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J. Bradford
,
A. S. Berman
, and
T. S. Lundgren

Abstract

The interfacial stability of two differentially rotating fluid layers in a tall, right circular cylinder is investigated analytically and experimentally. The differential speeds are such that the Ekman and Rossby numbers of the flow are small. A linearized stability analysis, including interfacial tension and viscous effects at the interface and end caps is performed on the nongeostrophic equations of motion. The nongeostrophic nature of the perturbed flow is due to the large height to radius ratio of the cylinder. The results yield stability boundaries which can be compared to quasi-geostrophic predictions for the same system. The nongeostrophic effects are found to stabilize the flow relative to the quasi-geostrophic predictions with the exception of narrow regions or “spikes” of instability in parameter space which are not accounted for by the quasi-geostrophic equations.

Experiments are conducted in which stability boundaries corresponding to wavenumbers n = 1 and n = 2 are determined. Good agreement is found with the viscous, nongeostrophic predictions, including a clear experimental reproduction of the distinctive “spike regions”. Qualitative observations also are made of amplitude and frequency modulated finite-amplitude baroclinic waves in the unstable regions.

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