Efficiency and Accuracy of Non-Hydrostatic Modeling of Free-Surface Flows

Efficiency and accuracy of a fully non-hydrostatic three-dimensional model are examined through simulation of linear and nonlinear dispersive waves. The model uses an implicit method to solve the unsteady, three-dimensional, Navier-Stokes equations and the fully nonlinear free-surface boundary conditions. A new top-layer pressure treatment that takes the non-hydrostatic pressure into account is implemented. The model results are verified against analytical solutions, indicating that the model using a small number of vertical layers is capable of effectively simulating the free-surface elevation. By further examining the performance of the model in resolving nonlinearity and dispersion of surface wave characteristics, we demonstrate the efficiency and accuracy of the model. To extend the model's application, a generic length scale approach is adopted in the non-hydrostatic model, yielding the k-kl (Mellor-Yamada Level 2.5), k-epsilon, k-omega and gen turbulent closure models. This newly developed non-hydrostatic model is used to simulate wind-driven circulations under different turbulent closure models.