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Non-axisymmetric instability of a rotating sheet of gas in a rotating environment

Published online by Cambridge University Press:  29 March 2006

Takeo Sakurai
Takeo Sakurai
Affiliation:
Department of Aeronautical Engineering, Faculty of Engineering, Kyoto University, Kyoto 606, Japan
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Abstract

We discuss non-axisymmetric instability of a thin cylindrical sheet of a gas which rotates concentrically with a rigidly rotating environment. For the sake of simplicity, we restrict ourselves to a linear single-mode analysis of a two-dimensional disturbance for which the axial component of the wavenumber vector vanishes. We further restrict ourselves to two limiting cases. In case 1 the gas can be treated as incompressible, while in case 2 the effect of radial stratification caused by the centrifugal force is extremely strong. In case 1 there are two unstable modes: a travelling and a stationary disturbance with respect to a system of co-ordinates which rotates with the environment. For each disturbance, we show the domains of instability on ρ vs. ω diagrams, where ρ is the density and ω is the angular velocity of the sheet non-dimensionalized with respect to those of the environment. A negative-viscosity phenomenon is also described. In case 2 both the travelling and the stationary disturbances are stabilized by the strong radial stratification. An outline of a WKB method of approximation is given.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 75 , Issue 3 , 11 June 1976 , pp. 513 - 524
Copyright
© 1976 Cambridge University Press

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