Vol. 11 No. 3 (2012): Mapana Journal of Sciences
Research Articles

On the Nonlinear Stability of Inviscid Homogeneous Shear Flows in Sea Straits of Arbitrary Cross Sections

  • V Ramakrishnareddy,
  • M Subbiah
V Ramakrishnareddy
Department of Mathematics, Pondicherry University, Pondicherry-605014, India
M Subbiah
Department of Mathematics, Pondicherry University, Pondicherry-605014, India
DOI: https://doi.org/10.12723/mjs.22.2

Published 2012-07-08

Keywords

  • Nonlinear stability,
  • inviscid shear flows,
  • variable bottom,
  • sea straits.

Abstract

In this paper we study the nonlinear stability of steady flows of inviscid homogeneous fluids in sea straits of arbitrary cross sections. We use the method of Arnol'd [1] to obtain two general stability theorems for steady basic flows with respect to finite amplitude disturbances. For the special case of plane parallel shear flows we find a finite amplitude extension of the linear stability result of Deng et al [2]. We also present some examples of basic flows which are stable to finite amplitude disturbances.

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