Comparison of turbulence models for stage-discharge rating curve prediction in reach-scale compound channel ¯ows using two-dimensional ®nite element methods C.A.M.E. Wilson a, * , P.D. Bates b , J.-M. Hervouet c a Environmental Water Management Research Centre, Cardiff School of Engineering, Cardiff University, Cardiff, Wales CF24 3TB, UK b School of Geographical Sciences, University of Bristol, Clifton, Bristol BS8 1SS, UK c Department Laboratoire National d'Hydraulique, EDF Chatou, Paris, France Received 21 February 2001; revised 1 August 2001; accepted 27 September 2001 Abstract This paper attempts to assess the accuracy of constant eddy viscosity, Elder and k ± e turbulence models in the numerical simulation of reach-scale compound channel ¯ows using two-dimensional (2D) ®nite element methods. Assessment was conducted using benchmark stage-discharge data collected from straight and meandering compound channel con®gurations at the UK Engineering and Physical Science Research Council (EPSRC) Flood Channel Facility. For mesh resolutions and topologies used in reach-scale studies, all models were found to be adequate predictors (,5% error in predicted ¯ow depth) of the stage-discharge relationship at moderate overbank ¯ows (Figs. 1 and 2). However, at inbank and low overbank ¯ows the Elder and k ± e turbulence models can reproduce stage-discharge points with much greater accuracy than the constant eddy viscosity model. Hence, for an unsteady simulation where low ¯ows are relevant a constant eddy viscosity turbulence closure may prove problematic. In terms of computed lateral distributions of depth-averaged velocity for both channel con®gurations, at higher depths (Relative depth  0.666) all turbulence models predict the velocity with greater accuracy than at a lower depth (Relative depth  0.333). At this latter depth, all turbulence models predict the depth-averaged longitudinal velocity distribu- tion with poor accuracy (.20% error). Also, sensitivity of the turbulence parameter calibration with respect to the predicted ¯ow depth showed that the constant eddy viscosity model's performance can be highly dependent on the choice of turbulence parameter value. q 2002 Elsevier Science B.V. All rights reserved. Keywords: Hydrodynamics; Numerical model; Flood routing; Compound channel ¯ow 1. Introduction An accurate assessment of the stage-discharge rela- tionship is fundamental for ¯ood management and in the design of waterways. There are many methods for determiningtheconveyancecapacityandtheextentof ¯ood inundation, and these generally fall into two categories: empirical and numerical approaches. A number of researchers have proposed empirical meth- ods, primarily based on data from small and large ¯umes that contain regularly meandering compound channels (Wark et al., 1994; Shiono et al., 1999; Greenhill and Sellin, 1993). However for practical use, a prediction method that can be applied generic- ally to natural rivers needs to be developed. Also, these empirical methods typically use a one-dimen- sional (1D) approach based on a reach-averaged Journal of Hydrology 257 (2002) 42±58 www.elsevier.com/locate/jhydrol 0022-1694/02/$ - see front matter q 2002 Elsevier Science B.V. All rights reserved. PII: S0022-1694(01)00553-4 * Corresponding author. E-mail address: wilsonca@cardiff.ac.uk (C.A.M.E. Wilson).