On the hydrodynamic and hydromagnetic stability of swirling flows

Some general stability criteria for non-dissipative swirling flows are derived, and extended to the case of an electrically conducting fluid in the presence of axial magnetic field and current. In particular it is shown that the analogy between a rotating and a stratified fluid holds in this case, and that an important determinant of stability is a ‘Richardson number’ based on the analogue of the density gradient and the shear in the axial flow.