Effects of spatial filtering on instantaneous wall-normal integrals

Recently, Ragan et al. (2025) demonstrated a proof of concept for Turbulence-Resolving Integral Simulation on an open-channel flow. This framework for predicting wall-bounded turbulence uses a moment-of-momentum integral approach to capture the instantaneous flow in its wall-normal integrated representation, i.e., the flow is represented on a two-dimensional (streamwise/spanwise) grid. This talk discusses the application of spatial filtering on the two-dimensional grid to represent the (very-)large-scale motions, or (V)LSMs. Specifically, a spectral cutoff filter is employed to remove fluctuations smaller than the prescribed filter width. It turns out that the spectral cutoff wavenumber of k_xh=k_zh=16 is sufficient in retaining (V)LSMs. This filter width is equivalent to an isotropic grid spacing of h/5, where h is the channel height. Without filtering, the Angular Momentum Integral equation (Elnahhas & Johnson 2022) shows that ~39-43% of the turbulent enhancement by skin friction is resolved by the wall-normal integral. By applying the mentioned filter, this value drops down to ~35-40%.