Turbulence damping as a measure of the flow dimensionality

TL;DR

This paper investigates how turbulence damping relates to flow dimensionality in fluid layers, demonstrating that eddy viscosity influences damping and that the anomaly coefficient measures the transition between 2D and 3D turbulence behaviors.

Contribution

It introduces the anomaly coefficient as a novel measure of flow dimensionality and links it to turbulence suppression and self-organization in fluid layers.

Findings

High anomaly coefficient suppresses inverse energy cascade.

Eddy viscosity increases bottom damping in three-dimensional flows.

Flow can self-organize into coherent structures when turbulence is effectively two-dimensional.

Abstract

The dimensionality of turbulence in fluid layers determines their properties. We study electromagnetically driven flows in finite depth fluid layers and show that eddy viscosity, which appears as a result of three-dimensional motions, leads to increased bottom damping. The anomaly coefficient, which characterizes the deviation of damping from the one derived using a quasi-two-dimensional model, can be used as a measure of the flow dimensionality. Experiments in turbulent layers show that when the anomaly coefficient becomes high, the turbulent inverse energy cascade is suppressed. In the opposite limit turbulence can self-organize into a coherent flow.