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The paper develops proposals for a model of turbulence in which the Reynolds stresses are determined from the solution of transport equations for these variables and for the turbulence energy dissipation rate ε. Particular attention is given to the approximation of the pressure-strain correlations; the forms adopted appear to give reasonably satisfactory partitioning of the stresses both near walls and in free shear flows.Numerical solutions of the model equations are presented for a selection of strained homogeneous shear flows and for two-dimensional inhomogeneous shear flows including the jet, the wake, the mixing layer and plane channel flow. In addition, it is shown that the closure does predict a very strong influence of secondary strain terms for flow over curved surfaces.

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Proposals are made for modelling the pressure-containing correlations which appear in the transport equations for Reynolds stress and heat flux in a simple way which accounts for gravitational effects and the modification of the fluctuating pressure field by the presence of a wall. The predicted changes in structure are shown to agree with Young's (1975) measurements in a free stratified shear flow and with the Kansas data on the atmospheric surface layer.