Bridging Inertial and Dissipation Range Statistics in Rotating Turbulence

TL;DR

This paper explores the link between inertial and dissipation range statistics in rotating turbulence using simulations and multifractal analysis, revealing explicit relations and validating them across models and direct numerical simulations.

Contribution

It introduces an explicit relation between inertial range scaling exponents and dissipation rate multifractal dimensions in rotating turbulence, validated through multiple simulation approaches.

Findings

Explicit relation between inertial and dissipation range statistics.

Good agreement between shell model and Navier-Stokes simulations.

Decreased intermittency with increased rotation strength.

Abstract

We investigate the connection between the inertial range and the dissipation range statistics of rotating turbulence through detailed simulations of a helical shell model and a multifractal analysis. In particular, by using the latter, we find an explicit relation between the (anomalous) scaling exponents of equal-time structure functions in the inertial range in terms of the generalised dimensions associated with the energy dissipation rate. This theoretical prediction is validated by detailed simulations of a helical shell model for various strengths of rotation from where the statistics of dissipation rate, and thus the generalised dimensions, as well as the inertial range, in particular the anomalous scaling exponents, are extracted. Our work also underlines a surprisingly good agreement---such as in the spatial structure of the energy dissipation rates and the decrease in inertial range intermittency with increasing strengths of rotation---between solutions of the Navier--Stokes equation in a rotating frame with those obtained from low-dimensional, dynamical systems such as the shell model which are not explicitly anisotropic. Finally, we perform direct numerical simulations of the Navier--Stokes equation, with the Coriolis force incorporated, to confirm the robustness of the conclusions drawn from our multifractal and shell model studies.