Multilayer shallow water equations with complete Coriolis force. Part 3. Hyperbolicity and stability under shear

DOI10.1017/jfm.2013.121zbMath1287.76067OpenAlexW1977263764MaRDI QIDQ5417355

Paul J. Dellar, Andrew L. Stewart

Publication date: 21 May 2014

Published in: Journal of Fluid Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/jfm.2013.121

zbMATH Keywords

internal waveswaves in rotating fluidsocean processes

Mathematics Subject Classification ID

Hydrology, hydrography, oceanography (86A05) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) General theory of rotating fluids (76U05) Rotation in hydrodynamic stability (76E07) Stability and instability of geophysical and astrophysical flows (76E20)

Related Items (9)

An energy and potential enstrophy conserving numerical scheme for the multi-layer shallow water equations with complete Coriolis force ⋮ Local Well-Posedness of the Two-Layer Shallow Water Model with Free Surface ⋮ Reduced differential transform method for the treatment of internal atmospheric waves phenomenon ⋮ Modeling medicine propagation in tissue: generalized statement ⋮ Unnamed Item ⋮ On the rigid-lid approximation for two shallow layers of immiscible fluids with small density contrast ⋮ The Kelvin-Helmholtz Instabilities in Two-Fluids Shallow Water Models ⋮ The multilayer shallow water system in the limit of small density contrast ⋮ Structure-Preserving Reduced- Order Modeling of Non-Traditional Shallow Water Equation

Cites Work

• Unnamed Item
• Short-wave instabilities and ill-posed initial value problems
• Analysis and computation with stratified fluid models
• Nonhydrostatic two-layer models of incompressible flow
• Necessary and insufficient conditions for well-posed Cauchy problems
• Multilayer shallow water equations with complete Coriolis force. Part 2. Linear plane waves
• Baroclinic stability under non-hydrostatic conditions
• Note on a paper of John W. Miles
• Stability Properties and Nonlinear Mappings of Two and Three-Layer Stratified Flows
• On the hydraulics of Boussinesq and non-Boussinesq two-layer flows
• Shallow water equations with a complete Coriolis force and topography
• Multilayer shallow water equations with complete Coriolis force. Part 1. Derivation on a non-traditional beta-plane
• The influence of the horizontal component of Earth's angular velocity on the instability of the Ekman layer
• Convective instability when the temperature gradient and rotation vector are oblique to gravity. I. Fluids without diffusion
• A derivation of equations for wave propagation in water of variable depth
• Stability of a potential vorticity front: from quasi-geostrophy to shallow water
• Inertial nonlinear equilibration of equatorial flows
• On the stability of superposed streams of Fluids of different densities
• Effect of variation in density on the stability of superposed streams of Fluid
• Cross-equatorial channel flow with zero potential vorticity under the complete Coriolis force
• Near-inertial waves in the ocean: beyond the ‘traditional approximation’
• Comments on "Explicit criterion for the positive definiteness of a general quartic form"
• Shear instability for stratified hydrostatic flows
• Symmetric hyperbolic linear differential equations
• On the stability of heterogeneous shear flows

This page was built for publication: Multilayer shallow water equations with complete Coriolis force. Part 3. Hyperbolicity and stability under shear