Oscillations of a fluid in a circular cylinder with bottom elevation

The problem of standing waves in a circular cylindrical vessel with an elevation on the bottom is formulated and numerically solved in the long wave approximation using an accelerated convergence algorithm. As a result of the calculations, the natural frequency of the fundamental wave mode is determined with a high accuracy. To compare the theoretical results, new experimental data on the excitation of standing surface gravity waves in a circular cylindrical vessel with parabolic and conical elevations at the bottom are presented. It is shown that the calculated and measured natural frequencies of the fundamental wave mode in vessels with the profiled bottom coincide between themselves.