Closure modeling and direct simulation of vegetation drag in flow through emergent vegetation Su Jin Kim 1 and Thorsten Stoesser 1 Received 17 February 2011 ; revised 26 August 2011 ; accepted 1 September 2011 ; published 13 October 2011. [1] This paper presents numerical simulations of flow through emergent vegetation. Two simulation strategies are evaluated, (1) Reynolds-averaged Navier-Stokes (RANS)- based simulations employing a vegetation closure model and (2) low-resolution large-eddy simulation (LES). RANS-based models offer efficiency in terms of computational resources, however, it is demonstrated herein that the accuracy of RANS models depends strongly on empirical parameters of the corresponding vegetation closure model. The method of low-resolution LES is an efficient alternative to a fully resolved LES, simulates vegetation drag directly, and does not require empirical parameter input. Predictions of the vegetative flow resistance of emergent vegetation using low-resolution LES are in fairly good agreement with measurements, in particular for low and moderate vegetation densities. This is because prevailing stream- and spanwise-velocity gradients, vertical velocity profiles, and recirculation zones are calculated with reasonable accuracy. Citation: Kim, S. J., and T. Stoesser (2011), Closure modeling and direct simulation of vegetation drag in flow through emergent vegetation, Water Resour. Res., 47, W10511, doi:10.1029/2011WR010561. 1. Introduction [2] Vegetation on the banks or floodplains of rivers and streams significantly affects the horizontal and vertical ve- locity distributions as well as the turbulence statistics. Accu- rate quantification of the bulk effects of flow-vegetation interaction is a significant challenge in the field of open- channel hydraulics and is, for instance, of great importance for the design of flood protection or stream restoration schemes [Stoesser et al., 2003]. [3] Over the last four decades, the tool of computational fluid dynamics (CFD) has been developed and refined. CFD models are able to provide accurate flow predictions of many flows of practical hydraulic and/or hydrological interest. In general, the methods of direct numerical simulation (DNS), large-eddy simulation (LES), and Reynolds-averaged-Navier Stokes (RANS) have evolved. LES lies between the extreme approaches of DNS, where all turbulent fluctuations are computed and no turbulence model is required, and steady RANS, where only the mean velocity field is computed and all the unsteady effects of turbulence are accounted for by a turbulence model. Nowadays, RANS is considered a compu- tationally efficient engineering tool, while DNS and LES are much more expensive and are mainly used in research. LES and DNS offer a substantial increase in accuracy over time- averaged approaches, particularly when large-scale turbulent structures dominate the flow [e.g., Rogallo and Moin, 1984]. [4] In the mid 90s, various RANS models were devel- oped to simulate the flow through vegetation and different turbulence models were employed to calculate the Reynolds stresses that are a result of Reynolds averaging. RANS models are operated on coarser grids and the additional form drag due to vegetation is accounted for through sub- grid forces that are added to the momentum and turbulence model transport equations. This treatment should be referred to as vegetation closure model; RANS models offer reasonable accuracy in the prediction of the time- averaged flow field [Choi and Kang, 2004; Defina and Bixio, 2005; Fischer-Antze et al., 2001; Lopez and Garcia, 2001; Naot et al., 1996; Neary, 2000, 2003; Nicholas and McLelland, 2004; Tsujimoto and Shimizu, 1994], but agreement with measured turbulence quantities is some- times poor [Defina and Bixio, 2005; Neary, 2003]. This is mainly because steady RANS models do not resolve flow– vegetation interaction. Vortex shedding and local velocity gradients are absent, hence RANS models require addi- tional drag-related terms in the turbulence models’ trans- port equations to account for vegetation-related turbulence production and its dissipation. Drag force terms in the mo- mentum and drag-related terms in the turbulence model transport equations, require a priori estimates of the drag coefficient and additional empirical constants. [5] Most vegetation closure models use the drag force formula, i.e., F D ¼ 0:5u 2 0 A P C D , with  being the density of the working fluid, u 0 the free stream velocity, A P the pro- jected area of the plant, and C D the drag coefficient, which is an empirical parameter. In many experimental investiga- tions of flow through vegetation the cylinder analogy is made use of, i.e., vegetation can be idealized as a bunch of rigid circular cylinders. The calculation of vegetation drag is then straightforward and the only uncertainty is in the selection of C D . However, even though many RANS based studies that used the drag force approach report a reasonably good match of predicted velocity profiles with observed ones, some inaccuracies were found in the prediction of the 1 School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, Georgia, USA. Copyright 2011 by the American Geophysical Union. 0043-1397/11/2011WR010561 W10511 1 of 15 WATER RESOURCES RESEARCH, VOL. 47, W10511, doi:10.1029/2011WR010561, 2011