Motion of Two-Dimensional Starting Plume

Dimensional analysis is used to show that the shape and velocity distribution of a two-dimensional starting plume when expressed in a dimensionless form is a constant and that the ratio of the velocity of the leading edge to the third power of the flux of density difference times the gravitational constant from the line source is a constant, C. Experiments in which velocities were measured with neutrally buoyant particles were carried out showing that the plume consisted of a cylindrical cap and a wedge shaped tail and that the ratio of the radius of the cylinder to the total length of the plume, n, was approximately one third. The value of C was 1.20 with a standard deviation of 0.03. A model in which the cap is treated as a solid moving cylinder was used to obtain a relationship between C and the rate of spread. A distribution of doublets, sources and sinks was found which defined the flow field outside the vorticity-containing region.