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LES and RANS simulation of wind- and wave-forced oceanic turbulent boundary layers in shallow water with wall modeling

Mario Juha's picture

Large-eddy simulation (LES) and Reynolds-averaged Navier-Stokes (RANS) simulation of wind and wave forced oceanic turbulence in unstratified shallow water are performed in order to investigate the influence of wall modeling on results. The LES is also used to investigate the dependence of results on downwind and crosswind lengths of the computational domain, representative of a shallow shelf coastal ocean (10-to-30 m deep) unaffected by lateral boundaries. In an unstratified water column, wind and surface gravity-wave forcing generate Langmuir turbulence with largest scales consisting of full-depth Langmuir circulation (LC), counter rotating vortices aligned in the direction of the wind. The LC is known to enhance vertical mixing of momentum throughout the bulk flow, inducing a deviation of the near-bottom mean downwind velocity from the classical log law. In RANS simulations, a traditional wall treatment based on the assumption that the flow satisfies the classical law of the wall is not able to lead to a good representation of the deviation from the log law caused by LC without fine-tuning of one of the coefficients in the law of the wall. An alternative RANS approach is developed via a recent wall treatment presented in [1] based on weak imposition of the no-slip bottom boundary condition, leading to an accurate representation of the log-law deviation induced by the turbulence without having to tune input coefficients. From that standpoint, this weak enforcement of bottom boundary conditions is more robust and better suited for predictive modeling of flows with full-depth LC. In the case of LES, it is found that the deviation of the downwind velocity from the log law caused by the LC is well-resolved without the need to fine tune coefficients in traditional wall treatments. Finally, the use of wall modeling facilitates simulations with expanded domains over horizontal directions (downwind and crosswind). These expanded domains allow resolution of multiple interacting full-depth Langmuir cells. It is found that the horizontal size of the domain does not greatly impact depth profiles of turbulence statistics such as mean velocity and root-mean-square of velocity.

[1] Y. Bazilevs, C. Michler, V. Calo, T. Hughes. Weak Dirichlet boundary conditions for wall-bounded turbulent flows. Computer Methods in Applied Mechanics and Engineering, 196 (2007), pp. 4853–4862

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