Dynamical model of steadily forced isotropic turbulence

TL;DR

This paper introduces a dynamical model for steady isotropic turbulence that captures the inertial range dynamics, reproduces the Kolmogorov spectrum, and predicts intermittency effects and transient behavior.

Contribution

The model provides a viscosity-independent description of small-scale turbulence and explains the transient power-law evolution and crossover scaling with system size.

Findings

Reproduces Kolmogorov spectrum in stationary turbulence

Predicts intermittency corrections for higher moments

Identifies crossover time scaling as L^{11/3}

Abstract

A dynamical model is proposed for isotropic turbulence driven by steady forcing that yields a viscosity independent dynamics for the small-scale (inertial) regime. This reproduces the Kolmogorov spectrum for the two-point velocity correlation function in the fully developed (stationary) stage, while predicting intermittency corrections for higher order moments. The model also yields a transient stage with a power-law time evolution. The crossover time to fully developed turbulence scales with the turbulent system size as $\sim L^{11/3}$. The physical origin of the transient behavior is explained.