The unsteady flow within a rotating torus

J. P. Denier, R. J. Clarke, R. E. Hewitt, A. L. Hazel

Research output: Chapter in Book/Report/Conference proceedingConference abstractpeer-review

Abstract

We consider the temporal evolution of a viscous incompressible fluid in a torus of finite curvature; a problem first investigated by Madden and Mullin (1994), herein referred to as MM. The system is initially in a state of rigid-body rotation (about the axis of rotational symmetry) and the container's rotation rate is then changed impulsively. We describe the transient flow that is induced at small values of the Ekman number, over a time scale that is comparable to one complete rotation of the container. We show that (rotationally symmetric) eruptive singularities (of the boundary layer) occur at the inner or outer bend of the pipe for a decrease or an increase in rotation rate respectively. Moreover, there is a ratio of initial-to-final rotation frequencies for which eruptive singularities can occur at both the inner and outer bend simultaneously. We also demonstrate that the flow is susceptible to a combination of axisymmetric centrifugal and non-axisymmetric inflectional instabilities. The inflectional instability arises as a consequence of the developing eruption and is shown to be in qualitative agreement with the experimental observations of MM. Detailed quantitative comparisons are made between asymptotic predictions and finite (but small) Ekman number Navier-Stokes computations using a finite-element method.

Original languageEnglish
Title of host publicationEuropean Turbulence Conference 14
Subtitle of host publicationaccepted talks proceedings
Number of pages2
Publication statusPublished - 2013
Externally publishedYes
EventEuropean Turbulence Conference (14th : 2013) - Lyon, France
Duration: 1 Sep 20134 Sep 2013

Conference

ConferenceEuropean Turbulence Conference (14th : 2013)
Abbreviated titleetc14
CountryFrance
CityLyon
Period1/09/134/09/13

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