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Boundary layer flow of air over water on a flat plate

Published online by Cambridge University Press:  26 April 2006

John J. Nelson ,
Amy E. Alving  and
Daniel D. Joseph
John J. Nelson
Affiliation:
United States Air Force Wright Laboratories, Wright-Patterson Air Force Base, OH 45433-7913, USA
Amy E. Alving
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, 110 Union Street, S.E., Minneapolis, MN 55455, USA
Daniel D. Joseph
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, 110 Union Street, S.E., Minneapolis, MN 55455, USA The Minnesota Supercomputer Institute, University of Minnesota, 110 Union Street, S.E., Minneapolis, MN 55455, USA
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Abstract

A non-similar boundary layer theory for air blowing over a water layer on a flat plate is formulated and studied as a two-fluid problem in which the position of the interface is unknown. The problem is considered at large Reynolds number (based on x), away from the leading edge. We derive a simple non-similar analytic solution of the problem for which the interface height is proportional to x1/4 and the water and air flow satisfy the Blasius boundary layer equations, with a linear profile in the water and a Blasius profile in the air. Numerical studies of the initial value problem suggest that this asymptotic non-similar air–water boundary layer solution is a global attractor for all initial conditions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 284 , 10 February 1995 , pp. 159 - 169
Copyright
© 1995 Cambridge University Press

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