A full non-hydrostatic numerical model was used to simulate the solitary wave over a flat bottom. The simulated solitary wave profiles with different wave heights were validated by theoretical analysis. The calculated viscous wave damping over a flat bottom was compared with an analytical formula. In the bottom boundary layer, the fluid viscous effects and turbulent characteristics are important compared to flows in the outer domain where the potential flow is commonly adopted ignoring viscosity. The present work contributed to highlight the flow structures and hydrodynamic characteristics within the very thin boundary layer where the sedimentation is vigorous.
There are numerous studies on the solitary wave using analytical method (Peregrine, 1967; Grimshaw, 1970, 1971). The potential flow theory is significantly popular in dealing with wave dynamics, in which the viscous effect has been ignored. Although the analytical method is successful in predicting the wave profile, the shear stress on solid wall and the wave damping cannot be successfully calculated. However, the shear stress on bottom or solid wall (e.g. a bridge pier), is critical to determine the dynamic forces. For sand bed deposition or erosion, it is very important how to accurately calculate the shear stress on the bottom.
In order to consider the viscous effects on solitary wave propagation, Liu and Orfila (2004) and Liu et al. (2006) proposed a method considering the viscous effects by integrating the wall boundary layer flow, and developed depth-averaged Boussinesq-type equations. Compared to a fully three-dimensional Navier-Stokes equation model, the Boussinesq equation model is efficient and economical in computational costs, but lower accurate because of some simplification. Numerical models based on Navier-Stokes equation are much more accurate, but unaffordable for large scale flow simulation using free surface capturing scheme, for example VOF method. In the decades, a three-dimensional non-hydrostatic model is extended from the shallow water equation (SWE). The non-hydrostatic model has been used to simulate the dispersive waves.
