| Non-hydrostatic pressure, which deviates from the linear distribution of pressure, called hydrostatic assumption, becomes significant and critical for modeling free surface flows when the vertical motion of flows is no longer negligible such as a short wave motion, a wave or current motion over steep topographic variation, and a wave or current motion in a curved channel.; Through an extensive review of literature, a non-hydrostatic free surface model based on a single-valued height function is proposed to efficiently apply in a large computational domain. The Navier-Stokes equations (NSE) for wave application or the Reynolds averaged Navier-Stokes equations (RANS) for current implementation is employed to formulate mathematic model, and solved by a fractional step approach, often called projection method. A new top-layer boundary condition, which improves the efficiency and accuracy of the model, is suggested to close a kinematic boundary condition at the free surface.; The proposed model, first, is implemented for wave motions: a relatively deep-water waves with steep bottom topography, a nonlinear motion of waves around surface-piercing cylinders, and a dispersive motion of waves in a curved channel. Numerical results show that the non-hydrostatic model can successfully resolve the effect of non-linearity as well as dispersion when a reflection, refraction, shoaling, and diffraction transform a train of wave. The modeling results support the existing non-linear diffraction theory in estimating wave run-up around surface-piercing structures, and show the role of dispersion in generating higher harmonics in a curved channel.; By embedding a generalized length-scale turbulence model that provides flexibility in choosing an appropriate eddy viscosity for different turbulent flows, the proposed non-hydrostatic model is further extended into open-channel current applications. In a mildly and a strongly curved channel, the model shows its performance to resolve the secondary motion of Prandtl's first kind when the centrifugal force and vorticity plays an important role. Non-hydrostatic effect in a curved channel is also investigated numerically by comparing the non-hydrostatic model with a quasi-hydrostatic model. This numerical investigation reports that the non-hydrostatic pressure of effect is not only the function of curvature but also water depth. |
