Elliptical instability of a rapidly rotating, strongly stratified fluid

The elliptical instability of a rotating stratified fluid is examined in the regime of small Rossby number and order-one Burger number corresponding to rapid rotation and strong stratification. The Floquet problem describing the linear growth of disturbances to an unbounded, uniform-vorticity elliptical flow is solved using exponential asymptotics. The results demonstrate that the flow is unstable for arbitrarily strong rotation and stratification; in particular, both cyclonic and anticyclonic flows are unstable. The instability is weak, however, with growth rates that are exponentially small in the Rossby number. The analytic expression obtained for the growth rate elucidates its dependence on the Burger number and on the eccentricity of the elliptical flow. It explains in particular the weakness of the instability of cyclonic flows, with growth rates that are only a small fraction of those obtained for the corresponding anticyclonic flows. The asymptotic results are confirmed by numerical solutions of Floquet problem.Comment: 17 page

Effects of deleting cannabinoid receptor-2 on mechanical and material properties of cortical and trabecular bone

Acknowledgements We thank Dr J.S. Gregory for assistance with Image J and Mr K. Mackenzie for assistance with Micro-CT analysis. Funding ABK was funded by a University of Aberdeen, Institute of Medical Sciences studentship and the Overseas Research Students Awards Scheme.Peer reviewedPublisher PD

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Copyright 2013 Elsevier B.V., All rights reserved.Peer reviewedPreprin

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