Simulation of flows over wavy rough boundaries

Numerical calculation of large-scale flows appearing in the natural environment almost always involves simplification of the boundary geometry. It is not only impossible, but also meaningless, to represent all the details of the terrain with trees and vegetation, not to mention smaller objects like little stones in simulating a wind field in a localized area, or irregular bank and bed forms of natural meandering rivers. Flows in rivers and oceans have, in addition, a complex boundary on the free surface, whose shape is not just given but determined by the motion of water. The overall effects of small and random irregularities are accounted for as roughness, but larger undulations would have to be considered a part of the boundary shape. In fact the roughness and the boundary shape cannot be distinguished so easily. The numerical resolution of the flow field requires determination of what is to be considered roughness and what should be considered as the boundary shape. If the small-scale irregularities are smoothed out, the motion associated with the details is lost. In the context of large-eddy simulation (LES), this will give rise to additional subgrid-scale stresses. It has been pointed out by Nikora et al. (2001) that the small details of irregularities of even the time-averaged flow near the rough bed of an open channel must be treated by spatial averaging, which also leads to an additional stress. In simulation of the atmospheric boundary layer over a forest canopy, the extra resistance due to the roughness of the canopy is added in the flow (e.g. Yamada (1982)). In an LES, it is found (Brown, Hobson & Wood (2001) and Chow & Street (2002)) that these additional stresses need to be distributed over a much larger area in order to obtain the correct logarithmic law for an atmospheric boundary layer. Various studies of numerical simulation of smooth-surface wall flows have indicated that proper representation of the near-wall flow is essential for accurate reproduction of the main flow. Proper representation of the flow near rough and irregular boundaries can also be very important in computation of flows over rough surfaces. The main objectives of the present work is to study the effects of smoothing of the boundary on the large-eddy simulation as well as filtering of small-scale fluctuations of the flow, and to investigate modeling methods of the subgrid scale stresses and the boundary conditions when the boundary geometry is complex and irregular. We do this by conducting a direct simulation of model flow over a wavy boundary with distinct length scales. Small waves are used to simulate the surface irregularities that large-eddy simulations may not be able to resolve. A large body of work on rough surface flows does not address the effects of smoothing boundary shapes and we look at the simulation results from this point of view. Effects of smoothing the free-surface waves have been pointed out by Hodges & Street (1999). A model for inviscid surface waves has been proposed by Dimas & Fialkowski (2000). Extension of the present line of work to moving wavy surfaces can be applied to freesurface fluctuations as well.