title: Drag of buoyant vortex rings.
abstract: Extending from the model proposed by Vasel-Be-Hagh et al. [J. Fluid Mech. 769, 522 (2015)], a perturbation analysis is performed to modify Turner's radius by taking into account the viscous effect. The modified radius includes two terms; the zeroth-order solution representing the effect of buoyancy, and the first-order perturbation correction describing the influence of viscosity. The zeroth-order solution is explicit Turner's radius; the first-order perturbation modification, however, includes the drag coefficient, which is unknown and of interest. Fitting the photographically measured radius into the modified equation yields the time history of the drag coefficient of the corresponding buoyant vortex ring. To give further clarification, the proposed model is applied to calculate the drag coefficient of a buoyant vortex ring at a Bond number of approximately 85; a similar procedure can be applied at other Bond numbers.
authors.affiliation: Turbulence and Energy Laboratory, Lumley Centre for Engineering Innovation, University of Windsor, Ontario N9B 3P4, Canada.
authors.forename: Ahmadreza
authors.initials: A
authors.lastname: Vasel-Be-Hagh
authors.affiliation: Turbulence and Energy Laboratory, Lumley Centre for Engineering Innovation, University of Windsor, Ontario N9B 3P4, Canada.
authors.forename: Rupp
authors.initials: R
authors.lastname: Carriveau
authors.affiliation: Turbulence and Energy Laboratory, Lumley Centre for Engineering Innovation, University of Windsor, Ontario N9B 3P4, Canada.
authors.forename: David S-K
authors.initials: DS
authors.lastname: Ting
authors.affiliation: Research School of Earth Sciences, Australian National University, Canberra, ACT 0200, Australia.
authors.forename: John Stewart
authors.initials: JS
authors.lastname: Turner