An Eulerian Galilean-Invariant Theory for Homogeneous Turbulence, with Application to Inhomogeneous Turbulence with Arbitrary Mean Flows

Abstract

A Galilean-invariant homogeneous-turbulence theory within Eulerian framework is proposed for the study of the small-scale turbulence. Two Galilean-invariant quantities, the one-time velocity covariance and the convection-free response, are chosen as fundamental ones instead of the usual two-time velocity covariance and response. The Direct-Interaction formalism is applied to find governing equations for these two quantities. Using them, Kolmogorov's law may be derived with the reasonable estimate of Kolmogorov's constant. This theory is also applied to the evaluation of the Reynolds stresses in the inhomogeneous turbulence with arbitrary mean flows. Results obtained are shown to coincide with those from the previous work (A. Yoshizawa: J. Phys. Soc. Jpn. 46 (1979) 669 and 47 (1979) 1665), apart from a slight change of numerical factors.