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A note on the stability of columnar vortices

Published online by Cambridge University Press:  20 April 2006

Kerry A. Emanuel
Affiliation:
Center for Meteorology and Physical Oceanography, MIT, Cambridge, MA 02139

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).

Type
Research Article
Copyright
© 1984 Cambridge University Press

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References

Emanuel, K. A. 1979 Inertial instability and mesoscale convective systems. Part I: Linear theory of inertial instability in rotating viscous fluids. J. Atmos. Sci. 36, 24252449.Google Scholar
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Howard, L. N. & Gupta, A. S. 1962 On the hydrodynamic and hydromagnetic stability of swirling flows. J. Fluid Mech. 14, 463476.Google Scholar
Leibovich, S. & Stewartson, K. 1983 A sufficient condition for the instability of columnar vortices. J. Fluid Mech. 126, 335356.Google Scholar
Pedley, T. J. 1969 On the instability of viscous flow in a rapidly rotating pipe. J. Fluid Mech. 35, 97115.Google Scholar
Rotunno, R. 1978 A note on the stability of a cylindrical vortex sheet. J. Fluid Mech. 87, 761771.Google Scholar
Staley, D. O. & Gall, R. L. 1984 Hydrodynamic instability of small eddies in a tornado vortex. J. Atmos. Sci. 41, 422429.Google Scholar
Ward, N. B. 1972 The exploration of certain features of tornado dynamics using a laboratory model. J. Atmos. Sci. 29, 11941204.Google Scholar
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