Numerical study of nonlinear shallow water waves produced by a submerged moving disturbance in viscous flow

Two-dimensional solitary waves generated by a submerged body moving near the critical speed in a shallow water channel are studied numerically. The incompressible Navier–Stokes equations in a curvilinear free-surface-fitted coordinate system are solved by the finite difference method. The present numerical results are compared with the existing experimental data, and with the numerical solutions of two inviscid-flow models, i.e. the general Boussinesq equation and the forced Korteweg-de Vries equation. It is found that the viscous effect in the boundary layer around the body and on the bottom of the channel plays an important role in the generation of solitary waves on the free surface. Hence the Navier–Stokes solutions have a better agreement with the experimental data than those obtained from two inviscid-flow models. The effect of the submergence depth of the body on the waves generated is also investigated. It reveals that waves are insensitive to the submergence depth of the body, except for a small region quite close to the bottom of the water channel.