Stability Of Shear Shallow Water Flows with Free Surface

DOI10.1137/16M1098164zbMath1365.76058arXiv1610.04331MaRDI QIDQ5272525

Maxim P. Pavlov, Gennady A. El, Alexander Chesnokov, Sergey L. Gavrilyuk

Publication date: 30 June 2017

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.04331

zbMATH Keywords

hydrodynamic stabilityshear flowshyperbolicityshallow water wavesfree surface flows

Mathematics Subject Classification ID

Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) First-order nonlinear hyperbolic equations (35L60) Parallel shear flows in hydrodynamic stability (76E05)

Related Items (6)

Integrable systems of the intermediate long wave type in \(2 + 1\) dimensions ⋮ Simple two-layer dispersive models in the Hamiltonian reduction formalism ⋮ Hamiltonian aspects of three-layer stratified fluids ⋮ Wavefronts and modal structure of long surface and internal ring waves on a parallel shear current ⋮ Formation and evolution of roll waves in a shallow free surface flow of a power-law fluid down an inclined plane ⋮ Hyperbolic model for free surface shallow water flows with effects of dispersion, vorticity and topography

Cites Work

• Stability criterion of shear fluid flow and the hyperbolicity of the long-wave equations
• Equations of long waves with a free surface. II: Hamiltonian structure and higher equations
• Reductions of kinetic equations to finite component systems
• Symmetry constraints for dispersionless integrable equations and systems of hydrodynamic type
• Is Landau Damping Possible in a Shear Fluid Flow?
• Introduction to Hydrodynamic Stability
• Stability Properties and Nonlinear Mappings of Two and Three-Layer Stratified Flows
• Linear Stability of Parallel Inviscid Flows of Shallow Water and Bubbly Fluid
• Long Eddies in Sheared Flows
• ANALYTICAL AND NUMERICAL SOLUTIONS OF THE SHALLOW WATER EQUATIONS FOR 2D ROTATIONAL FLOWS
• Shear instability for stratified hydrostatic flows
• Simple waves on shear flows: similarity solutions
• Some Properties of Long Nonlinear Waves
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