Recursive renormalization-group calculation for the eddy viscosity and thermal eddy diffusivity of incompressible turbulence

Yigang Cao, Wan Ki Chow

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5 Citations (Scopus)

Abstract

The recursive renormalization-group method with an asymptotically free conditional average is conducted for calculating the effective eddy viscosity and thermal eddy diffusivity of incompressible turbulence. For different values of spatial rescaling factor Λ, the dependence of renormalized eddy viscosity on wave number is examined at the zeroth- and the first-order truncations of expansion of subgrid-scale energy spectrum density in Taylor series, respectively. A strong cusp-like behavior is observed near the supergrid-subgrid cutoff for the first order. This is in agreement with the result of testing-field model. However, no cusp behavior is found for the zeroth order. Calculation of Kolmogorov constant CKindicates a special region where CKis insensitive to Λ. The first order shows a range much larger than that for the zeroth order, and gives CK=1.56±0.04 in the range of 0.4≤Λ≤0.8, consistent with the generally accepted experimental values (1.2-2.2). Furthermore, the wave-number dependence of renormalized thermal eddy diffusivity is investigated, and no cusp behavior is observed around the supergrid-subgrid cutoff at the first-order truncation of expansion of subgrid-scale energy spectrum density, different from that of renormalized eddy viscosity. The Batchelor constant CBis also found insensitive to Λ in the range of 0.4≤Λ≤0.8, and is estimated to be 1.15±0.05, in good agreement with the result of ε-renormalization group approach.
Original languageEnglish
Pages (from-to)320-338
Number of pages19
JournalPhysica A: Statistical Mechanics and its Applications
Volume339
Issue number3-4
DOIs
Publication statusPublished - 15 Aug 2004

Keywords

  • Eddy viscosity
  • Recursive renormalization group
  • Thermal eddy diffusivity

ASJC Scopus subject areas

  • Mathematical Physics
  • Statistical and Nonlinear Physics

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