A model for large-amplitude internal solitary waves with trapped cores
MetadataShow full item record
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. Numerical solutions of time-dependent non-hydrostatic equations initiated with the new stagnant-core DJL solutions show that for the ambient stratification considered, the waves are stable up to a critical amplitude above which shear instability destroys the initial wave. Steadily propagating trapped-core waves formed by lock-release initial conditions also agree well with the theoretical wave properties despite the presence of a "leaky" core region that contains vorticity of opposite sign from the ambient flow.
© The Authors, 2010. This article is distributed under the terms of the Creative Commons Attribution 3.0 License. The definitive version was published in Nonlinear Processes in Geophysics 17 (2010): 303-318, doi:10.5194/npg-17-303-2010.
Suggested CitationNonlinear Processes in Geophysics 17 (2010): 303-318
The following license files are associated with this item:
Showing items related by title, author, creator and subject.
Rypina, Irina I.; Pratt, Lawrence J. (Copernicus Publications on behalf of the European Geosciences Union&the American Geophysical Union, 2017-05-03)Fluid parcels can exchange water properties when coming into contact with each other, leading to mixing. The trajectory encounter mass and a related simplified quantity, the encounter volume, are introduced as a measure ...
Gebbie, Geoffrey A.; Hsieh, Tsung-Lin (Copernicus Publications on behalf of the European Geosciences Union & the American Geophysical Union, 2017-07-19)The Lagrange multiplier method for combining observations and models (i.e., the adjoint method or "4D-VAR") has been avoided or approximated when the numerical model is highly nonlinear or chaotic. This approach has been ...
Ostrovsky, Lev A.; Helfrich, Karl R. (Copernicus Publications on behalf of the European Geosciences Union and the American Geophysical Union, 2011-02-14)Strongly nonlinear internal waves in a layer with arbitrary stratification are considered in the hydrostatic approximation. It is shown that "simple waves" having a variable vertical structure can emerge from a wide class ...