Scale Separation Scheme for Simulating Superfluid Turbulence: Kelvin-Wave Cascade

TL;DR

This paper introduces an efficient numerical scheme to simulate Kelvin wave cascades on vortex lines, clarifying the cascade spectrum exponent and resolving previous theoretical and simulation discrepancies in superfluid turbulence.

Contribution

The paper presents a novel numerical scheme for simulating Kelvin wave cascades, enabling precise determination of the cascade spectrum exponent and addressing prior conflicting results.

Findings

Successfully resolves the cascade spectrum exponent

Unambiguously distinguishes between competing theories

Potentially applicable to full superfluid turbulence simulations

Abstract

A Kolmogorov-type cascade of Kelvin waves--the distortion waves on vortex lines--plays a key part in the relaxation of superfluid turbulence at low temperatures. We propose an efficient numeric scheme for simulating the Kelvin wave cascade on a single vortex line. The idea is likely to be generalizable for a full-scale simulation of different regimes of superfluid turbulence. With the new scheme, we are able to unambiguously resolve the cascade spectrum exponent, and thus to settle the controversy between recent simulations [1] and recently developed analytic theory [2]. [1] W.F. Vinen, M. Tsubota and A. Mitani, Phys. Rev. Lett. 91, 135301 (2003). [2] E.V. Kozik and B.V. Svistunov, Phys. Rev. Lett. 92, 035301 (2004).