On Damped Resonant Interactions

Abstract

It is shown that the evolution equations for a triad of weakly damped, resonantly interacting waves are isomorphic to the corresponding equations for undamped waves (and therefore may be integrated in term of elliptic functions) if the damping coefficient is the same for each member of the triad. This condition is satisfied for topographic Rossby waves for which dissipation is through a turbulent Ekman layer and the wavelengths are small compared with the Rossby radius of deformation.