Structure of a Bathtub Vortex : Importance of the Bottom Boundary Layer - CNRS - Centre national de la recherche scientifique Accéder directement au contenu
Article Dans Une Revue Theoretical and Computational Fluid Dynamics Année : 2010

Structure of a Bathtub Vortex : Importance of the Bottom Boundary Layer

Résumé

A bathtub vortex in a cylindrical tank rotating at a constant angular velocity [omega] is studied by meansof a laboratory experiment, a numerical experiment and a boundary layer theory. The laboratory and numerical experiments show that two regimes of vortices in the steady-state can occur depending on [omega] and the volume flux Q through the drain hole: when Q is large and [omega] is small, a potential vortex is formed in which angular momentum outside the vortex core is constant in the non-rotating frame. However, when Q is small or [omega] is large, a vortex is generated in which the angular momentum decreases with decreasing radius. Boundary layertheory shows that the vortex regimes strongly depend on the theoretical radial volume flux through the bottomboundary layer under a potential vortex : when the ratio of Q to the theoretical boundary-layer radial volume flux Qb (scaled by 2π R2([omega] ν)12 ) at the outer rim of the vortex core is larger than a critical value (of order 1), the radial flow in the interior exists at all radiiand Regime I is realized, where R is the inner radius of the tank and ν the kinematicviscosity.When the ratio is less than the critical value, the radial flow in the interior nearlyvanishes inside a critical radius and almost all of the radial volume flux occurs only in the boundary layer,resulting in Regime II in which the angular momentum is not constant with radius. This criterion is found to explain the results of the laboratory and numerical experiments very well.
Fichier principal
Vignette du fichier
Yukimoto_10172.pdf (106.62 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03545896 , version 1 (27-01-2022)

Identifiants

Citer

Shinji Yukimoto, Hiroshi Niino, Takashi Noguchi, Ryuji Kimura, Frédéric Moulin. Structure of a Bathtub Vortex : Importance of the Bottom Boundary Layer. Theoretical and Computational Fluid Dynamics, 2010, 24 (1-4), pp.323-327. ⟨10.1007/s00162-009-0128-3⟩. ⟨hal-03545896⟩
15 Consultations
35 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More