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=1,2,3x106). For Fr=1.75 (wet conditions), we observe a weak dependence on the Re-L. 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 Re-L 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 Re-L. Further, in the dry conditions, a breaking wave is noticed to occur at higher Re-L, while breaking waves are not observed for the smallest studied Re-L. Based on the results, we conclude that the wave shape for FSBFS cannot be characterized by the Froude number alone.

Automated summary

The study on wave formation behind the free surface backward facing step (FSBFS) shows that the wave shape cannot be solely characterized by the Froude number. Different conditions of step draught and inflow boundary layer profiles lead to variations in wave characteristics.