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arXiv · 1809.10909

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

H. Alemi Ardakani·T. J. Bridges·F. Gay-Balmaz·Y. Huang·C. Tronci
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Abstract

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

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H. Alemi Ardakani, T. J. Bridges, F. Gay-Balmaz, Y. Huang, C. Tronci. 2018-09-28. A variational principle for fluid sloshing with vorticity, dynamically coupled to vessel motion. https://doi.org/10.1098/rspa.2018.0642

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