Langevin based turbulence model and its relationship with Kappa distributions

Abstract

Abstract Kappa distributions (or $$\kappa $$ κ -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 $$\kappa $$ κ -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 $$\kappa $$ κ -like distributions. We observe a robust relation between the $$\kappa $$ κ 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 $$\kappa $$ κ parameter; namely $$\kappa \sim \text {Re}\,k^{-5/3}$$ κ ∼ 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.