Pattern formation of quantum Kelvin-Helmholtz instability in binary superfluids

TL;DR

This paper investigates the nonlinear pattern formation in quantum superfluids caused by shear-flow instability, revealing how the Weber number governs different dynamical regimes and pattern types in binary Bose-Einstein condensates.

Contribution

It introduces a quantum extension of the Weber number to characterize shear-flow instabilities and demonstrates the resulting pattern formation and crossover behaviors in binary superfluids.

Findings

For We  1, flutter-finger patterns and vortex generation occur.

For We  1, zipper and sealskin patterns emerge depending on segregation and velocity.

The Weber number determines the transition between vortex formation and pattern types.

Abstract

We study theoretically nonlinear dynamics induced by shear-flow instability in segregated two-component Bose-Einstein condensates in terms of the Weber number, defined by extending the past theory on the Kelvin-Helmholtz instability in classical fluids. Numerical simulations of the Gross-Pitaevskii equations demonstrate that dynamics of pattern formation is well characterized by the Weber number $We$, clarifying the microscopic aspects unique to the quantum fluid system. For $We \lesssim 1$, the Kelvin-Helmholtz instability induces flutter-finger patterns of the interface and quantized vortices are generated at the tip of the fingers. The associated nonlinear dynamics exhibits a universal behavior with respect to $We$. When $We \gtrsim 1$ in which the interface thickness is larger than the wavelength of the interface mode, the nonlinear dynamics is effectively initiated by the counter-superflow instability. In a strongly segregated regime and a large relative velocity, the instability causes transient zipper pattern formation instead of generating vortices due to the lack of enough circulation to form a quantized vortex per a finger. While, in a weakly segregating regime and a small relative velocity, the instability leads to sealskin pattern in the overlapping region, in which the frictional relaxation of the superflow cannot be explained only by the homogeneous counter-superflow instability. We discuss the details of the linear and nonlinear characteristics of this dynamical crossover from small to large Weber numbers, where microscopic properties of the interface become important for the large Weber number.