A perturbation approach to large eddy simulation of wave-induced bottom boundary layer flows

We present the development, validation, and application of a numerical model for the simulation of bottom boundary layer (BL) flows induced by arbitrary finite amplitude waves. Our approach is based on coupling a 'near-field' local Navier-Stokes (NS) model with a 'far-field' inviscid flow model, which simulates large scale incident wave propagation and transformations over a complex ocean bottom, to the near-field, by solving the Euler equations, in a fully nonlinear potential flow boundary element formalism. The inviscid velocity provided by this model is applied through a (one-way) coupling to a NS solver with large eddy simulation (LES), to simulate near-field, wave-induced, turbulent bottom BL flows (using an approximate wall boundary condition by assuming the existence of a log-sublayer). Although a three-dimensional (3D) version of the model exists, applications of the wave model in the present context have been limited to two-dimensional (2D) incident wave fields (i.e. long-crested swells), while the LES of near-field wave-induced turbulent flows is fully 3D. Good agreement is obtained between the coupled model results and analytic solutions for both laminar oscillatory BL flow and the steady streaming velocities caused by a wave-induced BL, even when using open boundary conditions in the NS model. The coupled model is then used to simulate wave-induced BL flows under fully nonlinear swells, shoaling over a sloping bottom, close to the breaking point. Finally, good to reasonable agreement is obtained with results of well-controlled laboratory experiments for rough turbulent oscillatory BLs, for both mean and second-order turbulent statistics.