D.E. Pelinovsky and R.H.J. Grimshaw
Instability analysis of internal solitary waves
in a nearly uniformly stratified fluid
Phys. Fluids A 9, 3343-3352 (1997)
Abstract:
Long finite-amplitude internal solitary waves propagating
in a stratified fluid with nearly uniform stratification
are considered within an asymptotic approximation
leading to a nonlocal evolution equation of the Korteweg-de
Vries (KdV) type. Analytical properties of this equation
and its solitary wave solutions are studied and a
criterion for solitary wave instability is derived. This
criterion coincides with that for solitary waves in a local
generalized KdV equation. Applications of these results
reveal that strengthening of the stratification might lead
to destabilization of smooth solitary waves and their
blow-up into vortex-type wave structures.
Keywords:
2ND-ORDER THEORY, WEAK SHEAR, TOPOGRAPHY, EVOLUTION, FLOW