Scaling of decaying shallow axisymmetric swirl flows

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Abstract

There is a lack of rigour in the usual explanation for the scaling of the vertical velocity of shallow flows based on geometrical arguments and the continuity equation. In this paper we show, by studying shallow axisymmetric swirl flows, that the dynamics of the flow are crucial to determine the proper scaling. In addition, we present two characteristic scaling parameters for such flows: Red2 for the radial velocity and Red3 for the vertical velocity, where Re is the Reynolds number of the swirl flow and d=H/L is the flow aspect ratio with H the fluid depth and L a typical horizontal length scale. This scaling contradicts the common assumption that the vertical velocity should scale with the primary motion proportional to the aspect ratio d. Moreover, if this scaling applies, then the primary flow can be considered as quasi-two-dimensional. Numerical simulations of a decaying Lamb–Oseen vortex served to test the analytical results and to determine their range of validity. It was found that the primary flow can be considered as quasi-two-dimensional only if dRe1/23 and dRe1/31.
LanguageEnglish
Pages471-484
Number of pages14
JournalJournal of Fluid Mechanics
Volume648
Issue number1
DOIs
StatePublished - 2010

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axisymmetric flow
scaling
Aspect ratio
aspect ratio
Vortex flow
Reynolds number
continuity equation
Fluids
Computer simulation
radial velocity
vortices
fluids

Cite this

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title = "Scaling of decaying shallow axisymmetric swirl flows",
abstract = "There is a lack of rigour in the usual explanation for the scaling of the vertical velocity of shallow flows based on geometrical arguments and the continuity equation. In this paper we show, by studying shallow axisymmetric swirl flows, that the dynamics of the flow are crucial to determine the proper scaling. In addition, we present two characteristic scaling parameters for such flows: Red2 for the radial velocity and Red3 for the vertical velocity, where Re is the Reynolds number of the swirl flow and d=H/L is the flow aspect ratio with H the fluid depth and L a typical horizontal length scale. This scaling contradicts the common assumption that the vertical velocity should scale with the primary motion proportional to the aspect ratio d. Moreover, if this scaling applies, then the primary flow can be considered as quasi-two-dimensional. Numerical simulations of a decaying Lamb–Oseen vortex served to test the analytical results and to determine their range of validity. It was found that the primary flow can be considered as quasi-two-dimensional only if dRe1/23 and dRe1/31.",
author = "{Dur{\'a}n Matute}, M. and L.P.J. Kamp and R.R. Trieling and {Heijst, van}, G.J.F.",
year = "2010",
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Scaling of decaying shallow axisymmetric swirl flows. / Durán Matute, M.; Kamp, L.P.J.; Trieling, R.R.; Heijst, van, G.J.F.

In: Journal of Fluid Mechanics, Vol. 648, No. 1, 2010, p. 471-484.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Scaling of decaying shallow axisymmetric swirl flows

AU - Durán Matute,M.

AU - Kamp,L.P.J.

AU - Trieling,R.R.

AU - Heijst, van,G.J.F.

PY - 2010

Y1 - 2010

N2 - There is a lack of rigour in the usual explanation for the scaling of the vertical velocity of shallow flows based on geometrical arguments and the continuity equation. In this paper we show, by studying shallow axisymmetric swirl flows, that the dynamics of the flow are crucial to determine the proper scaling. In addition, we present two characteristic scaling parameters for such flows: Red2 for the radial velocity and Red3 for the vertical velocity, where Re is the Reynolds number of the swirl flow and d=H/L is the flow aspect ratio with H the fluid depth and L a typical horizontal length scale. This scaling contradicts the common assumption that the vertical velocity should scale with the primary motion proportional to the aspect ratio d. Moreover, if this scaling applies, then the primary flow can be considered as quasi-two-dimensional. Numerical simulations of a decaying Lamb–Oseen vortex served to test the analytical results and to determine their range of validity. It was found that the primary flow can be considered as quasi-two-dimensional only if dRe1/23 and dRe1/31.

AB - There is a lack of rigour in the usual explanation for the scaling of the vertical velocity of shallow flows based on geometrical arguments and the continuity equation. In this paper we show, by studying shallow axisymmetric swirl flows, that the dynamics of the flow are crucial to determine the proper scaling. In addition, we present two characteristic scaling parameters for such flows: Red2 for the radial velocity and Red3 for the vertical velocity, where Re is the Reynolds number of the swirl flow and d=H/L is the flow aspect ratio with H the fluid depth and L a typical horizontal length scale. This scaling contradicts the common assumption that the vertical velocity should scale with the primary motion proportional to the aspect ratio d. Moreover, if this scaling applies, then the primary flow can be considered as quasi-two-dimensional. Numerical simulations of a decaying Lamb–Oseen vortex served to test the analytical results and to determine their range of validity. It was found that the primary flow can be considered as quasi-two-dimensional only if dRe1/23 and dRe1/31.

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