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| Titel |
A model for large-amplitude internal solitary waves with trapped cores |
| VerfasserIn |
K. R. Helfrich, B. L. White |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1023-5809
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics ; 17, no. 4 ; Nr. 17, no. 4 (2010-07-15), S.303-318 |
| Datensatznummer |
250013701
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| Publikation (Nr.) |
 copernicus.org/npg-17-303-2010.pdf |
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| Zusammenfassung |
| 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. |
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