Nonlinear fluid motions in a container due to the discharge of an electric current

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Abstract
The nonlinear electromagnetic stirring induced in a hemispheroidal container by the axisymmetric discharge of an electric current is investigated. The electric current is discharged into the fluid from a circular electrode which is at the centre of the equatorial plane of the container, the remaining part of the equatorial plane being a free surface. The equations of the problem are solved semi-analytically and results are presented for several sets of data. In the case of a point electrode when the current exceeds a critical value we have velocity breakdown. Here it is shown that, as the size of the area through which the current is discharged increases, the intensity of the flow field decreases, and thus for a larger electrode a larger amount of current can be discharged without velocity breakdown. When, however, the current is sufficiently large the solution becomes unstable, and this indicates velocity breakdown. Finally in an Appendix the solution for the case of a point discharge in a semi-infinite fluid is expressed in analytic (series) form.