Safety factor for time-dependent axisymmetric flows of barotropic gas and ideal incompressible fluid

Abstract

The safety factor q(r, z, t) is proved to be a material conservation law for the time-dependent axisymmetric barotropic compressible gas flows and ideal incompressible fluid flows with constant density ρ. Infinite families of conserved quantities connected with the safety factor are derived. The existence of maximal vortex rings and vortex blobs which are frozen into the axisymmetric inviscid gas and fluid flows is demonstrated. A stratification in the space of ideal gas and fluid flows is obtained: if two axisymmetric states of the barotropic gas or fluid with constant density ρ are dynamically connected, then their total numbers of vortex rings must be equal (the same for the total numbers of vortex blobs) and the infinitely many corresponding conserved quantities must coincide.