On the dissipation of internal solitons in coastal seas

Abstract

Previous descriptions of the turbulent decay of an internal soliton have been based on an adiabatic assumption in which the soliton parameters continuously change in time in response to the dissipation. A complete leading order description of a decaying internal soliton including both horizontal and vertical dissipation is given. It is shown that the adiabatic ansatz fails to fully describe a decaying internal soliton under the influence of weak dissipation. Physically, the breakdown is the consequence of the fact that an adiabatically decaying internal soliton is unable to simultaneously satisfy averaged energy and mass balance relations. An extended region with vertical momentum flux develops behind the decaying soliton in order to compensate for the additional mass lost in the adiabatically decaying internal soliton. The leading order evolution of this extended region is described as is its connection to the stream function field associated with the internal soliton. The magnitude of the vertical flux associated with this region scales linearly with the dissipation parameters. The transition of this extended region back to zero is accomplished through the formation of a spatially decaying packet of linear internal gravity waves.