LOW-REYNOLDS-NUMBER TWO-EQUATION TURBULENCE MODELLING FOR OPEN CHANNEL FLOW: DEVELOPMENT AND EVALUATION OF FREE SURFACE BOUNDARY CONDITIONS ON THE DISSIPATION RATE EQUATION

An eddy viscosity turbulence model (EVM) is applied to open channel flows characterized by lowto-moderate bulk flow rates. The turbulence model is of the "two-equation" k-(epsilon) type (where k is the turbulent kinetic energy and (epsilon) the rate of viscous dissipation of k), and specifically is a lowReynoldsnumber variant of the standard model. Two-equation EVMs are widely used in hydraulic engineering, and the present work seeks first to examine the applicability of the approach to free surface flows. Having identified some fundamental limitations within the EVM framework, the paper then proceeds to explore the possibility of improving the vertical profiles of eddy viscosity, (nu)t returned by such models. Particular attention is paid to the specification of the free surface boundary condition applied to the (epsilon)-transport equation and comparison is made with Direct Numerical Simulation and laser-Doppler data for open channel flow. Four alternative boundary conditions are examined: the first two of these are defined in terms of "local" (surface) parameters and consist of the widely applied zero gradient form (which is justified theoretically in the present work) together with a new "limiting form" specification of free surface (epsilon). The limiting form boundary condition is based upon the substitution of Taylor series expansions for fluctuating velocity into the k-transport equation, and comparisons with data establish that this new formulation yields a significant improvement over the zero gradient form in the prediction of upperchannel eddy viscosity profiles. Two further non-local (outer scale) free surface boundary conditions on the (epsilon)-equation are also considered. Despite the improvements afforded by the limiting form boundary condition, a general finding of the present study is that turbulence levels throughout the channel depth are somewhat under-predicted at the flow rates under consideration.