Nonlinear Processes in Geophysics www.nonlin-processes-geophys.net 1023-5809 1607-7946 17 4 2010 10.5194/npg-17-303-2010 http://www.nonlin-processes-geophys.net/17/303/2010/ http://www.nonlin-processes-geophys.net/17/303/2010/npg-17-303-2010.html http://www.nonlin-processes-geophys.net/17/303/2010/npg-17-303-2010.pdf 303 318 2010-07-15 A model for large-amplitude internal solitary waves with trapped cores K. R. Helfrich khelfrich@whoi.edu B. L. White Department of Physical Oceanography, Woods Hole Oceanographic Institution, Woods Hole, MA, USA Department of Marine Sciences, University of North Carolina, Chapel Hill, Chapel Hill, NC, USA Large-amplitude internal solitary waves in continuously stratified systems 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 speeds above a critical value. As typically modeled, these recirculating 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 homogeneous density and velocity, but unknown shape, is assumed. The core density is arbitrary, but generally set equal to the ambient density on the streamline bounding the core. The flow outside the core satisfies the DJL equation. The flow in the core is given by a vorticity-streamfunction relation that may be arbitrarily specified. For simplicity, the simplest choice of a stagnant, zero vorticity core in the frame of the wave is assumed. A pressure matching condition is imposed along the core boundary. Simultaneous numerical solution of the DJL equation and the core condition gives the exterior flow and the core shape. 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