3. Kern E. Kenyon, Steady top-heavy shear flows

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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