Applied Scientific Research 53:119-137, 1994. l 19 @ 1994 Kluwer Academic Publishers. Printed in the Netherlands. Modelling of Rapid Pressure-Strain in Reynolds Stress Closures - Difficulties Associated with Rotational Mean Flows ARNE V. JOHANSSON, MAGNUS HALLBACK and ERIK LINDBORG Department of Mechanics, Royal Institute of Technology 10044 Stockholm, Sweden Received 16 March 1993; accepted in revised form 20 June 1994 Abstract. Intercomponent energy transfer within the context of Reynolds stress closures is studied. Attention is focussed on the rapid limit of homogeneous flow situations where this energy transfer is caused solely by the rapid pressure strain rate. We present and analyze the performance of the recently proposed rapid pressure strain rate model of Johansson & Hallb~ick(J Fluid Mech. 1994) in various homogeneous (rapid) flow situations, and compare with results obtained with other models from the literature and rapid distortion solutions. The prediction difficulties associated with rotational mean flows are analyzed. A generally formulated test case, which as special cases comprises, e.g. plane strain and homogeneous shear flow, is used to illustrate the modelling difficulties associated with rotational mean flows. An axisymmetric case is used to demonstrate that parts of the spectrum with anti-reflectional symmetry, which are instrumental for the dynamics when rotational effects are present, are totally missed in classical Reynolds stress closures. A closer prediction in cases with strong influence of rotation would require introduction of other transported quantities. Key words: RST-models, pressure strain, rotation 1. Introduction There is a general trend in today's turbulence modelling efforts to aim for increased generality and better handling of complex flow situations where, e.g., effects of strong streamline curvature or system rotation may be important. Since the kinet- ic energy equation is unaffected by, e.g., system rotation, the lowest level of single-point closure at which such effects enter explicitly is that in which transport equations are formulated for the individual Reynolds stress components. In these, the Coriolis force gives rise to terms that directly will influence the intercomponent transfer. Launder, Tselepidakis and Younis (1987) showed that even with relatively simple modelling of the terms involved, a Reynolds stress model is capable of cap- turing the main effects of system rotation on a plane turbulent channel flow. The tendency to develop a distinctly asymmetric velocity profile cannot be predicted with, e.g., a standard k - e model, but was here clearly shown to result from the inherent dynamics of the Reynolds stress transport equations. We will refer to closure schemes with transport equations for the velocity correlations, ~i~j, and the total dissipation rate, e, as classical Reynolds stress models. For more background information the reader is referred to, e.g., the review of Launder (1989). Instead of using uiuj as the quantities for which transport