%0 Journal Article
%T Quasi-conservation laws for compressible 3D Navier-Stokes flow
%A J. D. Gibbon
%A D. D. Holm
%J Physics
%D 2012
%I arXiv
%R 10.1103/PhysRevE.86.047301
%X We formulate the quasi-Lagrangian fluid transport dynamics of mass density $\rho$ and the projection $q=\bom\cdot\nabla\rho$ 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 $q$.
%U http://arxiv.org/abs/1206.3414v2