A dissipative random velocity field for fully developed fluid turbulence

TL;DR

This paper introduces a stochastic model for fully developed turbulent flow that captures key statistical features, including intermittency and energy transfer, with a single adjustable parameter validated through simulations and analytical methods.

Contribution

The paper presents a novel stochastic velocity field model incorporating vorticity stretching and long-range correlations, validated against experimental turbulence data.

Findings

Model reproduces velocity gradient tensor geometry

Captures power-law structure functions with intermittency

Analytically derives structure function exponents spectrum

Abstract

We investigate the statistical properties, based on numerical simulations and analytical calculations, of a recently proposed stochastic model for the velocity field of an incompressible, homogeneous, isotropic and fully developed turbulent flow. A key step in the construction of this model is the introduction of some aspects of the vorticity stretching mechanism that governs the dynamics of fluid particles along their trajectory. An additional further phenomenological step aimed at including the long range correlated nature of turbulence makes this model depending on a single free parameter $\gamma$ that can be estimated from experimental measurements. We confirm the realism of the model regarding the geometry of the velocity gradient tensor, the power-law behaviour of the moments of velocity increments (i.e. the structure functions), including the intermittent corrections, and the existence of energy transfers across scales. We quantify the dependence of these basic properties of turbulent flows on the free parameter $\gamma$ and derive analytically the spectrum of exponents of the structure functions in a simplified non dissipative case. A perturbative expansion in power of $\gamma$ shows that energy transfers, at leading order, indeed take place, justifying the dissipative nature of this random field.