A two-dimensional, small-perturbation theory for the steady motion of thin lifting airfoils in an incompressible conducting fluid, with the uniform applied magnetic field perpendicular to (and in the plane of) the undisturbed, uniform flow field, is described. The conductivity of the fluid is assumed to be such that the magnetic Reynolds number, Rm, of the flow is large but finite. Within this assumption, a theory based on superposition of sinusoidal modes is constructed and applied to some simple thin airfoil problems.

It is shown that with this particular field geometry the Alfvén wave mechanism is important in making possible very deep penetration into the flow field of currents and their associated vorticity. It is also shown that the current penetration for an airfoil is much larger than for a wavy wall of wavelength equal to the airfoil chord.

A value of Rm = 5 is found to be a good approximation to infinity in this study; in fact, use of the present technique for values of Rm of the order of unity is permissible. These results provide an indication of what is meant by ‘large’ magnetic Reynolds number in two-dimensional magneto-aerodynamics.

A theory of a jet in a rotating, viscous fluid is developed. It is suggested that it may be related to a jet observed in an experiment with a rotating spherical shell of liquid and, in addition, may partly explain the existence of the subsurface equatorial current in the Pacific Ocean. The fundamental physical idea is that of a balance of vorticity brought into the jet by advection and diffused by friction. The necessary approximations are borrowed from boundary-layer theory. The linear case is solved completely and inferences about the non-linear jet are obtained by dimensional reasoning.

The model proposed by Phillips (1957) for the generation of water waves by the random fluctluations of normal pressure already present in a turbulent wind is generalized to include energy transfer associated with the interaction between surface wave and mean air flow (Miles 1957). It is found that this energy transfer may increase by an order of magnitude the surface displacements produced by a given distribution of pressure fluctuations in the principal stage of development.