Title

Instability and mode interactions in a differentially driven rotating cylinder

Authors

Authors

J. M. Lopez; J. E. Hart; F. Marques; S. Kittelman;J. Shen

Comments

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Abbreviated Journal Title

J. Fluid Mech.

Keywords

BAROCLINIC INSTABILITY; SHEAR-FLOW; GEOMETRY; LAYERS; WAVE; Mechanics; Physics, Fluids & Plasmas

Abstract

The flow in a completely filled rotating cylinder driven by the counter-rotation of the top endwall is investigated both numerically and experimentally. The basic state of this system is steady and axisymmetric, but has a rich structure in the radial and axial directions. The most striking feature, when the counter-rotation is sufficiently large, is the separation of the Ekman layer on the top endwall, producing a free shear layer that separates regions of flow with opposite senses of azimuthal velocity. This shear layer is unstable to azimuthal disturbances and a supercritical symmetry-breaking Hopf bifurcation to a rotating wave state results. For height-to-radius ratio of 0.5 and Reynolds number (based on cylinder radius and base rotation) of 1000, rotating waves with azimuthal wavenumbers 4 and 5 co-exist and are stable over an extensive range of the ratio of top to base rotation. Mixed modes and period doublings are also found, and a bifurcation diagram is determined. The agreement between the Navier-Stokes computations and the experimental measurements is excellent. The simulations not only capture the qualitative features of the multiple states observed in the laboratory, but also quantitatively replicate the parameter values over which they are stable, and produce accurate precession frequencies of the various rotating waves.

Journal Title

Journal of Fluid Mechanics

Volume

462

Publication Date

1-1-2002

Document Type

Article

Language

English

First Page

383

Last Page

409

WOS Identifier

WOS:000177385900016

ISSN

0022-1120

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