Abstract
In this chapter, a three-dimensional nonhydrostatic numerical model for simulation of the unsteady free-surface stratified flows is presented. The model is based on the 3D Reynolds-averaged Navier–Stokes equations for Boussinesq fluid. The concept of eddy viscosity and diffusivity is used with the two-equation model of turbulence to define turbulent stresses and scalar fluxes. A sigma-coordinate system is used to represent the bottom and free-surface, and it also simplifies the boundary vertical conditions. The model equations in the vertical sigma-coordinate system are integrated with mode splitting technique and the decomposition of pressure and velocity fields on hydrostatic and nonhydrostatic components. The model is validated against several applications that show the importance of the nonhydrostatic effects. Density-stratified flows with free-surface occur in a variety of geophysical and technological processes. Nonhydrostatic effects are important in a wide spectrum of such flow problems, even in the case when the horizontal scales of processes are in much more vertical scale.
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