FORCED, ANGLED PLUMES

In this paper a simple mathematical model is used to describe the curved, turbulent plume formed by injecting a constant flux of buoyant fluid into a stationary, unstratified ambient at an angle to the vertical. The main assumptions are the entrainment assumption: the entrainment into the turbulent plume is at a rate proportional to the local mean along-plume velocity, and the Boussinesq approximation: the density difference between the plume and the ambient is relatively small. A unified theory is presented which allows practical predictions to be made of plume trajectories and concentrations without recourse to complex turbulent modelling. It is found that all such plumes can be traced back to a virtual origin, and that the shape of the plume depends only on the angle of the plume to the vertical at the virtual origin. Various properties of the plume such as mean velocity, radius and density are predicted as functions of distance along the plume. Angled plumes made in laboratory experiments are described and compared with the theoretical predictions. The applications and limitations of the theoretical model are discussed.