Laminar boundary layers and damping of finite amplitude solitary wave in a wave flume

Abstract

In this paper, the laminar viscous effects on finite amplitude solitary wave propagation in a wave flume with a rectangular cross section are investigated. The laminar viscous effects are most important in the laminar boundary layers adjacent to the bottom and sidewalls of the flume. The closed-form solutions of Clamond and Fructus [“Accurate simple approximation for the solitary wave,” C. R. Mec. 331, 727 (2003)] provide the free stream velocity to derive the boundary layer flows. The rotational velocities inside the bottom and sidewall boundary layers are first obtained analytically after linearization. Numerical solutions for the nonlinear boundary layer flows are also calculated. The importance of the nonlinearity is discussed. The laminar viscous damping rate is estimated by balancing the energy dissipation inside the boundary layers and the rate of wave energy change in the entire wave. Numerical results of the damping rate show the dependence on the viscosity of the fluid, the wave amplitude, the water depth, and the width of the wave flume. New laboratory experiments on the wave damping of finite amplitude solitary waves are also performed. The theoretical results are confirmed with the laboratory data. The methodologies introduced in this paper for obtaining boundary layer solutions and laminar viscous damping rate can be applied to other transient waves with finite amplitude.