Spin-up and spin-down in a half cone: A pathological situation or not?


Li, L., Patterson, M. D., Zhang, K. and Kerswell, R., 2012. Spin-up and spin-down in a half cone: A pathological situation or not? Physics of Fluids, 24 (11), 116601.

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    The spin-up and spin-down of a fluid in a rapidly-rotating, fluid-filled, closed half cone is studied both numerically and experimentally. This unusual set up is of interest because it represents a pathological case for the classical linear theory of Greenspan & Howard (J. Fluid Mech., 17, 385, 1963) since there are no closed geostrophic contours nor a denumerable set of inertial waves (even a modified theory incorporating Rossby waves by Pedlosky & Greenspan - J. Fluid Mech., 27, 291, 1967 - relies on geostrophy to leading order). The linearised spin-up/-down dynamics in a half cone is found to dominated by topographical effects which force an ageostrophic leading balance and cause the large-scale starting vorticity to coherently move into the 'westward' corner of the half cone for both spin-up and spin-down. Once there, viscous boundary layer effects take over as the dominant process ensuring that the spin-up/-down time scales conventionally with E^{−1/2} , where E is the Ekman number. The numerical coefficient in this timescale is approximately a quarter of that for a full cone when the semi-angle is 30^o . Nonlinear spin up from rest is also studied as well as an impulsive 50% reduction in the rotation rate which shows boundary layer separation and small scales. We conclude that spin-up in a rapidly-rotating half cone is not pathological because the fluid dynamics is fundamentally the same as that in a container with small topography: in both topography-forced vortex stretching is to the fore.


    Item Type Articles
    CreatorsLi, L., Patterson, M. D., Zhang, K. and Kerswell, R.
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    URLURL Type
    DepartmentsFaculty of Engineering & Design > Architecture & Civil Engineering
    Research CentresCentre for Space, Atmospheric and Oceanic Science
    Publisher StatementPhysFluids_24_116601.pdf: Copyright 2013 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Li, L, Patterson, MD, Zhang, K & Kerswell, R 2012, 'Spin-up and spin-down in a half cone: A pathological situation or not?' Physics of Fluids, vol 24, no. 11, 116601 and may be found at
    ID Code28281


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