Stability of shear shallow water flows with free surface

A. A. CHESNOKOV, G. A. El, S. L. Gavrilyuk, M. V. Pavlov

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

Stability of inviscid shear shallow water flows with free surface is studied in the framework of the Benney equations. This is done by investigating the generalized hyperbolicity of the integrodifferential Benney system of equations. It is shown that all shear flows having monotonic convex velocity profiles are stable. The hydrodynamic approximations of the model corresponding to the classes of flows with piecewise linear continuous and discontinuous velocity profiles are derived and studied. It is shown that these approximations possess Hamiltonian structure and a complete system of Riemann invariants, which are found in an explicit form. Sufficient conditions for hyperbolicity of the governing equations for such multilayer flows are formulated. The generalization of the above results to the case of stratified fluid is less obvious, however, it is established that vorticity has a stabilizing effect.

Original languageEnglish
Pages (from-to)1068-1087
Number of pages20
JournalSIAM Journal on Applied Mathematics
Volume77
Issue number3
DOIs
Publication statusPublished - 2017

Keywords

  • Free surface flows
  • Hydrodynamic stability
  • Hyperbolicity
  • Shallow water waves
  • Shear flows

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