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An Isaac Newton Institute Workshop

Effective Computational Methods for Highly Oscillatory Problems: The Interplay between Mathematical Theory and Applications

Adiabatic invariance and geometric phase in slowly deforming domains

3rd July 2007

Authors: Djoko Wirosoetisno (University of Durham), Jacques Vanneste (University of Edinburgh)


We consider the evolution of a 2d perfect fluid as its domain is deformed slowly in a prescribed fashion. Subject to some assumptions, the leading-order Eulerian flow is found to be steady and depend only on the instantaneous form of the boundary; it is thus an adiabatic invariant of the system. Also to leading order, the Lagrangian particle trajectory is found to consist of a dynamical and a geometric component, in the fashion of the Hannay-Berry phase.

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