Vortex rings in axially rotating fluids

Terry, Helen (2019) Vortex rings in axially rotating fluids. PhD thesis, University of Nottingham.

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Abstract

Rotating turbulent flows are found in many geophysical, astrophysical and industrial applications. These turbulent flows can be considered to be comprised of a collection of coherent structures. An understanding of these smaller coherent structures can allow insight into the behaviour of the larger turbulent motion as a whole. This thesis focuses on the effect of rotation on one particular type of coherent structure - the vortex ring - and is motivated by the belief that greater knowledge of how individual vortex rings behave in rotating fluids will lead to a better understanding of rotating turbulent flows.

The first part of this thesis presents exact solutions of spherical vortices propagating steadily along the axis of a rotating ideal fluid. It is shown that Hill’s spherical vortex and Moffatt’s family of swirling vortices are able to persist in a rotating fluid with the boundary of the spherical vortex swirling in such a way as to exactly cancel out the background rotation of the system. The flow external to the spherical vortex exhibits fully nonlinear inertial wave motion and above a critical rotation rate, closed streamlines may form in this outer fluid region and hence carry fluid along with the spherical vortex. As the rotation rate is further increased, further concentric ‘sibling’ vortex rings are formed.

The latter part of this thesis is a numerical investigation into the effect of rotation on vortices in viscous fluids. The presence of azimuthal swirl is critical to vortex ring behaviour and similarities are drawn between the behaviour of swirling vortices in non-rotating flows and initially swirl-free vortex rings in rotating flows which subsequently induce swirl of their own. The findings corroborate past work that suggests vortex motion in rotating fluids can be highly unstable. However, the newly-discovered exact solutions of spherical vortices in rotating ideal fluids are then used to demonstrate that vortex motion in rotating viscous fluids need not be as unstable as previously thought.

Finally, as an extremal member of the Fraenkel-Norbury family of vortices this work contrasts the behaviour of Hill’s spherical vortex to vortex rings in this family with narrower vortex cores.

Item Type: Thesis (University of Nottingham only) (PhD)
Supervisors: Scase, Matthew
Billingham, John
Keywords: vortex rotating fluid, turbulent flows, vortices, vortex rings, hydrodynamics
Subjects: Q Science > QA Mathematics > QA801 Analytic mechanics
Faculties/Schools: UK Campuses > Faculty of Science > School of Mathematical Sciences
Item ID: 56753
Depositing User: Terry, Helen
Date Deposited: 04 Sep 2019 12:25
Last Modified: 07 May 2020 08:16
URI: http://eprints.nottingham.ac.uk/id/eprint/56753

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