Natural Oscillations of a Heavy Fluid in an Elliptic Vessel

The problem of the natural oscillations of a heavy ideal fluid in a vertical elliptic basin (vessel) of finite depth is investigated. The eigenvalue and eigenfunction problem with Neumann boundary conditions is solved using a numerical-analytic approach developed by the authors. For the five lowest oscillation modes the natural frequencies and shapes are determined with high accuracy over a wide range of variation of the eccentricity. Graphical dependences of theoretical and applied interest are constructed and commented on.