Ekman Layer Dissipation in an Eastward-Traveling Modon

Abstract

A perturbation solution for an eastward-traveling modon in the presence of a bottom Ekman boundary layer is presented. The modon radius, translation speed and wavenumber are allowed to be functions of a slow time and the geostrophic pressure is expanded in the small damping coefficient E½(2r0), where E and r0 are the vertical Ekman and Rossby numbers, respectively. The modon amplitude and translation speed decay exponentially and the modon wavenumber increases exponentially as the slow time increases. The resulting dissipation in the streamfunction and vorticity is qualitatively similar to the McWilliams and others numerical solution, although it is unable to describe the eventual transition to Rossby waves. For oceanic and atmospheric scales the decay takes place over a 100- and 10-day time scale respectively, with the modon traveling about 5 modon radii before complete dissipation.