Multiplicative models for turbulent energy dissipation

Summary

We consider models for describing the intermittent distribution of the energy dissipation rate per unit mass, ε, in high-Reynolds-number turbulent flows. These models are based on a physical picture in which (in one-dimensional space) an eddy of scale r breaks into b smaller eddies of scale r/b. The energy flux across scales of size r is rε _r , where ε _r is the average of ε over a linear interval of size r. This energy flux can be written as the product of factors called multipliers. We discuss some properties of the distribution of multipliers. Using measured multiplier distributions obtained from atmospheric surface layer data on ε, we show that quasi-deterministic models (multiplicative models) can be developed on a rational basis for multipliers with bases b = 2 and 3 (that is, binary and tertiary breakdown processes). This formalism allows a unified understanding of some apparently unrelated previous work, and its simplicity permits the derivation of explicit analytic expressions for quantities such as the probability density function of rε _r , which agree very well with measurements. Other related applications of multiplier distributions are presented. The limitations of this approach are discussed when bases larger than three are invoked.

This is the enlarged version of the text to appear in the Proceedings of the International Congress of Theoretical and Applied Mechanics, Haifa, 1992.