Condensate in quasi two-dimensional turbulence

TL;DR

This paper uses direct numerical simulations to study how large-scale structures form in thin-layer turbulence, revealing a tight link between 3D turbulence acting as an effective viscosity and the arrest of condensate growth.

Contribution

It demonstrates that small-scale 3D turbulence in thin layers dissipates large-scale energy, providing a viscosity-independent mechanism for condensate saturation.

Findings

Large-scale structures form via inverse cascade in thin-layer turbulence.

Small-scale 3D turbulence acts as an effective viscosity.

The saturation energy of the condensate is quantitatively predicted.

Abstract

We investigate the process of formation of large-scale structures in a turbulent flow confined in a thin layer. By means of direct numerical simulations of the Navier-Stokes equations, forced at an intermediate scale, we obtain a split of the energy cascade in which one fraction of the input goes to small scales generating the three-dimensional direct cascade. The remaining energy flows to large scales producing the inverse cascade which eventually causes the formation of a quasi two-dimensional condensed state at the largest horizontal scale. Our results shows that the connection between the two actors of the split energy cascade in thin layers is tighter than what was established before: the small scale three-dimensional turbulence acts as an effective viscosity and dissipates the large-scale energy thus providing a viscosity-independent mechanism for arresting the growth of the condensate. This scenario is supported by quantitative predictions of the saturation energy in the condensate.