Small-Amplitude Periodic Sloshing Modes of a Liquid in a Vertical Right Circular Cylinder with a Concave Spheroidal Bottom

摘要

The small-amplitude periodic sloshing modes of a liquid in a vertical right circular cylinder with a concave spheroidal bottom are calculated for the case in which there is not sufficient liquid to cover the bottom entirely. Equilibrium free surfaces of the liquid were calculated by the program CAPIL for the case in which the ratio of the minor and major semi-axes of the spheroidal bottom was 0.724. Perturbations about these surfaces were calculated by the program SLOSH. For the fill heights that were studied, and to the accuracy of these calculations the same critical Bond number, B/sub crit/, was found for instability of the free surface as was found in the static analysis of Concus and Karasalo for the same test problem. Furthermore, and in agreement with their calculation, no equilibrium surfaces were found for this problem for fill heights greater than 0.503 and for Bond numbers B