The 17/5 spectrum of the Kelvin-wave cascade

TL;DR

This paper uses direct numerical simulations to confirm the 17/5 Kelvin-wave cascade spectrum, demonstrating the unphysical nature of the previously proposed 11/3 spectrum through visual evidence.

Contribution

It provides the first direct numerical validation of the 17/5 Kelvin-wave cascade spectrum and refutes the earlier 11/3 spectrum based on symmetry considerations.

Findings

Confirmed the 17/5 spectrum via simulations

Visualized the unphysical 11/3 spectrum

Clarified the nature of Kelvin-wave cascades

Abstract

Direct numeric simulation of the Biot-Savart equation readily resolves the 17/5 spectrum of the Kelvin-wave cascade from the 11/3 spectrum of the non-local (in the wavenumber space) cascade scenario by L'vov and Nazarenko. This result is a clear-cut visualisation of the unphysical nature of the 11/3 solution, which was established earlier on the grounds of symmetry.