Vortex evolution in non-axisymmetric impulsive spin-up from rest

Diane Marie Henderson, J. M. Lopez, D. L. Stewart

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

The flow evolution of water in a completely filled rectangular container, impulsively rotated from rest to a steady angular speed, is investigated experimentally and numerically. The pathlines of the fluid from rest to solid-body rotation primarily follow one of two possible configurations that have been described previously in the literature. The first, consisting of two cyclones that form following the separation and roll-up of the sidewall boundary layers and an anticyclone that forms subsequently, results in a pattern on the path to spin-up of cyclonic-anticyclonic-cyclonic vorticity. In the second configuration the cyclones migrate into the interior of the container and merge, resulting in a pattern on the path to spin-up of anticyclonic-cyclonic-anticyclonic vorticity. The experiments provide a parameterization of the possible evolutionary configurations as a function of horizontal and vertical aspect ratios and Reynolds numbers. Critical Reynolds numbers for vortex merger are determined experimentally. Evolutionary configurations in addition to the primary two are observed; in particular symmetry breaking occurs at high Reynolds numbers causing complicated patterns of flow evolution. For some flow conditions at high Reynolds numbers, more than one evolutionary pattern is observed for the same external parameters. The experiments are conducted with a rigid lid showing that a free surface is not required for vortex merger. Numerical integrations of the two-dimensional Navier-Stokes equations (a situation corresponding to the limiting case of a container of infinite depth, where there are no effects from the top and bottom and all flow is horizontal) reproduce qualitatively many of the features of the experimental observations, in particular the merger events. The numerical results show that neither vertical flow due to Ekman boundary layers at the top and bottom nor a free surface are necessary for the observed vortex merger.

Original languageEnglish (US)
Pages (from-to)109-134
Number of pages26
JournalJournal of Fluid Mechanics
Volume324
DOIs
StatePublished - Oct 10 1996

Fingerprint

Vortex flow
Reynolds number
vortices
Containers
containers
Vorticity
cyclones
high Reynolds number
Boundary layers
configurations
vorticity
boundary layers
anticyclones
Parameterization
Navier Stokes equations
Aspect ratio
numerical integration
parameterization
Experiments
Navier-Stokes equation

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

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abstract = "The flow evolution of water in a completely filled rectangular container, impulsively rotated from rest to a steady angular speed, is investigated experimentally and numerically. The pathlines of the fluid from rest to solid-body rotation primarily follow one of two possible configurations that have been described previously in the literature. The first, consisting of two cyclones that form following the separation and roll-up of the sidewall boundary layers and an anticyclone that forms subsequently, results in a pattern on the path to spin-up of cyclonic-anticyclonic-cyclonic vorticity. In the second configuration the cyclones migrate into the interior of the container and merge, resulting in a pattern on the path to spin-up of anticyclonic-cyclonic-anticyclonic vorticity. The experiments provide a parameterization of the possible evolutionary configurations as a function of horizontal and vertical aspect ratios and Reynolds numbers. Critical Reynolds numbers for vortex merger are determined experimentally. Evolutionary configurations in addition to the primary two are observed; in particular symmetry breaking occurs at high Reynolds numbers causing complicated patterns of flow evolution. For some flow conditions at high Reynolds numbers, more than one evolutionary pattern is observed for the same external parameters. The experiments are conducted with a rigid lid showing that a free surface is not required for vortex merger. Numerical integrations of the two-dimensional Navier-Stokes equations (a situation corresponding to the limiting case of a container of infinite depth, where there are no effects from the top and bottom and all flow is horizontal) reproduce qualitatively many of the features of the experimental observations, in particular the merger events. The numerical results show that neither vertical flow due to Ekman boundary layers at the top and bottom nor a free surface are necessary for the observed vortex merger.",
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Vortex evolution in non-axisymmetric impulsive spin-up from rest. / Henderson, Diane Marie; Lopez, J. M.; Stewart, D. L.

In: Journal of Fluid Mechanics, Vol. 324, 10.10.1996, p. 109-134.

Research output: Contribution to journalArticle

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