ANALYTICAL THEORY OF THE DESTRUCTION TERMS IN DISSIPATION RATE TRANSPORT-EQUATIONS

Modeled dissipation rate transport equations are often derived by invo king various hypotheses to close correlations in the corresponding exa ct equations. D. C. Leslie [Modern Developments in the Theory of Turbu lence (Oxford University, Oxford, 1972)] suggested that these models m ight be derived instead from Kraichnan's [J. Fluid Mech. 47 (1971)] wa venumber space integrals for inertial range transport Stower. This sug gestion is applied to the destruction terms in the dissipation rate eq uations for incompressible turbulence, buoyant turbulence, rotating in compressible turbulence, and rotating buoyant turbulence. Model consta nts like C-epsilon 2 are expressed as integrals; convergence of these integrals implies the absence of Reynolds number dependence ii the cor responding destruction term. The dependence of C-epsilon 2 on rotation rate emerges naturally; sensitization of the modeled dissipation rats equation to rotation is not required. A buoyancy related effect which is absent in the exact transport equation for temperature variance di ssipation, but which sometimes improves computational predictions; als o arises naturally, The time scale in the modeled transport equation d epends on whether Bolgiano or Kulmogorov inertial range scaling applie s. A simple extension af these methods leads to a preliminary dissipat ion rate equation for rotating buoyant turbulence. (C) 1996 American I nstitute of Physics.