# Emergence of Multi-Scaling in a Random Force-Stirred Fluid

## TL;DR

This paper investigates the transition to strong turbulence in a randomly forced fluid, revealing multi-scaling phenomena and intermittent events, with theoretical predictions validated by numerical simulations.

## Contribution

It introduces a theory describing multi-scaling and anomalous exponents in turbulence transition, linking rare events to multiple effective Reynolds numbers.

## Key findings

- Transition to strong turbulence occurs at R_λ > 3.
- Multi-scaling explains intermittent rare events.
- Theory aligns quantitatively with numerical simulations.

## Abstract

We consider transition to strong turbulence in an infinite fluid stirred by a gaussian random force. The transition is {\bf defined} as a first appearance of anomalous scaling of normalized moments of velocity derivatives (dissipation rates) emerging from the low-Reynolds-number Gaussian background. It is shown that due to multi-scaling, strongly intermittent rare events can be quantitatively described in terms of an infinite number of different "Reynolds numbers" reflecting multitude of anomalous scaling exponents. The theoretically predicted transition disappears at $R_{\lambda}\leq 3$. The developed theory, is in a quantitative agreement with the outcome of large-scale numerical simulations.