Elongation of vortex street in soap films

In flowing soap films, it is known that the vorticity field is correlated to the thickness field and that the thickness variation propagates at the Marangoni elastic wave speed. In this circumstance, we modify the point vortex model in the regime where the system's characteristic speed U is comparable to the velocity field propagation speed c in the medium. We show that the the stability condition of von Kármán vortex streets, h/l=0.28, where h and l are the transverse and longitudinal spacing between vortices, scales with 1/(1 + U/c). This result suggests that the vortex streets may look elongated when U/c≈1.