The stability of unbounded two- and three-dimensional flows subject to body forces: some exact solutions

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Abstract
A formulation, previously employed to find exact Navier-Stokes solutions for planar disturbances in two- and three-dimensional flows with spatially uniform rates of strain, is here adapted to incorporate the contribution of various types of body force. In the absence of body forces, it is known that unbounded flows with constant vorticity and elliptical streamlines are unstable to certain planar disturbances, which are amplified by a Floquet mechanism. The influence of a Coriolis force upon this instability mechanism is here described in detail, as an illustration of the general formulation. The results are likely to be of geophysical interest and may also have relevance to the breakdown of closed-eddy structures in turbulence. The final section of the paper reviews other systems for which analogous exact solutions may be obtained.

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