ISSN:
1089-7666
Source:
AIP Digital Archive
Topics:
Physics
Notes:
A weakly nonlinear analysis of the dynamics of a two-dimensional, laminar flow in a long channel with a sudden expansion and the transition from symmetric to asymmetric states is presented. The asymptotic analysis is based on a study of the unsteady Navier–Stokes equations around the critical Reynolds number, Rec, where a bifurcation occurs. It explores the special nonlinear interactions between the unsteady, convective, and viscous effects. The analysis results in an ordinary, nonlinear, first-order differential equation (similar to the Landau equation) which describes the evolution of the perturbation's amplitude as function of Re near Rec. The analytical solution shows that when Re〈Rec the symmetric state is stable. However, when Re≥Rec the symmetric state in the channel loses its stability and evolves into an asymmetric state. The flow evolution, as described by the nonlinear model, shows agreement with time history plots from simulations using the unsteady Navier–Stokes equations. The linear stability characteristics of both the symmetric and asymmetric states are also found from the nonlinear approach and match with the previous results. The analysis provides new insight into the previous experimental and numerical results and sheds light on the nonlinear transition of a viscous flow in an expanding channel. © 1999 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.870227
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