# Emergence of skewed non-Gaussian distributions of velocity increments in isotropic turbulence

## TL;DR

This paper introduces an exactly solvable stochastic model that explains the emergence of skewed, heavy-tailed velocity increment distributions in isotropic turbulence, aligning well with numerical data across scales and Reynolds numbers.

## Contribution

The authors develop a novel multiscale stochastic model that captures the skewness and heavy tails of velocity increments in turbulence, extending understanding of non-Gaussian behaviors.

## Key findings

- Model accurately fits numerical turbulence data across scales.
- Single scale limit fails to reproduce background density.
- Multiscale mechanism is crucial for distribution shape.

## Abstract

Skewness and non-Gaussian behavior are essential features of the distribution of short-scale velocity increments in isotropic turbulent flows. Yet, although the skewness has been generally linked to time-reversal symmetry breaking and vortex stretching, the form of the asymmetric heavy tails remain elusive. Here we describe the emergence of both properties through an exactly solvable stochastic model with a scale hierarchy of energy transfer rates. From a statistical superposition of a local equilibrium distribution weighted by a background density, the increments distribution is given by a novel class of skewed heavy-tailed distributions, written as a generalization of the Meijer $G$-functions. Excellent agreement in the multiscale scenario is found with numerical data of systems with different sizes and Reynolds numbers. Remarkably, the single scale limit provides poor fits to the background density, highlighting the central role of the multiscale mechanism. Our framework can be also applied to describe the challenging emergence of skewed distributions in complex systems.