A Simple Model for the Shear-induced Decay of an Internal Solitary Wave

Internal solitary waves (ISWs) are a common feature of the coastal zone and marginal seas, especially close to shelf breaks, and are observed to mix the water column at the depth of maximum density gradient. For a two-layer system separated by a thin interface with a finite density gradient, the Richardson number in the interface fails below 1/4 if, in the simplest case, the ISW amplitude exceeds 2(hH1)1/2, where h is the interface thickness and H1 the thickness of the upper layer. Assuming that mixing then thickens the interface and that the potential energy for this comes from the ISW, we derive formulas for the damping rate of the ISW. The model is generalized to allow for a stratified upper layer; a Richardson number of less than 1/4 now requires that the displacement of the base of the upper layer exceeds 0.82 times the thickness of the layer. The ISW damping rate is sensitive to the ratio of the mixing depths above and below the base of the upper layer but can be plausibly matched to field observations.