Solutions for the flows induced by lazy, forced and pure turbulent plumes
In this thesis an analytical modelling approach is employed to predict and gain insight into the flows induced by turbulent plumes and jets above slender horizontal slots, in otherwise quiescent uniform environments. To supplement the solutions, the effect on the environment of a plume driven by an off-source supply of buoyancy was also considered. The solutions derived provide an advancement on existing idealised models for the jet and plume induced flows, and moreover, complement a number of key advances that have been made in our understanding of plume flows in recent years. The theory of functions of a complex variable, which has not previously been applied in such an application, has been utilised as a fundamental tool throughout the work. This has enabled the entrainment behaviour and geometry of the plumes to be accounted for when developing the induced flow solutions. A novel conformal mapping has been devised specifically to account for the curved perimeter of the contracting lazy plume. This modelling approach is robust in that future developments to aspects of the modelling, for instance, the formulation of a new entrainment closure, can be straightforwardly accounted for using the method. The induced flow solutions exhibit a range of flow patterns which are dependent on the source Richardson number of the plume flow. A pure plume induces a uniform horizontal flow. Forced and lazy plumes correspond to a relative deficit and excess in source buoyancy flux compared to the pure plume, respectively. Generally, forced plumes induce downwardly inclined flows, in contrast to lazy plumes, which induce upwardly inclined flows. Consistent with these solutions, the notionally lazy plume driven by a vertical uniform off-source supply of buoyancy induces an upwardly inclined flow. In addition to an improved understanding of induced flows, our solutions have provided us with insight into the plume flow. Notably, the solution corresponding to the forced plume has led us to fundamentally question existing models describing the plume and, in particular, closures that have been employed to model entrainment. We find that the existing well accepted closures exhibit some form of non-physical flow behaviour.
Plumes, Induced flows, Lazy, Forced, Entrainment, Mathematical modelling, Conformal mapping, Theory of functions of a complex variable
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