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Variational principles for magnetohydrodynamics were introduced by previousauthors both in Lagrangian and Eulerian form. In previous works [1] Yahalom &Lynden-Bell and later Yahalom [2] introduced a simpler Eulerian variationalprinciple from which all the relevant equations of Magnetohydrodynamics can bederived. The variational principles were given in terms of four independentfunctions for non-stationary flows and three independent functions forstationary flows. This is less than the seven variables which appear in thestandard equations of magnetohydrodynamics which are the magnetic field, thevelocity field and the density . In the case that the magnetohydrodynamic flowhas a non trivial topology such as when the magnetic lines are knotted ormagnetic and stream lines are knotted, some of the functions appearing in theLagrangian are non-single valued. Those functions play the same rule as thephase in the Aharonov-Bohm celebrated effect [3].

Barotropic Magnetohydrodynamics as a Four Function Field Theory with Non-Trivial Topology and Aharonov-Bohm Effects