The development of a buoyant vortex in stationary and plane stagnation flows

Abstract : The evolution of a buoyant vortex (thermal) in stationary and irrotational plane stagnation flows (with vertical velocity opposing thermal's upward movement) is studied using both direct numerical simulation (DNS) and theoretical tools. The influence of external flow on the spatio-temporal development of the buoyant fluid is explored through the ratio τ between the two relevant time scales associated with the ambient flow and buoyancy (viscous and diffusive effects, although included, are taken to be relatively small). The evolution of the flows considered is governed by τ and initial height of the thermal. Once released from rest, thermal's evolution is composed of two stages: an initial phase in which circulation is being generated, followed by a phase where the circulation is approximately constant, and both separated by a transitional regime which is related to the formation of a 'hole' in the buoyant structure. Time evolution of vorticity and density fields, center of mass of the thermal and its circulation are tracked using DNS for different regimes. Application of Kelvin-Bjerknes' theorem shows that during the initial stage, circulation grows linearly with time before reaching a constant value. When τ is increased, the ambient fluid penetrates earlier into the buoyant mass, causing quicker formation of the buoyant vortex ring, reducing the attainable maximum circulation. To predict the integral quantities of the thermal, a simple inviscid Lagrangian model is proposed in which the initial disturbance is composed of a stack of thin vortex elements. The model predicts well the circulation and kinematic characteristics of the thermal during the less studied initial stage of the thermal's evolution. The evolution of the thermal is found to be governed by a feedback mechanism. Accordingly, it is shown that the generation of circulation is proportional to the temporal height of the disturbance which depends on the induced velocity (and the imposed base-flow velocity); this in-turn depends on the circulation and the shape of the disturbance. Finally, theoretical analysis (in agreement with DNS) shows that the fluid impulse of the thermal grows linearly in a stationary fluid, and is found to grow/decay exponentially in plane stagnation flow, the temporal evolution of which is only a function of the ratio τ (and its initial value).
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Contributeur : Denis Roura <>
Soumis le : vendredi 18 juillet 2014 - 08:40:34
Dernière modification le : jeudi 10 mai 2018 - 02:02:42

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Galon Alon, Jimmy Philip, Jacob Cohen. The development of a buoyant vortex in stationary and plane stagnation flows. European Journal of Mechanics - B/Fluids, Elsevier, 2011, 30 (3), pp.288-298. 〈10.1016/j.euromechflu.2011.02.001〉. 〈hal-01025506〉

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