In the present study, we examine the consistency and validity of the Boussinesq and KdV equations in describing nonlinear water waves generated by vertical slender bodies moving with near critical speed in a rectangular channel. Our study is focused on investigating the effect of disturbance length L on wave generation, and whether the two long wave models, which in theory require L to be much greater than water depth H, can actually be applied to cases where L/H = O(1). Our numerical results based on the KdV and Boussinesq wave models show that, if L is sufficiently long, the dominant factor affecting wave amplitude and period will be the ratio of the maximum disturbance width (i.e., beam of a vertical strut) over the channel width, while L has little effect. This confirms Ertekin's (1984) and Mei's (1986) earlier results on the "blockage coefficient". When L is of the same order of H, we found that, as L decreases, it weakens the forcing strength significantly. Results from our towing tank experiments with Froude number ranging from 0.8 to 1.07 revealed that the long wave models give good predictions for resonantly forced long waves even when L is slightly shorter than water depth.
In 1982, Wu and Wu discovered from numerical simulations based on Wu's (1981) generalized Boussinesq model that upstream advancing solitary waves (also called run-away solitons) can be generated periodically by a steadily moving pressure distribution moving with near critical speed on the free surface. Even though there had been earlier observations of run-away solitons in several experimental studies, Wu and Wu's study provided the first theoretical understanding of the phenomenon. Later, more theoretical analysis based on mass conservation and energy principles was given in Wu (1987).
