Power Law Solutions for Vertical Plumes

This paper investigates solutions to the problem of a vertically rising turbulent plume generated when a source of light fluid is introduced into a heavier ambient fluid of large extent. The particular solutions considered are those in which the plume width, maximum velocity, and maximum density deficiency can be expressed as a simple power of the vertical distance. It is found that this type of solution exists not only for the well-known cases of point and line sources in a uniform ambient fluid, but also for certain cases of: (1) a finite area source in a uniform ambient fluid; and (2) a point, line or finite area source in a stably and unstably stratified fluid.