Some Likely behaviours for Axisymmetric Rising Plumes in a Quiescent uniform Ambient through Warm Discharge

An investigation into some possible behaviours of rising plumes with a quadratic dependence relation assumption was made with the consideration that the plumes arises from a virtual sources. Our results showed that both forced and pure plumes provides buoyancy flux at the source. Meanwhile, the lazy plume rises with a significant volume flux and finite temperature with zero volume flux for both the forced plume and pure at the source. The forced plume also possesses some significant upward momentum flux and zero momentum flux for the pure plume. Determination of zero-buoyancy height and the fountain-top height are key when it comes to rising plumes. If the ambient water depth into consideration is less than the zero-buoyancy height then the warm water will definitely spread outwards as surface gravity current; otherwise, it will form a fountain.Our results showed that the upward momentum flux attains its pick at; and changes sign in the buoyancy force at this point while the momentum flux tends to zero with a finite final volume flux Qf from its maximum rise height. Meanwhile, as M0 approaches the value , so the Qf and the Q0 tends to the value. It is worth stating also that the fountain-top height will be of great significant if the focus is on erosion of an ice cover. We therefore suggest maintaining a low source Froude number which will result to minimising impact on the lake floor or on the surface. Though, some level of carefulness is needed whenever we intend to make use of the present results to foretell the behaviour of real plumes. In particular, if laboratory experiments are required either to examine the theory or to model larger-scale flows in the environment. Lastly, with the entrainment model, it is required that the plume will be fully turbulent, a condition usually obtained with a Reynolds number Re > 2000. This can be likened to the power station warm discharge which will definitely be fully turbulent with it large volume flux. These are basic conditions on the validity of the assumptions. There are some limitations as stated in the conclusion. But then, the overall numerical results here are very good as they present us with more insight into rising plume with the quadratic dependence relation assumption.