Computation of Normal Modes of a Rotating, Viscous, Incompressible Fluid with a Capillary Free Boundary

摘要

A method for the computation of normal modes of a rotating, viscous, incompressible fluid with a capillary free boundary is studied. The variational formulation of the linearized problem using a finite-element discretization leads to a quadratic eigenvalue problem. The problem can be solved efficiently using an inverse iteration procedure. The effect on the eigenfrequencies of viscosity, boundary conditions, contact angle, and angular velocity of the container is investigated for a variety of container shapes.