A note on the stability of columnar vortices

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Abstract
Recently, Leibovich & Stewartson (1983) developed a sufficient condition for the instability of columnar vortices with radial shears in both the azimuthal and axial velocities, while others (e.g. Staley & Gall 1984) have found instabilities in numerical simulations which conform exactly to expectations based on the Leibovich-Stewartson theory. The purpose of this brief note is to show that this three-dimensional stability problem is isomorphic to the classical two-dimensional inertialThe instability discussed here is sometimes referred to as ‘centrifugal instability’. stability problem when viewed in an appropriate local coordinate system. The instability is therefore clearly inertial in character, as suggested by Pedley (1969).

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