Solvable model in renormalization group analysis for effective eddy viscosity.
This study presents a solvable model in renormalization group analysis for the effective eddy viscosity. It is found fruitful to take a simple hypothesis that large-scale eddies are statistically independent of those of smaller scales. A limiting operation of renormalization group analysis yields an inhomogeneous ordinary differential equation for the invariant effective eddy viscosity. The closed-form solution of the equation facilitates derivations of an expression of the Kolmogorov constant C(K) and of the Smagorinsky model for large-eddy simulation of turbulent flow. The Smagorinsky constant C(S) is proportional to C(3/4)(K). In particular, we shall illustrate that the value of C(K) ranges from 1.35 to 2.06, which is in close agreement with the generally accepted experimental values (1.2 approximately 2.2).
Chang
Chien C
CC
Institute of Applied Mechanics, College of Engineering, National Taiwan University, Taipei 10764, Taiwan, Republic of China. changcc@gauss.iam.ntu.edu.tw
Lin
Bin-Shei
BS
Wang
Chi-Tzung
CT