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

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.