The boundary layer at the bottom of a solitary wave and implications for sediment transport

摘要

The present paper summarizes the theoretical and numerical results of recent studies of the bottom boundary layer generated by the propagation of a solitary wave which is often used as a model of a tsunami wave. The flow and the bottom shear stress are discussed as function of the parameters of the problem, i.e. (ⅰ) the ratio between the height H~* of the wave and the local water depth h~+, (ⅱ) the ratio between the thickness δ~+ of the bottom boundary layer and h~*, (ⅲ) the relative bottom roughness. In particular, the conditions leading to turbulence appearance, which are obtained by means of a linear stability analysis, are presented along with those obtained by means of direct numerical simulations of Navier-Stokes equations and the integration of the RANS equations. It is shown that turbulence tends to appear during the decelerating phase of the wave cycle, if the wave height is larger than a critical value which depends on the ratio between the thickness of the bottom boundary layer and h* and the relative bottom roughness. As the height of the wave increases, turbulence appears earlier and becomes more intense, thus enhancing mixing phenomena and the sediment transport rate.