Quasi-conservation laws for compressible 3D Navier-Stokes flow

Abstract

We formulate the quasi-Lagrangian fluid transport dynamics of mass density $\rho$ and the projection $q=\bom\cdot\nablaρ$ of the vorticity $\bom$ onto the density gradient, as determined by the 3D compressible Navier-Stokes equations for an ideal gas, although the results apply for an arbitrary equation of state. It turns out that the quasi-Lagrangian transport of $q$ cannot cross a level set of $\rho$. That is, in this formulation, level sets of $\rho$ (isopychnals) are impermeable to the transport of the projection $q$.

2 page note, to appear in Phys Rev E

Cited by in corpus (2)

• On the removal of the barotropic condition in helicity studies of the compressible Euler and ideal compressible MHD equations
• Stretching and folding processes in the 3D Euler and Navier-Stokes equations