We present large-eddy simulations (LES) of wind and wave-driven turbulent boundary layers in shallow water with Langmuir circulation using a variational multi-scale formulation of the Craik-Leibovich equations. The simulations are performed using Isogeometric Analysis (IGA) based on quadratic non-uniform rational basis spline (NURBS) basis functions. Wind and wave-driven turbulent boundary layers over a flat bottom surface representative of open ocean conditions in inner-shelf regions with turbulent Langmuir number $L{a}_t=0.7$ and wind stress friction Reynolds number $R{e}_{\tau }=395$ are first simulated. The present results agree well with the reference results based on a spectral LES with higher mesh resolution [1]. Then, to investigate the effect of seabed topography on the turbulence, we simulate turbulent boundary layers over a sloped bottom surface with wind and wave forcing parallel to the shore, representative of a surf-shelf transition zone. We find that the Langmuir cell size increases as the water column shallows approaching onshore and the cell center shifts to the onshore direction. The mean velocity and turbulent kinetic energy along the shore are quantified.

我们使用 Craik-Leibovich 方程的变分多尺度公式，展示了浅水中风和波浪驱动的湍流边界层的大涡模拟 (LES) 与朗缪尔环流。使用基于二次非均匀有理基样条（NURBS）基函数的等几何分析（IGA）进行仿真。风和波浪驱动的湍流边界层在平坦底面上代表具有湍流朗缪尔数的内陆架区域的开阔海洋条件$升{\mathrm{一种}}_{吨}=0.7$ 和风应力摩擦雷诺数 $\mathrm{电阻}{\mathrm{电子}}_{\tau }=395$首先是模拟。目前的结果与基于具有更高网格分辨率的光谱 LES 的参考结果一致 [1]。然后，为了研究海底地形对湍流的影响，我们模拟了倾斜底面上的湍流边界层，风和波浪的作用力平行于海岸，代表了海陆架过渡区。我们发现朗缪尔单元大小随着水体浅层接近陆上而增加，并且单元中心向陆上方向移动。沿海岸的平均速度和湍流动能被量化。