The application of gauge field theories to electrically coupled hydrodynamic flows is examined. Consideration of the gauge potentials associated with the equation of state constrain the equations of motion and reduce phase space to specific topological manifolds. The analysis presented suggests that the flow field associated with the steady-state convection of a fluid has solutions in the cohomology group H/sup 3/(T/sup 2//spl times/S/sup 1/,Y). In the case of electrically driven convection flows, if the applied electromagnetic field is periodic with period 2/spl pi/, the steady-state flow field is periodic with period 4/spl pi/.