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  • Open Access

Dynamic similarity of vortex shedding in a superfluid flowing past a penetrable obstacle

Junhwan Kwon1,2 and Yong-il Shin1,2,3,*

  • *Contact author: yishin@snu.ac.kr
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Phys. Rev. Research 8, 023246 – Published 5 June, 2026

DOI: https://doi.org/10.1103/wlft-tc8w

Abstract

We numerically investigate wake dynamics in a superfluid flowing past a penetrable obstacle. The penetrable obstacle does not fully deplete the density, and we define an effective diameter Deff from the Mach-1 contour of the time-averaged irrotational flow around the obstacle, which delineates the local supersonic region where quantized vortices nucleate. Using this flow-defined length, we construct a superfluid Reynolds number Res≡(v0−vc)Deff/(ℏ/m), with v0 being the flow speed, vc the critical velocity, and m the particle mass, and show that Res organizes the wake dynamics across obstacle sizes and strengths: the transition from dipole-row emission to alternating vortex cluster shedding occurs for Res≈2 and the Strouhal number and drag coefficient collapse onto universal curves versus Res. These results extend the notion of dynamic similarity in superfluid flows to penetrable obstacles and show that the dynamically relevant length scale is determined by the supersonic region rather than by the geometric obstacle size.

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Phys. Rev. Research 8, 023246– Published 5 June, 2026
  • Received 30 January 2026
  • Accepted 6 May 2026
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