A nonlinear model of motion of fluid mass in a cylindrical tank separated into compartments (Q2754756)

Potential of velocity of incompressible inviscid fluid for the studied problem with free surface is determined from solution of some boundary value problem for Laplace equation, which is found by variational technique. The direct method of solution of the variational problem consists in construction of the shape of free surface and the velocity potential in the form of series containing products of unknown time functions by coordinate functions. The latter are explicitly expressed in terms of Bessel functions. Time functions are determined from a system of differential equations. An approximate reduced system of equations enables one to study various vibrational motions of fluid and their stability under prescribed law of vessel motion, also at resonance.