We present direct numerical simulations of a temporally developing turbulent boundary layer along a moving flat plate piercing through the free surface. The influence of the Froude number on the results is examined. We confirm the findings in the literature, that the vorticity and secondary flows generated at the free surface for low Froude numbers ( F r ∼ 0 $Fr\sim 0$ ) is primarily due to anisotropy of the normal Reynolds stresses. At intermediate Froude numbers however, the vorticity generated at the free surface is related to the curvature of the interface, and is directly injected in the outer and logarithmic portions of the turbulent boundary layer. This has an impact on its overall structure with increased levels of turbulent kinetic energy production. The deformable interface results in changes to the velocity distribution in the near-surface region and loss of self-similarity within the log-law region of the boundary layer.

中文翻译：

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弗劳德数对具有自由表面的湍流边界层的影响

我们提出了沿着穿过自由表面的移动平板的时间发展湍流边界层的直接数值模拟。检查弗劳德数对结果的影响。我们证实了文献中的发现，即低弗劳德数 (F r ∼ 0 $Fr\sim 0$ ) 在自由表面产生的涡度和二次流主要是由于正常雷诺应力的各向异性。然而，在中等弗劳德数下，自由表面产生的涡度与界面的曲率有关，并直接注入湍流边界层的外部和对数部分。这对其整体结构产生影响，增加了湍流动能的产生。