Cavitational Flow and Magnetohydrodynamics

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Abstract
The study of cavitational flow is formulated as a free boundary problem for the Laplace equation in three dimensions. Constant pressure free streamlines are determined by a variational principle for the virtual mass that can be deduced from a similar result for vortex sheets. Steepest descent applied to minimization of the potential energy suggests a natural iterative scheme to calculate the shape of the cavity bounded by the free streamlines. Numerical methods enable one to estimate the drag and the geometry of the flow. Another version of the variational principle plays an important role in plasma physics and the theory of magnetic fusion. This method has significant applications to stellarators, which are toroidal configurations for confinement of hot plasma whose three-dimensional geometry leads to interesting mathematical problems. Large computer codes implementing the theory play a central role in the design of thermonuclear reactors.

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