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Title: Stability of shear shallow water flows with free surface
Authors: Chesnokov, A.A.
El, G.A.
Gavrilyuk, S.L.
Pavlov, Maxim V.
Keywords: Free surface flows
Shallow water waves
Shear flows
Hydrodynamic stability
Hyperbolicity
Issue Date: 2017
Publisher: © Society for Industrial and Applied Mathematics
Citation: CHESNOKOV, A.A. ...et al., 2017. Stability of shear shallow water flows with free surface. SIAM Journal on Applied Mathematics, 77(3), pp.1068-1087.
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.
Description: This paper was accepted for publication in the journal SIAM Journal on Applied Mathematics and the definitive published version is available at https://doi.org/10.1137/16M1098164
Version: Published version
DOI: 10.1137/16M1098164
URI: https://dspace.lboro.ac.uk/2134/24313
Publisher Link: https://doi.org/10.1137/16M1098164
ISSN: 1095-712X
Appears in Collections:Published Articles (Maths)

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