Rotating solitary wave at the wall of a cylindrical container

This paper deals with the theoretical modeling of a rotating solitary surface wave that was observed during water drainage from a cylindrical reservoir, when shallow water conditions were reached. It represents an improvement of our previous study, where the radial flow perturbation was neglected. This assumption led to the classical planar Korteweg–de Vries equation for the wall wave profile, which did not account for the rotational character of the base flow. The present formulation is based on a less restricting condition and consequently corrects the last shortcoming. Now the influence of the background flow appears in the wave characteristics. The theory provides a better physical depiction of the unique experiment by predicting fairly well the wave profile at least in the first half of its lifetime and estimating the speed of the observed wave with good accuracy.

Figure 1

(a) Experimental setup. Plexiglas cylindrical reservoir with a central drainage hole located at the bottom center of the container. (b) A typical solitary wave.

Figure 2

Free surface elevation (a) recorded at a given location considered as $\theta =0$; (b) in three snapshots of the wave at three successive times.

Figure 3

Wave speed in the laboratory frame of reference versus number of laps. The water depth was $H_0=25.5$ mm.

Figure 4

Comparison between theoretical and observed wave profiles at the same space position after various laps, starting from the initial stage of the wave formation, after (a) one, (b) three, (c) seven, (d) 15, (e) 19, and (f) 24 laps. The experimental conditions were as follows: constant water depth $H_0=25.5$ mm, initial swirl $\omega =120$ rpm, and initial water height $h=435$ mm.