INTERNAL SOLITARY WAVES

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.