Transient inverse energy cascade in free surface turbulence

TL;DR

This study investigates free-surface turbulence at high Reynolds numbers, revealing a transient inverse energy cascade influenced by layer thickness and boundary conditions, with implications for two-dimensional turbulence behavior.

Contribution

It demonstrates the existence of a transient inverse cascade in free-surface turbulence and highlights the impact of boundary conditions and layer thickness on turbulence dynamics.

Findings

Transient inverse cascade duration depends on layer thickness

Boundary conditions significantly influence turbulence behavior

Decaying turbulence does not follow an exponential decay law

Abstract

We study the statistics of free-surface turbulence at large Reynolds numbers produced by direct numerical simulations in a fluid layer at different thickness with fixed characteristic forcing scale. We observe the production of a transient inverse cascade, with a duration which depends on the thickness of the layer, followed by a transition to three-dimensional turbulence initially produced close to the bottom, no-slip boundary. By switching off the forcing, we study the decaying turbulent regime and we find that it cannot be described by an exponential law. Our results show that boundary conditions play a fundamental role in the nature of turbulence produced in thin layers and give limits on the conditions to produce a two-dimensional phenomenology.