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Nonlinear structures of transition in wall-bounded flows. (English) Zbl 0708.76075

Summary: We review recent developments on the numerical simulation of flow structures evolving during the nonlinear stages of transition to turbulence in wall-bounded flows. Plane Poiseuille flow and the Blasius boundary layer are considered as model problems for which simulations have been performed by solving the three-dimensional time-dependent incompressible Navier-Stokes equations in a spatially periodic integration domain. Numerical techniques including finite-difference, spectral and pseudospectral methods used in these simulations are also summarized.
The transition process considered here is a nonlinear phenomenon which arises from the amplification of initially small-amplitude two- and three-dimensional disturbances. During the later stages, nonlinear velocity-vorticity field interactions instigate the evolution of characteristic three-dimensional structures such as lambda vortices, horseshoe vortices and hairpin vortices. Significant advances have recently been made in both experimental and numerical studies of these structures. We give an account of the numerical work and compare with experiments.

MSC:

76F20 Dynamical systems approach to turbulence
76M25 Other numerical methods (fluid mechanics) (MSC2010)
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