Kelvin-wave turbulence generated by vortex reconnections

TL;DR

This paper investigates Kelvin wave turbulence generated by vortex reconnections, revealing that broad-spectrum forcing primarily results in a direct cascade with a specific spectral exponent, using a differential model approach.

Contribution

It introduces a differential model to analyze Kelvin wave turbulence with broad-spectrum forcing, showing the dominance of the direct cascade scaling.

Findings

Reconnection forcing acts like low-frequency forcing.

Direct cascade scaling (-17/5) dominates over inverse.

Broad spectrum forcing does not alter the main cascade behavior.

Abstract

Reconnections of quantum vortex filaments create sharp bends which degenerate into propagating Kelvin waves. These waves cascade their energy down-scale and their waveaction up-scale via weakly nonlinear interactions, and this is the main mechanism of turbulence at the scales less than the inter-vortex distance. In case of an idealised forcing concentrated around a single scale k0, the turbulence spectrum exponent has a pure direct cascade form -17/5 at scales k>k0 and a pure inverse cascade form -3 at k<k0. However, forcing produced by the reconnections contains a broad range of Fourier modes. What scaling should one expect in this case? In this Letter I obtain an answer to this question using the differential model for the Kelvin wave turbulence. The main result is that the direct cascade scaling dominates, i.e. the reconnection forcing is more or less equivalent to a low-frequency forcing.