ABSTRACT
Double-averaging methodology is commonly used for investigating spatially heterogeneous flows such as boundary layer flows over rough permeable walls, for example natural streams flowing over gravel beds. However, spatial averaging volume suitable for open channel flows over rough beds is very thin in the bed-normal direction, whereas for porous media flows within the bed, similar length in all three directions is more ideal. This scale mismatch can be addressed by allowing the averaging volume to vary in space, so that its size can be adjusted to the physical characteristics of particular flow regions. This paper revisits the double-averaged continuity and momentum equations for a spatially variable averaging volume derived by Pokrajac & de Lemos (2015). Compared to the conventional double-averaged continuity and Navier-Stokes equations, the new equations contain an additional term which accounts for the spatial variation of the averaging volume. The new averaging procedure is illustrated using an example from the literature, which involves a 3-dimensional Large Eddy Simulation (LES) of open channel flow over a porous bed consisting of 5 layers of uniform size spheres.
