A working theory of the bent‐over plume of hot gas

Abstract

AbstractAn ascending plume of hot gas is initially diffused by the turbulence which is induced by its own motion and later, but before all upward motion and buoyancy are lost, by the natural turbulence of the environment. A working solution is put forward for the first phase in terms of a spreading coefficient c and for the second in terms of a mixing rate k, and it is shown that the transition from one phase to the other should be quite well marked. Proposed laws for c and k as functions of wind speed lead to good agreement with Bosanquet's measurements of plume heights downwind from factory chimneys.The theory extends to conditions of thermal stratification. It shows that a final equilibrium level should always exist except when very light winds coincide with unstable stratification, and it indicates the buoyancy and stratification factors appropriate for scaling down to wind‐tunnel experiments. The relative roles of initial impetus and initial buoyancy are characterized by a modified form of the Froude number.