Secondary Flows in an Incompressible Fluid of Varying Density in a Rotating Reference Frame

This paper presents the theory of secondary flow generation for an incompressible fluid of spatially varying density due to rotation of the frame of reference. It is pointed out that, while Coriolis forces may deflect the relative streamlines, the generation of secondary vorticity and secondary circulation generally requires an appropriately oriented momentum gradient. In particular, secondary vorticity will not be generated by rotation of the frame of reference in the absence of momentum gradients perpendicular to the flow direction when the streamlines are plane curves. Consideration is given to the rotating dishpan experiment and to the apparently analogous physical examples of the vortex formation when water drains very slowly from a large tank, and the generation of circulation in a hurricane.