Kolmogorov spectrum of superfluid turbulence: numerical analysis of the Gross-Pitaevskii equation with the small scale dissipation

TL;DR

This paper numerically investigates the energy spectrum of superfluid turbulence using the Gross-Pitaevskii equation with a small-scale dissipation term, finding results consistent with the Kolmogorov law.

Contribution

It introduces a scale-specific dissipation in the Gross-Pitaevskii model to better understand the energy cascade in superfluid turbulence.

Findings

Energy spectrum aligns with Kolmogorov law

Small-scale dissipation effectively removes short wavelength excitations

Supports cascade process of quantized vortices in inertial range

Abstract

The energy spectrum of superfluid turbulence is studied numerically by solving the Gross-Pitaevskii equation. We introduce the dissipation term which works only in the scale smaller than the healing length, to remove short wavelength excitations which may hinder the cascade process of quantized vortices in the inertial range. The obtained energy spectrum is consistent with the Kolmogorov law.