STABILITY ANALYSIS FROM 4TH-ORDER EVOLUTION EQUATION FOR SMALL BUT FINITE-AMPLITUDE INTERFACIAL WAVES IN THE PRESENCE OF A BASIC CURRENT SHEAR

Authors
DHAR AK DAS KP
Citation
Ak. Dhar et Kp. Das, STABILITY ANALYSIS FROM 4TH-ORDER EVOLUTION EQUATION FOR SMALL BUT FINITE-AMPLITUDE INTERFACIAL WAVES IN THE PRESENCE OF A BASIC CURRENT SHEAR, Journal of the Australian Mathematical Society. Series B. Applied mathematics, 35, 1994, pp. 348-365
Citations number
14
Categorie Soggetti
Mathematics,Mathematics
Journal title
Journal of the Australian Mathematical Society. Series B. Applied mathematics → ACNP
ISSN journal
03342700
Volume
35
Year of publication
1994
Part
3
Pages
348 - 365
Database
ISI
SICI code
0334-2700(1994)35:<348:SAF4EE>2.0.ZU;2-N
Abstract
A fourth-order nonlinear evolution equation is derived for a wave prop agating at the interface of two superposed fluids of infinite depths i n the presence of a basic current shear. On the basis of this equation a stability analysis is made for a uniform wave train. Discussions ar e given for both an air-water interface and a Boussinesq approximation . Significant deviations are noticed from the results obtained from th e third-order evolution equation. which is the nonlinear Schrodinger e quation. In the Boussinesq approximation, it has been possible to comp are the present results with the exact numerical analysis of Pullin an d Grimshaw [12], and they are found to agree rather favourably.