**Titre/Title :**

A Model for Large-Amplitude Internal Solitary Waves with Trapped Cores

**Contact :**

Louis Gostiaux

**Résumé/Abstract :**

Large-amplitude internal solitary waves in continuously stratified fluids can be found by solution of the Dubreil-Jacotin-Long (DJL) equation. For finite ambient density gradients at the surface (bottom) for waves of depression (elevation) these solutions may develop recirculating cores for wave amplitudes above a critical value. The critical point is characterized by incipient overturning where the surface (bottom) velocity above (below) the crest equals the phase speed. Above the critical point the trapped cores contain densities outside the ambient range, may be statically unstable, and thus are physically questionable. To address these issues the problem for trapped-core solitary waves is reformulated. A finite core of uniform density and velocity, but unknown shape, is assumed. The core density is arbitrary, but generally set to that of the ambient fluid on the streamline bounding the core. The uniform core velocity is set equal to the wave phase speed. The exterior flow satisfies the DJL equation and a pressure continuity condition is imposed at the core boundary. Simultaneous numerical solution of the DJL equation and the core condition results in the exterior flow and the core shape. Properties of these solutions are discussed. Numerical solution of the two-dimensional, time-dependent nonhydrostatic equations using the theoretical solutions as initial conditions show that theoretical solutions remain stable up to a critical amplitude above which shear instability rapidly destroys the initial wave. Trapped-core waves formed by lock-release initial conditions also agree well with the theoretical predictions for wave properties despite differences in the core circulation.