Turbulent Diffusion-Cascade Interaction

TL;DR

This paper investigates how turbulent diffusion interacts with the turbulence cascade in non-homogeneous plane wakes, revealing that diffusion counteracts the cascade across scales and relates to dissipation rates.

Contribution

It demonstrates the continuous counteracting role of turbulent diffusion on the cascade in non-homogeneous wakes and quantifies the relationship between transfer rates and dissipation.

Findings

Turbulent diffusion opposes the cascade down to small scales.

The sum of transfer rates correlates with the turbulence dissipation rate.

The proportionality constant varies with wake location.

Abstract

In the decay region around the centreline of three qualitatively different turbulent plane wakes, the turbulence is non-homogeneous and two-point turbulent diffusion counteracts the turbulence cascade all the way down to scales smaller than the Taylor length. It is found that the sum of the inter-space transfer rate and the horizontal part of the inter-scale transfer rate of horizontal two-point turbulent kinetic energy is approximately proportional to the turbulence dissipation rate in the inertial range with a constant of proportionality between $-0.6$ and $-1$ depending on wake and location within the wake, except at the near-field edge of the decay region.