Energy transport due to pressure diffusion enhanced by helicity and system rotation in inhomogeneous turbulence

TL;DR

This paper investigates how helicity and system rotation enhance energy transport in inhomogeneous turbulence, proposing a new pressure diffusion model proportional to turbulent helicity validated by DNS results.

Contribution

A novel pressure diffusion model based on turbulent helicity is introduced to better describe energy transport in rotating turbulence.

Findings

Most energy transport enhancement is due to pressure diffusion.

The new model qualitatively captures the enhanced flux due to rotation.

The helical Rossby number estimates the importance of helicity-related flux.

Abstract

It is known that turbulent energy is rapidly transferred in the direction of the rotation axis in a rotating system, in comparison with the non-rotating case. In this study, this phenomenon is investigated as a problem of energy diffusion expressed by the Reynolds averaged Navier-Stokes (RANS) model. The conventional gradient-diffusion approximation for the turbulent energy flux cannot account for the enhanced energy transport observed in rotating inhomogeneous turbulence. In order to adequately describe the phenomenon, we propose a new model for the energy flux due to the pressure associated with the rotational motion of a fluid. The model of the energy flux is expressed to be proportional to the turbulent helicity. This property is closely related to the group velocity of inertial waves in a rapidly rotating fluid. The validity of the model is assessed using a direct numerical simulation (DNS) of inhomogeneous turbulence under rotation. It is shown that most of the turbulent energy transport enhanced by the system rotation is attributed to the pressure diffusion term. The spatial distribution of the energy flux due to the pressure related to the system rotation is similar to that of the turbulent helicity with negative coefficient. Hence, the new model which is proportional to the turbulent helicity is able to qualitatively account for the enhanced energy flux due to the system rotation. Finally, the helical Rossby number is proposed in order to estimate the relative importance of the energy flux enhanced by the turbulent helicity and the rotation, in comparison to the conventional gradient-diffusion approximation.