### Abstract

Language | English |
---|---|

Pages | 471-484 |

Number of pages | 14 |

Journal | Journal of Fluid Mechanics |

Volume | 648 |

Issue number | 1 |

DOIs | |

State | Published - 2010 |

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*Journal of Fluid Mechanics*, vol. 648, no. 1, pp. 471-484. DOI: 10.1017/S0022112009994034

**Scaling of decaying shallow axisymmetric swirl flows.** / Durán Matute, M.; Kamp, L.P.J.; Trieling, R.R.; Heijst, van, G.J.F.

Research output: Contribution to journal › Article › Academic › peer-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.

U2 - 10.1017/S0022112009994034

DO - 10.1017/S0022112009994034

M3 - Article

VL - 648

SP - 471

EP - 484

JO - Journal of Fluid Mechanics

T2 - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

IS - 1

ER -