Two-loop calculation of the turbulent Prandtl number

Abstract

The turbulent Prandtl number has been calculated in the two-loop approximation of the $\eps$ expansion of the stochastic theory of turbulence. The strikingly small value obtained for the two-loop correction explains the good agreement of the earlier one-loop result with the experiment. This situation is drastically different from other available nontrivial two-loop results, which exhibit corrections of the magnitude of the one-loop term. The reason is traced to the mutual cancellation of additional divergences appearing in two dimensions which have had a major effect on the results of previous calculations of other quantities.

11 pages, 3 figures

References in corpus (5)

• Renormalization-group approach to the stochastic Navier--Stokes equation: Two-loop approximation
• An improved $\eps$ expansion for three-dimensional turbulence: two-loop renormalization near two dimensions
• Large-Order Asymptotes for Dynamic Models Near Equilibrium
• Instantons for Dynamic Models from B to H
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Cited by in corpus (4)

• Stationary, isotropic and homogeneous two-dimensional turbulence: a first non-perturbative renormalization group approach
• Helical turbulent Prandtl number in the $A$ model of passive advection: Two loop approximation
• Hyperlogarithms in the theory of turbulence of infinite dimension
• Two-Loop Turbulent Helical Magnetohydrodynamics: Large-Scale Dynamo and Energy Spectrum