Scaling of decaying shallow axisymmetric swirl flows

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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.
TaalEngels
Pagina's471-484
Aantal pagina's14
TijdschriftJournal of Fluid Mechanics
Volume648
Nummer van het tijdschrift1
DOI's
StatusGepubliceerd - 2010

Vingerafdruk

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

Citeer dit

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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.",
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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, Nr. 1, 2010, blz. 471-484.

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

TY - JOUR

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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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