Large eddy simulation of fully-developed turbulent flow through submerged vegetation

Large Eddy Simulations (LES) are performed for an open channel flow through submerged vegetation with a water depth (h) to plant height (hp) ratio of h/hp=1.5 according to the experimental configuration of Fairbanks and Diplas (1998). Fairbanks and Diplas measured longitudinal and vertical velocities as well as turbulence intensities along several verticals in the flow and the data are used for the validation of the simulations. The code MGLET is used to solve the filtered Navier Stokes equations on a Cartesian non-uniform grid. In order to represent solid objects in the flow, the immersed boundary method is employed. The computational domain is idealized with a box containing four submerged circular cylinders and periodic boundary conditions are applied in both longitudinal and transverse directions. The predicted streamwise as well as vertical mean velocities are in good agreement with the LDA measurements. Furthermore, good agreement is found between calculated and measured streamwise r.m.s velocities. Largescale flow structures of different shape are present in the form of vortex rolls above the vegetation tops as well as von Karman type vortices generated by flow separation at the cylinders. In this paper the mean and instantaneous flow field is analyzed and further insight into the complex nature of flow through vegetation is provided based on Large Eddy Simulation. Choi and Kang (2001) used a Reynold's Stress model (RSM) accounting for the anisotropy of turbulence, to simulate the flow through rigid submerged vegetation elements. However, within the surface-layer region there was only minor improvement in the computed mean velocity, turbulent intensity and Reynolds stress profiles for the RSM relative to the k-ε or k-ω model. Mean flow features resolved by the steady RANS models include: (a) the suppression of the streamwise velocity profile in the vegetated zone, (b) the inflection of the velocity profile at the top of the vegetation zone, and (c) the vertical distribution of the turbulent shear stress, with its maximum value at the top of the vegetation zone. However, although mean velocities were predicted with satisfying accuracy, RANS models have been less successful at correctly predicting streamwise and vertical turbulence intensities, because these models cannot account for organized large-scale unsteadiness and asymmetries (coherent structures) resulting from turbulent flow instabilities. These coherent structures include: (a) the transverse and secondary vortices in the form of rolls and ribs (Finnegan, 2000), which occur at the top of the vegetation layer as a result of a Kelvin-Helmholtz instability due to the inflection of the streamwise velocity profile (Figure 1), and (b) 3D vortices produced by the complex interaction of the approach flow with the stem (e.g trailing or necklace vortices) and the enforced vortex shedding in the wake of the stem due to flow separation (Figure 2). Recently, modeling techniques that directly resolve large-scale, organized, unsteady structures in the flow and advanced numerical techniques for simulating flows around multiple flexible bodies were introduced for the simulation of such or similar flow problems, e.g. URANS simulations by Paik et al. (2003) or Large Eddy Simulations by Cui and Neary (2002). Such techniques elucidate the largescale coherent structures described above, their important role in vegetative resistance, and the interaction and feedback between the region within and outside the vegetation layer. The Large Eddy Simulation of flow through and above vegetation is not new and finds its origins in boundary-layer meteorology. To our knowledge, the first LES for flow over vegetation were presented by Deardoff (1972) in which the atmospheric boundary-layer over a wheat field was simulated. Further LES in boundary-layer meteorology were for the flow and the turbulent structures above forests, a flow problem that has been studied extensively with LES (e.g. Moeng, 1984, Shaw and Shumann, 1992, Kanda and Hino, 1993, Dwyer et al., 1997). The advantage of LES lies in the fact that a highly resolved temporal and spatial picture of the flow field can be obtained. The vertical distribution of Reynolds stresses and turbulent fluctuations as calculated with LES were found to be in good agreement with laboratory and field observations. These simulations show the enormous potential of LES in accurately predicting the flow and its associated time-dependent structures. In this paper we present Large-Eddy simulations of turbulent channel flow through a matrix of cylinders. The flow around the individual cylinders is fully resolved by a high resolution grid and the cylinder-matrix can be regarded as an idealized vegetation layer. The time-averaged velocity field as well as turbulence quantities are presented and compared with laboratory measurements. Moreover, large-scale structures are shown to occur above and within the vegetation layer. Figure 1: Kelvin-Helmholtz instabilities resulting in ribs and rolls above vegetation layers (from Finnegan 2000). Figure 2: Vortices originating at tall and short cylinders (from Kawamura et al, 1984).