期刊
OCEAN MODELLING
卷 78, 期 -, 页码 17-34出版社
ELSEVIER SCI LTD
DOI: 10.1016/j.ocemod.2014.02.005
关键词
Internal waves; Solitary waves; Shoaling waves; Weakly-nonlinear wave equations; Incompressible Euler equations
资金
- Discovery Grant - Natural Science and Engineering Research Council of Canada
- Canadian Foundation for Innovation
- Ontario Research Fund
- Canadian Foundation for Climate and Atmospheric Science (CFCAS)
In this study the evolution of internal solitary waves shoaling onto a shelf is considered. The results of high resolution two-dimensional numerical simulations of the incompressible Euler equations are compared with the predictions of several weakly-nonlinear shoaling models of the Korteweg-de Vries family including the Gardner equation and the cubic regularized long wave (or Benjamin-Bona-Mahoney) equation. Wave models in both physical x-t space and in s-x space are considered where s is a commonly used characteristic time variable. The effects of rotation, background currents and damping are ignored. The Boussinesq and rigid lid approximations are also used. The shoaling internal solitary waves generally fission into several waves. Reflected waves are negligible in the cases considered here. Several hyperbolic tangent stratifications are considered with and without a critical point. Among the equations in x-t space the cubic regularized long wave equation gives the best predictions. The Gardner equation in s-x space gives the best predictions of the shape of the leading waves on the shelf, but for many stratifications it predicts a propagation speed that is too large. (C) 2014 Elsevier Ltd. All rights reserved.
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