Kolmogorov scaling from random force fields

TL;DR

This paper demonstrates that classical turbulence scaling laws can be explained by a scale-independent Gaussian force field, supported by shell model simulations indicating consistent force fluctuations across scales.

Contribution

It introduces the idea that turbulence scaling laws are compatible with a Gaussian force field, linking force fluctuations to turbulence statistics.

Findings

Force fluctuations are scale independent in the inertial regime.

Lagrangian velocity statistics are influenced by typical force fields.

Multiscaling relates to extreme force field events.

Abstract

We show that the classical Kolmogorov and Richardson scaling laws in fully developed turbulence are consistent with a random Gaussian force field. Numerical simulations of a shell model approximation to the Navier-Stokes equations suggest that the fluctuations in the force (acceleration) field are scale independent throughout the inertial regime. We conjecture that Lagrangian statistics of the relative velocity in a turbulent flow is determined by the typical force field, whereas the multiscaling is associated to extreme events in the force field fluctuations.