation of energy and Lagrangian conservation of vorticity extrema, along with a slowly varying assumption concerning the evolution of the modon, are used to show that the radius and speed of the modon decrease exponentially. The e-folding time associated with the decay is shown to be of possible significance when compared to typical ocean eddy lifetimes.