Compressibility effects on quasistationary vortex and transient hole patterns through vortex merger

TL;DR

This paper investigates how compressibility influences vortex merging, revealing that it introduces a natural acoustic scale, affects oscillation frequencies, and accelerates the melting of vortex crystals.

Contribution

It demonstrates the impact of compressibility on vortex merger dynamics, including frequency scaling and vortex crystal stability, extending previous incompressible flow studies.

Findings

Oscillation frequency scales with Mach number as M^{-2}

Vortex crystals melt faster with increased compressibility

Natural acoustic mode is independent of vortex number

Abstract

The effect of compressibility in hydrodynamic vortex merging has been discussed. In the past, in incompressible limit it has been observed that the merging of a collection of intense point-like vortices arranged uniformly outside a circular vortex, can lead to quasistationary vortex patch and transient hole pattern inside the patch via nonlinear merger process. These patterns are akin to \textquoteleft vortex crystals\textquoteright. Compressibility can introduce a natural acoustic scale to the problem. We find that the natural mode is independent of the number of point-like vortices and the amplitude scales linearly with compressibility. Further it has been identified that after merging, the system exhibits oscillation at a natural frequency together with its harmonics and beats with its own harmonics. The power of the frequency is found to scale as $M^{-2}$, where $M$ is the Mach number. Also the vortex crystals formed out of the merging process are found to melt faster as compressibility is increased.