Langevin based turbulence model and its relationship with Kappa distributions

Iván Gallo-Méndez,Pablo S Moya

doi:10.1038/s41598-022-05996-0

Abstract

Kappa distributions (or kappa -like distributions) represent a robust framework to characterize and understand complex phenomena with high degrees of freedom, as turbulent systems, using non-extensive statistical mechanics. Here we consider a coupled map lattice Langevin based model to analyze the relation of a turbulent flow, with its spatial scale dynamic, and kappa -like distributions. We generate the steady-state velocity distribution of the fluid at each scale, and show that the generated distributions are well fitted by kappa -like distributions. We observe a robust relation between the kappa parameter, the scale, and the Reynolds number of the system, Re. In particular, our results show that there is a closed scaling relation between the level of turbulence and the kappa parameter; namely kappa sim text {Re},k^{-5/3}. We expect these results to be useful to characterize turbulence in different contexts, and our numerical predictions to be tested by observations and experimental setups.

Highlights

Kappa distributions represent a robust framework to characterize and understand complex phenomena with high degrees of freedom, as turbulent systems, using nonextensive statistical mechanics
The results clearly show the appearance of non-thermal heavy tails in the Velocity Distribution Function (VDF) at different scales, or, in other words, when calculating the distribution function of velocity fluctuations it can be seen that it contain high-energy tails that decay as a power law, for values greater than one standard deviation around the mean, and moving away from the Maxwellian equilibrium
In this paper we present a numerical study of the VDF generated in turbulent flows at different spatial scales, and different levels of turbulence

Summary

Introduction

Kappa distributions (or κ-like distributions) represent a robust framework to characterize and understand complex phenomena with high degrees of freedom, as turbulent systems, using nonextensive statistical mechanics. Considering a CML model similar to the proposed by Beck 25 with a white noise type forcing, we analyze the relation of a turbulent energy cascade on the spatial scale and the formation of κ-like distributions.

Results

Conclusion