Generation of solitary waves by forward- and backward-step bottom forcing (Q2718419)

The authors develop a numerical model based on Euler equations to describe the basic mechanism underlying the solitary waves produced by bottom topography. A finite difference scheme is used for computing waves and wave resistance due to different bottom topography moving steadily at the critical velocity in shallow water. Special attention is given to both positive forcing disturbance and negative forcing disturbance for wave generation in shallow water. A positive forcing disturbance contributes to the generation of upstream-advancing solitary waves, whereas the negative forcing disturbance generates upstream-running waves from its forward-step forcing and downstream-radiating waves from its backward-step forcing. These two wave systems do interact in the negative forcing region causing resulting waves that are quite different from those due to a positive forcing disturbance. An outline of the computational method is presented. Quantitative comparisons are made between numerical solutions for the amplitude of lead upstream waves for different forcing heights and the approximate solutions of \textit{N. F. Smyth} [Proc. R. Soc. Lond., Ser. A 409, 79-97 (1987; Zbl 0611.76122)] and \textit{R. H. J. Grimshaw} and \textit{N. Smyth} [J. Fluid Mech. 169, 429-464 (1986; Zbl 0614.76108)].