Effects of Spatial Filtering on Instantaneous Wall-Normal Integrals for Turbulent Channel Flows

Wall-bounded turbulent flows are challenging to predict efficiently due to the fine grid spacing required for direct numerical simulations. Large- and very-large-scale motions, however, are known to comprise a significant portion of the turbulent kinetic energy and Reynolds shear stress. It was recently demonstrated that the dynamics of large-scale motions can be represented at relatively low computational cost using (quasi-) two-dimensional (2-D) fields representing instantaneous wall-normal integrals. This possibility of turbulence-resolving integral simulations on a 2-D grid represents a potentially effective tradeoff between computational cost and physical fidelity. However, the precise nature of the wall-parallel length scales associated with these (quasi-) 2-D motions requires more careful investigation. For example, it is important to establish the target grid spacing for guiding model development. To that end, this paper performs an a priori analysis to determine the effect of spatial filtering on the ability of a 2-D instantaneous wall-normal integral field to resolve turbulent kinetic energy and Reynolds shear stress. Results from direct numerical simulation data of full-channel flows up to Formula: see text and open-channel (half-channel) flows up to Formula: see text indicate that Formula: see text is sufficient for resolving Formula: see text of the quasi-2-D component of the Reynolds shear stress, where Formula: see text is the open-channel height (or half-height of the full channel). This filter width is equivalent to a target grid spacing of Formula: see text.