Water wave resonance in a circular oscillating channel

Nonlinear surface waves in the form of tidal bores can have a profound impact on the flow in rivers and estauries. The waves can also be studied experimentally in a specially designed periodic channel at BTU Cottbus-Senftenberg [1],[2]. We hence analyze these surface waves in this narrow circular channel partially filled with water and compare the data with numerical simulations. The flow in the channel is blocked by a barrier and the channel oscillates in azimuthal direction with variable frequency,  maintaining the same maximum velocity. The response in terms of wave shape, maximum amplitude and root mean square of the surface deviations are numerically investigated and compared with experiments. Note that for the experimental setup a number of maximum eight ultrasound sensors can provide the local height evolution. Due to the oscillations, the barrier produces wave trains or hydraulic jumps which then propagate inside the channel. Reflections, damping and collisions take place. Some frequencies are  favourised and in the first approximation can also be calculated using a shallow water model. How will be seen, only the odd multiples of the basic frequency produce high answers (resonances).

[1] I.D. Borcia, R. Borcia, Wenchao Xu, M. Bestehorn, S. Richter, and U. Harlander. Undular bores in a large circular channel. European Journal of Mechanics - B/Fluids, 79, 67-73, 2020.

[2] I.D. Borcia, R. Borcia, S. Richter, Wenchao Xu, M. Bestehorn, and U. Harlander. Horizontal Faraday instability in a circular channel. Proceedings in Applied Mathematics and Mechanics (PAMM), 19, , 2019.