Condensates in thin-layer turbulence

TL;DR

This study uses direct numerical simulations to explore how thin-layer turbulence transitions from inverse cascade and condensate formation to two-dimensional flow as layer thickness decreases, revealing critical thresholds and complex behaviors.

Contribution

It introduces a mean field three-scale model that explains the transition to two-dimensionality and condensate formation in thin-layer turbulence.

Findings

Inverse cascade occurs below a critical layer thickness.

Flow becomes exactly two-dimensional below a second critical height.

Bi-stability and intermittent bursts are observed near critical points.

Abstract

We examine the steady state of turbulent flows in thin layers using direct numerical simulations. It is shown that when the layer thickness is smaller than a critical height, an inverse cascade arises which leads to the formation of a steady state condensate where most of the energy is concentrated in the largest scale of the system. For layers of thickness smaller than a second critical height, the flow at steady state becomes exactly two-dimensional. The amplitude of the condensate is studied as a function of layer thickness and Reynolds number. Bi-stability and intermittent bursts are found close to the two critical points. The results are interpreted based on a mean field three-scale model that reproduces some of the basic features of the numerical results.