Towards a full-scale version of Yakhot's model of strong turbulence

TL;DR

This paper extends Yakhot's turbulence model to small scales, deriving full-scale, parameter-free structure function models that align well with experimental data across all scales.

Contribution

It introduces a small-scale extension of Yakhot's model incorporating a new crossover length scale, enabling full-scale structure function modeling without free parameters.

Findings

Models replicate small scale limits and inertial-dissipation transition.

Derived closed-form, parameter-free structure functions for second and third order.

Good agreement with experimental data from dissipative to large scales.

Abstract

We present first elements of an extension of Yakhot's model of strong turbulence towards small scales. The analysis is based on an empirically observed relation for even order structure functions which extends from the inertial into the dissipation range. With this relation and Kolmogorov's four-fifth law, models for structure functions of orders two and three can be derived that replicate expected small scale limits and describe the transition from dissipative to inertial range scaling regimes correctly. An additional length scale parameter is introduced by the extension. It marks the crossover point from the inertial to the dissipation range and can be expressed as a function of the Reynolds number. In combination with a recently proposed large-scale extension of Yakhot's model, we ultimately obtain full-scale models for structure functions of second and third order. These expressions are closed--form, do not contain free parameters and are in good agreement with experimental data from the smallest dissipative scales up to the system scale.