Proper Orthogonal Decomposition of a Superfluid Turbulent Wake

Superfluid turbulent wakes behind a square prism are studied theoretically and numerically by proper orthogonal decomposition (POD). POD is a data science approach that can efficiently extract the principal vibration modes of a physical system, and is widely used in hydrodynamics, including applications in wake structure analysis. It is not straightforward to apply the conventional POD method to superfluid wake systems, as the superfluid velocity field diverges at the center of a vortex whose circulation is quantized. We successfully established a POD method by applying appropriate blurring to the vorticity distribution in a two-dimensional superfluid wake. It is shown that a coherent structure corresponding to two parallel arrays of alternating quantum vortex bundles, called the "quasi-classical" K\'arm\'an vortex street, is latent as a distinctive major mode in the superfluid turbulent wakes that were naively thought to be "irregular". Since our method is also effective for fluid density, it can be applied to the experimental data analysis for ultra-cold atomic gases.