THE DECAY OF MODONS DUE TO ROSSBY-WAVE RADIATION

A weakly radiating theory is developed to describe the decay of a west ward propagating dipole modon on a beta plane in the case of small bet a. The barotropic vorticity equation is expanded about an ''f-plane'' (beta=0) modon using the expansion parameter epsilon=betaL2/U. The the ory also assumes shape preservation of the modon. An expression is fou nd for the energy loss from the dipole due to Rossby wave radiation. T wo alternative constraints, one involving global enstropy conservation and the other assuming conservation of the maximal vorticity values i n the center of the dipole vortices, are used to derive expressions fo r the decay rate of the dipole. In both cases, the predicted decay is algebraic in time. These theories are tested in a numerical model for various values of c. It is found that enstrophy conservation is not a good constraint because fluid leaks from the dipole in filaments whose small scales ensure loss through numerical dissipation. The theory ba sed on the conservation of peak vorticity works well for small epsilon =0.2, and gives reasonable results for much larger values, up to epsil on=1.0. The theory is used to estimate the decay time of atmospheric b locking due to this radiation phenomenon, and the implied effect is si gnificant.