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Viscous incompressible fluid flow along a flat plate is modeled by the Navier-Stokes equations with appropriate boundary conditions. A series solution is assumed and a set of three nonlinear ordinary differential equations is derived by truncating the series. The Reynolds number appears in these three equations as a parameter. These equations are solved by numerical integration. We show that these solutions exhibit qualitatively different behavior for different values of the Reynolds number of the fluid. The various modes include an asymptotic approach to a time-independent state, laminar (periodic) flow, and turbulence. We give several computer-generated pictures of the various modes.

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©1985 The American Physical Society