Dynamics of an Ideal Fluid in a Wedge

It is common aboard spacecraft to passively contain/transport fuels, cryogens, waste, and other fluids through capillarity. Interior corners are commonly used to induce/retard flow. Residual accelerations (crew-docking, orbital maneuvers) can disturb the flow, ``sloshing'' the fluid, inducing unfavorable capillary surface instabilities. Here we consider a two-dimensional triangular wedge partially filled with an ideal fluid, with an interface held in equilibrium by surface tension. Small perturbations induce dynamical changes governed by the equations of motion, which are reduced to an operator equation. We report the natural frequencies and mode shapes for a pinned contact line.