Slow inviscid flows of a compressible fluid in spatially inhomogeneous systems

Abstract

An ideal compressible fluid is considered, with an equilibrium density being a given function of coordinates due to presence of some static external forces. The slow flows in such system, which do not disturb the density, are investigated with the help of the Hamiltonian formalism. The equations of motion of the system are derived for an arbitrary given topology of the vorticity field. The general form of the Lagrangian for frozen-in vortex lines is established. The local induction approximation for motion of slender vortex filaments in several inhomogeneous physical models is studied.

7 pages, revtex, no figures. The published version

References in corpus (4)

• Theory of Bose-Einstein condensation in trapped gases
• Finite time singularities in a class of hydrodynamic models
• Slow flows of an relativistic perfect fluid in a static gravitational field
• Interaction of a vortex ring with the free surface of ideal fluid

Cited by in corpus (22)

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• Spectral and dynamical analysis of a single vortex ring in anisotropic harmonically trapped three-dimensional Bose-Einstein condensates
• Quasi-stable quantum vortex knots and links in anisotropic harmonically trapped Bose-Einstein condensates
• Three-dimensional numerical simulation of long-lived quantum vortex knots and links in a trapped Bose-Einstein condensate
• Bubbles with attached quantum vortices in trapped binary Bose-Einstein condensates
• The dynamics of straight vortex filaments in a Bose-Einstein condensate with a Gaussian density profile
• Finite time singularities in a class of hydrodynamic models
• Parametric instability of oscillations of a vortex ring in a $z$-periodic Bose-Einstein condensate and the recurrence to starting state
• Current-sheet formation in incompressible electron magnetohydrodynamics
• Toroidal bubbles with circulation in ideal hydrodynamics. A variational approach
• Dynamics of quantum vortices in a quasi-two-dimensional Bose-Einstein condensate with two "holes"
• Hamilton's equations of motion of a vortex filament in the rotating Bose-Einstein condensate and their "soliton" solutions
• Discrete vortices on spatially nonuniform two-dimensional electric networks
• Stable and unstable vortex knots in a trapped Bose-Einstein condensate
• Variational principle for frozen-in vortex structures interacting with sound waves
• Some exact solutions of the local induction equation for motion of a vortex in a Bose-Einstein condensate with Gaussian density profile
• Vortex knots on three-dimensional lattices of nonlinear oscillators coupled by space-varying links
• The hodograph method applicability in the problem of long-scale nonlinear dynamics of a thin vortex filament near a flat boundary
• Ideal hydrodynamics inside as well as outside non-rotating black hole: Hamiltonian description in the Painlev{é}-Gullstrand coordinates
• Discrete Vortices in Systems of Coupled Nonlinear Oscillators: Numerical Results for an Electric Model
• Discrete Vortex Filaments on Arrays of Coupled Oscillators in the Nonlinear Resonant Mode
• Internal waves in a compressible two-layer atmospheric model: The Hamiltonian description