Stability of shear shallow water flows with free surface
journal contributionposted on 2017-03-06, 13:47 authored by A.A. Chesnokov, Gennady El, S.L. Gavrilyuk, Maxim V. Pavlov
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.
- Mathematical Sciences
Published inSIAM Journal on Applied Mathematics
CitationCHESNOKOV, A.A. ...et al., 2017. Stability of shear shallow water flows with free surface. SIAM Journal on Applied Mathematics, 77(3), pp.1068-1087.
Publisher© Society for Industrial and Applied Mathematics
- NA (Not Applicable or Unknown)
Publisher statementThis work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/
NotesThis 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