Ghost Effect and Bifurcation I: Bénard and Taylor-Couette Problems

Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)


In this chapter, typical bifurcation problems in classical fluid dynamics, the Benard and Taylor-Couette problems, and related problems, are discussed on the basis of kinetic theory. In addition to the study of the effect of gas rarefaction in the Benard problem, its behavior in the continuum limit is revisited in the framework of the asymptotic theory in Section 3.3 and is shown not to be correctly described by the classical fluid dynamics. In the Taylor-Couette problem, the effect of difference of the temperatures of the two cylinders is studied in the continuum limit on the basis of the asymptotic theory, and as in the Benard problem, the classical fluid dynamics is shown to fail its correct description. The ghost and non-Navier-Stokes effects discussed in Section 3.3 play a central role in these bifurcations in the continuum limit. In the same geometrical configuration as the Taylor-Couette problem, we consider the bifurcation when the two cylinders are made of the condensed phase of the gas. Then, evaporation and condensation take place on the cylinders. Owing to the evaporation and condensation, bifurcation takes place in the simplest case where the field is axially symmetric and uniform. When the restriction of axial uniformity is eliminated, Taylor-Couette roll type of flow can stably exist in addition to the axially uniform flow.


Bifurcation Point Continuum Limit Knudsen Number Outer Cylinder Bifurcation Curve 
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© Birkhäuser Boston 2007

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