Simulation of the Transformation of Internal Solitary Waves on Oceanic Shelves

Due to the horizontal variability of oceanic hydrology (density and current stratification) and the variable depth over the continental shelf, internal solitary waves transform as they propagate shorewards into the coastal zone. If the background variability is smooth enough, a solitary wave possesses a soliton-like form with varying amplitude and phase. This stage is studied in detail in the framework of the variable-coefficient extended Korteweg–de Vries equation where the variation of the solitary wave parameters can be described analytically through an asymptotic description a slowly-varying solitary wave. Direct numerical simulation of the variablecoefficient extended Korteweg–de Vries equation is performed for several oceanic shelves (North-west Shelf of Australia, Malin Shelf Edge, Arctic Shelf) to demonstrate the applicability of the asymptotic theory. It is shown that the solitary wave may maintain its soliton-like form for large distances (up to 100 km), and this confirms why internal solitons are observed widely in the world’s oceans. In some cases the background stratification contains critical points (when the coefficients of the nonlinear terms in the extended Korteweg–de Vries equation change sign), or does not vary sufficiently smoothly; in such cases the solitary wave deforms a group of secondary waves. This stage is studied numerically. Submitted for “Journal Physical Oceanography” Correspondence: Professor Roger Grimshaw, Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire LE11 3TU UK; email: [email protected]