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A variational principle is derived for two-dimensional incompressiblerotational fluid flow with a free surface in a moving vessel when both thevessel and fluid motion are to be determined. The fluid is represented by astream function and the vessel motion is represented by a path in the planarEuclidean group. Novelties in the formulation include how the pressure boundarycondition is treated, the introduction of a stream function into theEuler-Poincar\'e variations, the derivation of free surface variations, and howthe equations for the vessel path in the Euclidean group, coupled to the fluidmotion, are generated automatically.

A variational principle for fluid sloshing with vorticity, dynamically coupled to vessel motion