A two-dimensional mathematical model is described for the calculation of the depth-averaged velocity and temperature or concentration distribution in open-channel flows, an essential feature of the model being its ability to handle recirculation zones. The model employs the depth-averaged continuity, momentum and temperature/concentration equations, which are solved by an efficient finite-difference procedure. The ‘rigid lid’ approximation is used to treat the free surface. The turbulent stresses and heat or concentration fluxes are determined from a depth-averaged version of the so-calledk, ε turbulence model which characterizes the local state of turbulence by the turbulence kinetic energykand the rate of its dissipation ε. Differential transport equations are solved forkand ε to determine these two quantities. The bottom shear stress and turbulence production are accounted for by source/sink terms in the relevant equations. The model is applied to the problem of a side discharge into open-channel flow, where a recirculation zone develops downstream of the discharge. Predicted size of the recirculation zone, jet trajectories, dilution, and isotherms are compared with experiments for a wide range of discharge to channel velocity ratios; the agreement is generally good. An assessment of the numerical accuracy shows that the predictions are not influenced significantly by numerical diffusion.
Stability of Horizontal Vortices in Compound Open Channel Flow and Their 3-D Structure.
