On the forced oscillations in a precessing open cylindrical channel

In this paper, theoretical and experimental results of the forced oscillations in an open precessed cylindrical channel are reported. The theoretical part treats the problem using a linear inviscid irrotational approximation, where different inertial modes, such as resonance ones, are presented. A real-channel flume model was constructed for the experimental part, where three different control parameters were considered: the nutation angle, the rotation rate, and the average water depth. The experiments focused on tracking the different responses toward the provided forces to the system with comparison with the assumed theory where this was possible, as other nonlinear aspects appeared. The experimental observations were tracked using a charge-coupled device sensor type camera, which enabled the extraction of both quantitative and qualitative results. The measurement of the azimuthal velocity involved the use of an acoustic Doppler velocimeter, an approach that closely aligned with the theoretical linear model; this measured velocity was also compared with the three different control parameters. The system shows instabilities in the form of resonance collapse and triadic resonance; in addition, an experimental diagram involving variation in both Reynolds and Rossby numbers is provided.