Vortex line representation for flows of ideal and viscous fluids

Abstract

It is shown that the Euler hydrodynamics for vortical flows of an ideal fluid coincides with the equations of motion of a charged {\it compressible} fluid moving due to a self-consistent electromagnetic field. Transition to the Lagrangian description in a new hydrodynamics is equivalent for the original Euler equations to the mixed Lagrangian-Eulerian description - the vortex line representation (VLR). Due to compressibility of a "new" fluid the collapse of vortex lines can happen as the result of breaking (or overturning) of vortex lines. It is found that the Navier-Stokes equation in the vortex line representation can be reduced to the equation of the diffusive type for the Cauchy invariant with the diffusion tensor given by the metric of the VLR.

References in corpus (2)

• Matrix Fluid Dynamics
• Numerical evidence of breaking of vortex lines in an ideal fluid

Cited by in corpus (6)

• Compressible dynamics of magnetic field lines for incompressible MHD flows
• Anisotropic characteristics of the Kraichnan direct cascade in two-dimensional hydrodynamic turbulence
• Statistical features of freely decaying two-dimensional hydrodynamic turbulence
• Compressible vortex structures and their role in the onset of hydrodynamic turbulence
• Notes about collapse in magnetohydrodynamics
• On the MHD load and the MHD metage