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Applications of exact solutions to the Navier–Stokes equations: free shear layers

Published online by Cambridge University Press:  26 April 2006

Eric Varley  and
Brian R. Seymour
Eric Varley
Affiliation:
Department of Mechanical Engineering, Lehigh University, Bethlehem, PA. 18017, USA
Brian R. Seymour
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, V6T 1Z2, Canada
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Abstract

A family of exact solutions to the Navier—Stokes equations is used to analyse unsteady three-dimensional viscometric flows that occur in the vicinity of a plane boundary that translates and rotates with time-varying velocities. Such flows are important in the study of flows that are produced by rotating machinery. They are also useful in describing local behaviour in more complex global flows, such as that produced in a shear layer by the passage of a disturbance in the mainstream. An example is the flow produced in a turbulent shear layer by the passage of the core of a Rankine vortex. When the effect of viscosity is unimportant, the use of Lagrangian coordinates reduces the mathematical problem to that of solving a set of linear ordinary differential equations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 274 , 10 September 1994 , pp. 267 - 291
Copyright
© 1994 Cambridge University Press

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