Split energy cascade in turbulent thin fluid layers

TL;DR

This paper investigates the split energy cascade in thin fluid layers, revealing simultaneous inverse and direct cascades through high-resolution simulations, and highlights the coupling between 2D and 3D turbulence phenomena.

Contribution

It demonstrates the coexistence of inverse and direct energy cascades in thin fluid layers and emphasizes the role of 3D coupling in sustaining these cascades.

Findings

Inverse energy cascade occurs at large scales.

Direct energy cascade occurs at small scales.

Coupling with 3D velocity field is essential for flux constancy.

Abstract

We discuss the phenomenology of the split energy cascade in a three-dimensional thin fluid layer by mean of high resolution numerical simulations of the Navier-Stokes equations. We observe the presence of both an inverse energy cascade at large scales, as predicted for two-dimensional turbu- lence, and of a direct energy cascade at small scales, as in three-dimensional turbulence. The inverse energy cascade is associated with a direct cascade of enstrophy in the intermediate range of scales. Notably, we find that the inverse cascade of energy in this system is not a pure 2D phenomenon, as the coupling with the 3D velocity field is necessary to guarantee the constancy of fluxes.