- In the first issue of Journal of Fluid Mechanics Ian Proudman published a paper on the dynamical properties of a fluid between two concentric rotating spheres (Proudman, 1956). The angular velocities of the spheres were assumed only slightly different and the Reynolds number of the flow was large. It was found under non-slip boundary conditions that the cylindrical surface that touches the inner sphere and parallel to the axis of rotation is a singular surface in which velocity gradients are very large. Outside the cylinder the fluid rotates as a rigid body with the same angular velocity as the outer sphere. Inside the cylinder the fluid rotates with an angular velocity intermediate to the angular velocities of the spheres and there is also a meridional circulation. Later Stewartson (1966) presented a detailed investigation of structure of the shear layer near the cylindrical surface. One of the present authors (Ruzmaikin, 1989) pointed out a possible geophysical importance of these solutions. The liquid part of the Earth core occupying a shell between the inner solid core and the rock mantle can be considered as the fluid between two rotating spheres.