A Statistical Investigation of Shear Turbulence: the Reynolds-Stress Transport Equation

Abstract

The Reynolds-stress transport equation is investigated from a statistical viewpoint. Each term in the equation is evaluated from a shear-turbulence theory (A. Yoshizawa: J. Phys. Soc. Jpn. 47 (1979) 1665 and 50 (1981) 1792), which is based on the scale separation as to mean and fluctuating fields as well as Kraichnan’s propagator-renormalization formalism or the direct-interaction approximation (R. H. Kraichnan: J. Fluid Mech. 5 (1959) 417 and 83 (1977) 349). The detailed discussion is made on the modelling of the pressure-strain correlation or the so-called redistribution term in the transport equation, in relation to the turbulence closure modelling.