Volume 22: Pages 19-21, 2009
Steady top-heavy shear flows
Kern E. Kenyon 1
14632 North Lane, Del Mar, California 92014-4134, USA
In a two-layer shear flow beneath a stationary rigid horizontal plate with a layer of denser fluid moving with uniform steady speed on top of a motionless less dense layer, it is argued that the flow regime will be maintained if a certain nondimensional number is unity. Dividing the speed of the upper layer by the square root of twice the thickness of the upper layer times reduced gravity gives the required nondimensional number, where reduced gravity means gravity times the positive difference in density between the two layers divided by the density of the top layer. Densities are constant in each layer, the fluids are immiscible, and surface tension and friction are neglected. Bernoulli’s law is central to the physical argument. Observations are needed for comparison with the theoretical prediction.
Keywords: Top-Heavy Shear Flows, Coanda Effect
Received: March 20, 2007; Accepted: December 2, 2008; Published Online: February 19, 2009