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An experimental and analytical study of instability of asymmetric jetstream-like currents in a rotating fluid

Published online by Cambridge University Press:  29 March 2006

Martin Dunst
Affiliation:
Meteorologisches Institut, Universität Hamburg

Abstract

Considering the barotropic instability problem of the mean westerly current in the atmosphere we have performed a series of experiments in a rotating vessel (using water and a barotropic model) to study the behaviour of a zonal asymmetric basic current with respect to small perturbations. In the centre of a rotating cylindrical vessel (of large diameter and rotation rate ω) a smaller cylinder was installed, the rotation of which relative to the vessel, at a rate Δω, generates a nearly two-dimensional field of mean relative motion within a sharply defined region. The dominant zonal velocity component $\overline{v}$ shows monotonic radial decrease within this so-called friction zone. Now what happens if the relative rotation of the inner cylinder, the source of momentum, suddenly vanishes, i.e. δΩ = 0? The main result is that the basic zonal current $\overline{v}$, which now has an asymmetric radial profile ($\overline{v} = 0 $ at the inner cylinder and the outer edge of the friction zone), breaks down into vortices, the number of which, the integer wavenumber n, is a function of the parameter ε = δω/ω alone: n = n(ε); increasing ε eff effects a decrease of n. For a theoretical discussion of the experimental results we assume this to be a problem of barotropic instability and base our analytical considerations on the two-dimensional non-divergent vorticity equation, frictional forces being neglected. By applying a perturbation method and prescribing a realistic asymmetric basic current we can derive the relation ν = {[¾π/ln (ε + 1)½]2 + 1}½, which yields the real wavenumber v as a function of the parameter ε = δω/ω. The analytical results are in good agreement with the experiments.

Type
Research Article
Copyright
© 1973 Cambridge University Press

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References

Dunst, M. 1972 An experimental and analytical investigation of angular momentum exchange in a rotating fluid. J. Fluid Mech. 55, 301310.Google Scholar
Foote, J. R. & Lin, C. C. 1950 Some recent investigations in the theory of hydrodynamic stability. Quart. Appl. Math. 8, 265280.Google Scholar
Kuo, H. L. 1949 Dynamic instability of two-dimensional non-divergent flow in a barotropic atmosphere. J. Meteor. 6, 105122.Google Scholar
Lin, C. C. 1953 On the stability of the laminar mixing region between two parallel streams in a gas. N.A.C.A. Tech. Note, no. 2887, pp. 2021.Google Scholar
Lin, C. C. 1966 The Theory of Hydrodynamic Stability, pp. 122123. Cambridge University Press.
Lipps, F. B. 1962 The barotropic stability of the mean winds in the atmosphere. J. Fluid Mech. 12, 397407.Google Scholar
Long, R. R. 1960 A laminar planetary jet. J. Fluid Mech. 7, 632638.Google Scholar