The second-moment closure applied by Gibson & Launder (1978) to buoyant turbulent flows is here employed without modification to compute the effects of Coriolis forces on fully-developed flow in a rotating channel. The augmentation of turbulent transport on the pressure surface of the channel and its damping on the suction surface seem to be well captured by the computations, provided the flow near the suction surface remains turbulent. The rather striking alteration in shape of the mean velocity profile that occurs as the Rossby number is increased from 0.06 to 0.2 is shown to be explicable in terms of the modification to the intensity of the turbulent velocity fluctuations normal to the plate; for the larger value of Rossby number these fluctuations become larger than those in the flow direction causing what at low spin rates is a source of shear stress to become a sink.

The transport equations for the Reynolds stresses are closed by modeling the turbulence and mean-strain parts of the pressure-strain-rate correlation. The model constants are determined from simple relationships deduced from measurements in rectilinear and longitudinally curved shear flows. It is found that the effects of complex strain fields are more correctly predicted when the influence of the mean-strain part is reduced from levels indicated by rapid distortion theory, and the turbulence part is adjusted to conform approximately with the measured rates of return to isotropy. The case of the swirling jet is used to illustrate the improved performance of the model.

A complete second-order closure model of turbulence is used to predict the behavior of fully developed turbulent flows in open channels of both simple and compound cross sections. This level of closure entails the solution of seven differential transport equations for turbulence quantities and is found to reproduce fairly accurately the details of the turbulence-driven secondary motions that occur in the cross-stream planes. In particular, the number, location, and strength of the secondary-flow cells are well predicted, as is their effect on the bulk properties of the mean flow. Data from simple rectangular channels are used to check the model's sensitivity to the effects of a free surface, and data from compound channels, both symmetric and asymmetric, serve to validate the model for a range of parameters typical of those encountered in practice.

The paper reports on an alternative approach to modelling the turbulent scalar fluxes that arise from time averaging the transport equation for a scalar. In this approach, a functional relationship between these fluxes and various tensor quantities is constructed with guidance from the exact equations governing the transport of fluxes. Results from tensor representation theory are then used to obtain an explicit relationship between the fluxes and the terms in the assumed functional relationship. Where turbulence length– and time–scales are implied, these are determined from two scalar quantities: the turbulence kinetic energy and its rate of dissipation by viscous action. The general representation is then reduced by certain justifiable assumptions to yield a practical model for the turbulent scalar fluxes that is explicit and algebraic in these quantities and one that correctly reflects their dependence on the gradients of mean velocity and on the details of the turbulence. Examination of alternative algebraic models shows most to be subsets of the present proposal. The new model is calibrated using results from large–eddy simulations (LESs) of homogeneous turbulence with passive scalars and then assessed by reference to benchmark data from heated turbulent shear flows. The results obtained show the model to correctly predict the anisotropy of the turbulent diffusivity tensor. The asymmetric nature of this tensor is also recovered, but only qualitatively, there being significant quantitative differences between the model predictions and the LES results. Finally, comparisons with data from benchmark two–dimensional free shear flows show the new model to yield distinct improvements over other algebraic scalar–flux closures.

Published data from boundary layers on convex surfaces are used to assess the performance of a calculation method based on the solution of modeled transport equations for the Reynolds’ stresses and the dissipation rate of turbulence energy. For flows with large curvature, the model closely reproduces the suppression of turbulence and the diminished growth rate and skin friction. The recovery of flow distorted by curvature is also predicted with results broadly in accord with the measurements.