Effects of gravitational or electromagnetic fields on fluid motion.

It is shown in this paper that the effect of gravity on a stratified fluid is to inhibit steady motion in the direction of gravity; that, for small values of the magnetic viscosity, the effect of a main magnetic field is to make steady weak motions of a fluid independent of the distance along the lines of force; and that, again for small values of the magnetic viscosity, the effect of a uniform electric field is to make steady weak motions of a fluid rotationally symmetric with respect to an axis in the direction of the field. These results, together with a similar one of Proudman (1916) [1] for a fluid with general rotation, enable one to state that the effects of rotation, gravity, and electromagnetic fields (for small magnetic viscosity) are to endow the fluid with a certain anisotropic rigidity by “stiffening” it along the vorticity lines, the isopycnic surfaces or lines, or the lines of force, as the case may be. In the case of a weak steady motion or relative motion, this “stiffening” has the effect of reducing the a priori number of physical or at least mathematical dimensions of the motion by one.