Experiments on and calculation methods for flow in straight non-circular ducts involving turbulence-driven secondary motion are reviewed. The origin of the secondary motion and the shortcomings of existing calculation methods are discussed. A more refined model is introduced, in which algebraic expressions are derived for the Reynolds stresses in the momentum equations for the secondary motion by simplifying the modelled Reynolds-stress equations of Launder, Reece & Rodi (1975), while a simple eddy-viscosity model is used for the shear stresses in the axial momentum equation. The kinetic energy k and the dissipation rate ε of the turbulent motion which appear in the algebraic and the eddy-viscosity expressions are determined from transport equations. The resulting set of equations is solved with a forward-marching numerical procedure for three-dimensional shear layers. The model, as well as a version proposed by Naot & Rodi (1982), is tested by application to developing flow in a square duct and to developed flow in a partially roughened rectangular duct investigated experimentally by Hinze (1973). In both cases, the main features of the mean-flow and the turbulence quantities are simulated realistically by both models, but the present model underpredicts the secondary velocity while the Naot-Rodi model tends to overpredict it.

Experiments on and calculation methods for flow and pollutant spreading in meandering channels are reviewed. The shortcomings of existing calculation methods are discussed in the light of the complex three-dimensional nature of the flow situation. A mathematical model is presented which takes full account of the three-dimensionality of the flow and pollutant concentration fields. This model is based on the solution of the momentum equations governing the flow in the lateral, vertical and longitudinal directions with a three-dimensional numerical procedure together with the continuity equation. The turbulent stresses appearing in the momentum equations are calculated with a version of the k-ε turbulence model that accounts for streamline curvature effects on turbulence. The pollutant concentration field is subsequently obtained from a solution to its transport equation. The model is tested by application to three different meander situations for which velocity and concentration measurements are available from the literature, with channel width-to-depth ratios in the range 4–20, smooth and rough beds and various pollutant-discharge locations. Detailed comparisons of the velocity and concentration fields show generally good agreement. The effect of streamline curvature on the turbulent mass fluxes was found to be important only in the narrow channel with a smooth bed. Bed-generated turbulence appears to overrule this in the other two cases of a wide channel with a smooth bed and a narrow channel with a rough bed. The flow patterns show the presence of a single large eddy at most cross-sections in these cases, whereas the predictions indicate the presence of usually more than one eddy in the former case.

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