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Internal Solitary Waves
Author(s) -
Weidman P. D.,
Velarde M. G.
Publication year - 1992
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1992862167
Subject(s) - stratification (seeds) , planar , nonlinear system , internal wave , stratified flow , rotational symmetry , mechanics , stratified flows , waves and shallow water , shear (geology) , free surface , mathematical analysis , classical mechanics , physics , mathematics , geometry , geology , turbulence , thermodynamics , petrology , seed dormancy , botany , germination , computer graphics (images) , quantum mechanics , dormancy , computer science , biology
The expansion procedure introduced by Benney (1966) for weakly nonlinear, planar shallow‐water waves is used to provide an alternative derivation of the more general results of Benjamin (1966) for shallow fluid layers possessing arbitrary vertical stratification and horizontal shear. New solutions that include the effects of both shear and stratification are presented. The evolution equation for slowly varying cylindrical solitary waves traveling in a density‐stratified fluid is found using two‐timing techniques. Not surprisingly, one obtains the same coefficients for the nonlinear and dispersive terms as in the planar case. In the limit for uniform density it is shown that the free‐surface evolution equation of Miles (1978) for axisymmetric Boussinesq waves is recovered.