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The effect of compressibility in hydrodynamic vortex merging has beendiscussed. In the past, in incompressible limit it has been observed that themerging of a collection of intense point-like vortices arranged uniformlyoutside a circular vortex, can lead to quasistationary vortex patch andtransient hole pattern inside the patch via nonlinear merger process. Thesepatterns are akin to \textquoteleft vortex crystals\textquoteright.Compressibility can introduce a natural acoustic scale to the problem. We findthat the natural mode is independent of the number of point-like vortices andthe amplitude scales linearly with compressibility. Further it has beenidentified that after merging, the system exhibits oscillation at a naturalfrequency together with its harmonics and beats with its own harmonics. Thepower of the frequency is found to scale as $M^{-2}$, where $M$ is the Machnumber. Also the vortex crystals formed out of the merging process are found tomelt faster as compressibility is increased.

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