THE 3-DIMENSIONAL MOTION OF A LIQUID IN A CYLINDRICAL CONTAINER

An eigenfuction method is used for the determination of the three-dimensional motion of an inviscid heavy liquid in a cylindrical container. The explicit and exact solutions which are derived for the velocity potential and for the elevation of the free surface of the liquid concern two types of initial conditions, imposed on the free surface, and are expressed in terms of double series of the Bessel-Fourier type. The two-dimensional case concerning the fluid motion which is symmetric with respect to the axis of the container, is also examined and some interesting examples are given. © 1990 IOP Publishing Ltd.