Elliptical vortices and integrable Hamiltonian dynamics of the rotating shallow-water equations

DOI10.1017/S0022112091000162zbMath0850.76791MaRDI QIDQ4713671

Darryl D. Holm

Publication date: 25 June 1992

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

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) General theory of rotating fluids (76U05) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)

Related Items (10)

Elliptical flows perturbed by shear waves ⋮ On \(q\)-Gaussian integrable Hamiltonian reductions in anisentropic magneto-gasdynamics ⋮ The elliptical vortices, integrable Ermakov structure, Schrödinger connection, and Lax pair in the compressible Navier–Stokes equation ⋮ Ermakov–Ray–Reid Reductions of Variational Approximations in Nonlinear Optics ⋮ Universal and Integrable Aspects of an Elliptic Vortex Representation in 2+1‐Dimensional Magneto‐Gasdynamics ⋮ On the spectrum of hyperbolic flows ⋮ Ermakov-Ray-Reid Systems in (2+1)-Dimensional Rotating Shallow Water Theory ⋮ Integrable Substructure in a Korteweg Capillarity Model. A Karman-Tsien Type Constitutive Relation ⋮ Hybrid Ermakov-Painlevé IV Systems ⋮ The pulsrodon in 2+1-dimensional magneto-gasdynamics: Hamiltonian structure and integrability

Cites Work

• Magnetic tornadoes: Three-dimensional affine motions in ideal magnetohydrodynamics
• Gyroscopic analog for collective motion of a stratified fluid
• Elliptical vortices in shallow water
• On the stability of elliptical vortex solutions of the shallow-water equations
• Lyapunov stability of ideal stratified fluid equilibria in hydrostatic balance
• Some exact solutions to the nonlinear shallow-water wave equations
• The effect of rotation on the simpler modes of motion of a liquid in an elliptic paraboloid
• Some general theorems concerning the finite motion of a shallow rotating liquid lying on a paraboloid

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