A Variational Characterization of Fluid Sloshing with Surface Tension

Sloshing refers to the free surface motion of a fluid in a container. We study the linearized sloshing problem of an incompressible, inviscid, irrotational fluid in a container, where we focus on the regime where the effect of surface tension dominates the effect of gravity. This is especially important in the microgravity environment, where scientists and engineers have worked to improve our understanding of the behavior of a liquid propellant within a rocket. We are interested in studying the properties of sloshing frequencies and the corresponding modes.