Finite amplitude waves on barotropic shear layers and jets

Abstract

Abstract We give a detailed derivation of the amplitude equations governing weak, slowly modulated, varicose wavetrains on a barotropic, triangular jet on a β-plane. As one might expect, at wavenumbers that are neutral by linear theory, well-behaved wavetrain solutions can be found. Such solutions are not unique. The properties of the wavetrain (in particular, the form of the nonlinear coefficient in the amplitude equation) depend upon assumptions that one makes about the structure of the wave field in the region far from the jet. Such assumptions turn out to be equivalent to assumptions made about the initial conditions of the problem. This link is established by a wave packet analysis that retains separate, nondimensional parameters for the amplitude of the wavetrain and the length scale of the modulation envelope. We briefly state similar results for sinuous waves on a triangular jet and for waves on a shear layer composed of a strip of uniform potential vorticity.