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 ($R{e}_L=1,2,3\times {10}^6$). 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.

中文翻译：

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自由表面朝后的阶跃流上的缩放效应

对自由表面向后台阶（FSBFS）进行了一系列大涡模拟，以研究台阶后面的波形成。流体体积幻影流体方法用于捕获自由表面。先前的研究表明，波物理学取决于基于阶跃吃水的Froude数（Fr）。对于较小的Fr，踏板（横梁）的背面变湿，而对于较大的Fr，波与横梁平稳地分开。接近分隔湿气和干气口的临界Fr时，两种情况都可能发生。在这里，我们基于Fr分类并使用三种不同的流入边界层剖面来研究潮湿，临界和干燥条件（$\mathrm{[R}{Ë}_{\mathrm{大号}}=\mathrm{1个}，\mathrm{2个}，3\times {10}^6$）。对于Fr  =  1.75（潮湿条件），我们观察到对Re _L的依赖性很弱。在Fr  =  1.75处速度场的适当正交分解表明，在自由表面下方形成了连贯的涡街。在Fr  =  2.66（临界条件）下，我们观察到Re _L的增加导致波长减小，并且由于波的破裂而导致明显的气体夹带。对于Fr  =  3.17（干燥条件），我们还观察到Re _L增加时波长较短。此外，在干燥条件下，发现在较高的Re _L处发生断波。，而对于最小的研究Re _L，没有观察到破碎波。根据结果​​，我们得出结论，单靠Froude数无法表征FSBFS的波形。