Dynamics of compressible vortex filaments

We present an extension of the asymptotic theory of slender vortex filaments in incompressible flows (reviewed in ICNM-III 1998) to that in compressible flows. We derive the equations of motion of a filament and the equations for the evolution of the core structure, having an addition equation for the density variation in the core. Also we derive the consistency conditions on the initial data of the core structure as required by the asymptotic theory. We highlight how the equations and conditions for the compressible flows differ from those for the incompressible flows.