Date of Original Version
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.
DeJesus, E. X., & Kaufman, C. (1985). Nonperiodic flow in the numerical integration of a nonlinear differential equation of fluid dynamics. Physical Review A, 31(2), 903-909. doi: 10.1103/PhysRevA.31.903
Available at: http://dx.doi.org/10.1103/PhysRevA.31.903