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

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.