Computer Studies of Time-Dependent Turbulent Flows

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Abstract
Two aspects of turbulence can be studied with existing computer technology. One of these is the study of the initial stages in the breakdown of a laminar flow into turbulence. The other is the study of the gross effects of turbulence on a mean flow. The laminar instability problem is hampered by difficulties in calculating high Reynolds number flows, because finite difference approximations introduce diffusionlike truncation errors that can obscure the effects of a real viscosity. These errors also influence the computational stability of numerical solutions. If only the mean effects of turbulence on a flow are of interest, the difficulties in calculating high Reynolds number flows can usually be avoided, because the effective turbulent viscosity is often larger than the molecular viscosity and is not as likely to be obscured by finite difference errors. A method of this type is presented, in which the turbulence is characterized by three field variables: a turbulence energy density, a turbulence viscosity, and a turbulence scale of size. These variables satisfy transport equations describing convection, creation, diffusion, and decay processes. Since these equations are highly nonlinear, numerical solutions are necessary to extract their full potential.