|M.Sc Student||Alon Gali|
|Subject||The Development of a Buoyant Vortex (Thermal) in Stagnant|
and Irrotational Shear Flows
|Department||Department of Aerospace Engineering||Supervisor||Professor Jacob Cohen|
|Full Thesis text|
The evolution of a buoyant vortex (thermal) in stationary and irrotational plane stagnation flows 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 development of thermals released from rest is composed of two phases: an initial phase in which circulation is being generated, followed by a subsequent phase where the circulation is constant. The transition between the first and the second stages is related to the formation of a ‘hole’ in the buoyant structure. Numerical simulations show that in comparison with the stationary case, when stagnation base-flow is applied the ambient fluid penetrates earlier into the buoyant mass, causing quicker formation of the buoyant vortex ring. Consequently, the growth of circulation ceases earlier resulting in a lower value of the maximum circulation.
The initial growth rate of the circulation is theoretically predicted to be proportional to the density difference and the vertical extension along the structure’s symmetry line. This prediction is verified numerically by varying the initial density difference and the disturbance’s geometry. In an attempt to describe the time development of the circulation, a simple inviscid Lagrangian model is proposed. Accordingly, the initial disturbance is composed of a series of thin elements placed one on top of the other. The growth of the circulation is determined by applying Kelvin-Bjerknes’ theorem and assuming volume conservation. Employing the model, the circulation growth during the less studied initial stage of the thermal’s evolution is well predicted. For stronger stagnation flows, the prediction is valid for longer times. Finally, theoretical analysis verified numerically, shows that the fluid impulse grows linearly in a stationary fluid, and is found to grow/decay exponentially in plane stagnation flow. The temporal evolution of the fluid impulse depends only on the ratio τ (and its initial value).