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The steady oblique path of buoyancy-driven disks and spheres

Published online by Cambridge University Press:  19 July 2012

David Fabre ,
Joël Tchoufag  and
Jacques Magnaudet
David Fabre
Affiliation:
Université de Toulouse; INPT, UPS; IMFT (Institut de Mécanique des Fluides de Toulouse); Allée Camille Soula, F-31400 Toulouse, France
Joël Tchoufag
Affiliation:
Université de Toulouse; INPT, UPS; IMFT (Institut de Mécanique des Fluides de Toulouse); Allée Camille Soula, F-31400 Toulouse, France
Jacques Magnaudet*
Affiliation:
Université de Toulouse; INPT, UPS; IMFT (Institut de Mécanique des Fluides de Toulouse); Allée Camille Soula, F-31400 Toulouse, France CNRS; IMFT; F-31400 Toulouse, France
*
†Email address for correspondence: magnau@imft.fr
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Abstract

We consider the steady motion of disks of various thicknesses in a weakly viscous flow, in the case where the angle of incidence (defined as that between the disk axis and its velocity) is small. We derive the structure of the steady flow past the body and the associated hydrodynamic force and torque through a weakly nonlinear expansion of the flow with respect to . When buoyancy drives the body motion, we obtain a solution corresponding to an oblique path with a non-zero incidence by requiring the torque to vanish and the hydrodynamic and net buoyancy forces to balance each other. This oblique solution is shown to arise through a bifurcation at a critical Reynolds number which does not depend upon the body-to-fluid density ratio and is distinct from the critical Reynolds number corresponding to the steady bifurcation of the flow past the body held fixed with . We then apply the same approach to the related problem of a sphere that weakly rotates about an axis perpendicular to its path and show that an oblique path sets in at a critical Reynolds number slightly lower than , in agreement with available numerical studies.

JFM classification

Nonlinear Dynamical Systems: Bifurcation Aerodynamics: Flow-structure interactions Wakes/Jets: Wakes
Type
Papers
Information
Journal of Fluid Mechanics , Volume 707 , 25 September 2012 , pp. 24 - 36
Copyright
Copyright © Cambridge University Press 2012

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