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Scaling effects on the free surface backward facing step flow

A set of large eddy simulations for the free surface backward facing step (FSBFS) are carried out to study wave formation behind the step. The volume-of-fluid ghost fluid method is employed to capture the free surface. Previous studies have indicated that the wave physics depend on the step draught-based Froude number (Fr). For small Fr, the rear face of the step (transom) becomes wet, while for large Fr, the wave separates smoothly from the transom. Close to a critical Fr separating wet and dry transoms, both conditions may occur. Here, we study wet, critical, and dry conditions based on the Fr classification with three different inflow boundary layer profiles ( ReL=1,2,3×106). For Fr = 1.75 (wet conditions), we observe a weak dependence on the ReL. A proper orthogonal decomposition of the velocity field at Fr = 1.75 shows a coherent vortex street forming beneath the free surface. At Fr = 2.66 (critical conditions), we observe that an increase in the ReL results in a decrease in the wavelength and pronounced gas entrainment due to wave breaking. For Fr = 3.17 (dry conditions), we also observe shorter wavelength at increased ReL. Further, in the dry conditions, a breaking wave is noticed to occur at higher ReL, while breaking waves are not observed for the smallest studied ReL. Based on the results, we conclude that the wave shape for FSBFS cannot be characterized by the Froude number alone.