A note on solitary waves along potential vorticity fronts on anf-plane

The effects of short waves on the propagration of velocity discontinuity along the interface of two uniform potential vorticity, zones on anf-plane is examined. It is shown, using a multiple scale analysis, that the dispersion introduced by the short waves can balance the nonlinear steepening effects predicted by the semigeostrophic theory. The time evolution of a shear disturbance along the front is governed by a Korteweg-de Vries equation. Numerical solutions of the solitary waves along the front are presented.