The Lagrangian-Averaged Navier-Stokes-α (LANS-α) turbulence model was implemented for the first time in a coastal hydrodynamic model. We present in this paper the details of the implementation, as well as the difficulties encountered. To overcome the difficulties, a convolution filter was used instead of the Helmoltz operator, and incompressibility was imposed in both rough and smooth velocities. The results of the second numerical implementation were tested against the results of simulations without LANS-α for a realistic application showing the tidal dynamic in Alderney Race, Normandy, France, which has the strongest currents in western Europe. The behavior of LANS-α is consistent with the conclusions of former studies, which supports our results. The findings are: i) LANS-α re-energizes the flow recovering higher-resolution turbulence statistics in lower-resolution simulations, leading to 30% savings in computing time, ii) LANS-α produces the two kinds of inertial range for barotropic turbulence, with turbulent energy decays in $k^{-5/3}$ and in $k^{-3}$ (k being the wave number) and iii) LANS-α strongly characterizes the turbulence induced by deformation. In the future, these results need to be compared to measurements and to other turbulence modeling approaches, including dissipative LES or DNS, to evaluate their relevance for the community.

拉格朗日平均Navier-Stokes- α（LANS - α）湍流模型是在沿海水动力模型中首次实现的。我们在本文中介绍了实现的详细信息以及遇到的困难。为了克服这些困难，使用了卷积滤波器代替Helmoltz算子，并且在粗糙和光滑的速度上都施加了不可压缩性。在没有LANS- α的模拟结果的基础上，对第二个数值实现的结果进行了测试，以实际显示在法国诺曼底的Alderney Race的潮汐动态，该潮汐在西欧具有最强的潮流。LANS- α的行为与以前的研究结论是一致的，这支持了我们的结果。研究结果是：i）LANS - α在较低分辨率的模拟中重新激发流动以恢复高分辨率的湍流统计数据，从而节省了30％的计算时间； ii）LANS- α为正压湍流产生了两种惯性范围，随着湍流能量的衰减${ķ}^{-5/3}$ 和在 ${ķ}^{-3}$（k是波数）和iii）LANS- α强烈表征了由变形引起的湍流。将来，需要将这些结果与测量结果以及其他湍流建模方法（包括耗散LES或DNS）进行比较，以评估其与社区的相关性。