# Non-universal velocity probability densities in two-dimensional turbulence: the effect of large-scale dissipation

## TL;DR

This study investigates how different large-scale dissipation mechanisms in forced two-dimensional turbulence influence the statistical properties of velocity and vorticity, revealing that the type of dissipation significantly affects the Gaussianity of velocity statistics.

## Contribution

It demonstrates that the form of large-scale dissipation critically impacts the statistical behavior of turbulence, especially the Gaussianity of velocity distributions, which was previously less understood.

## Key findings

- Velocity statistics are near-Gaussian with linear and quadratic drag.
- Velocity statistics become non-Gaussian with hypo-drag due to vortex properties.
- Vortex arrangements and extremum distributions influence velocity statistics.

## Abstract

We show that some statistical properties of forced two-dimensional turbulence have an important sensitivity to the form of large-scale dissipation which is required to damp the inverse cascade. We consider three models of large-scale dissipation: linear "Ekman" drag, non-linear quadratic drag, and scale selective hypo-drag that damps only low-wavenumber modes. In all cases, the statistically steady vorticity field is dominated by almost axisymmetric vortices, and the probability density function of vorticity is non-Gaussian. However, in the case of linear and quadratic drag, we find that the velocity statistics is close to Gaussian, with non-negligible contribution coming from the background turbulent flow. On the other hand, with hypo-drag, the probability density function of velocity is non-Gaussian and is predominantly determined by the properties of the vortices. With hypo-drag, the relative positions of the vortices and the exponential distribution of the vortex extremum are important factors responsible for the non-Gaussian velocity statistics.