TY - JOUR

T1 - Stability of shear shallow water flows with free surface

AU - CHESNOKOV, A. A.

AU - El, G. A.

AU - Gavrilyuk, S. L.

AU - Pavlov, M. V.

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

KW - Free surface flows

KW - Hydrodynamic stability

KW - Hyperbolicity

KW - Shallow water waves

KW - Shear flows

UR - http://www.scopus.com/inward/record.url?scp=85021984633&partnerID=8YFLogxK

U2 - 10.1137/16M1098164

DO - 10.1137/16M1098164

M3 - Article

AN - SCOPUS:85021984633

VL - 77

SP - 1068

EP - 1087

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 3

ER -