Nonlinear Phenomena in Complex Systems, 2006, Vol.9, No.2, pp.109-114

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2006, Vol.9, No.2, pp.109-114

What Rayleigh-Bénard, Taylor-Couette and Pipe Flows Have in Common.
Bruno Eckhardt, Siegfried Grossmann, and Detlef Lohse

The very close correspondence between the three types of thermally or shear driven fluid flows is elucidated. Expressions for the relevant currents of temperature, angular momentum, and axial velocity by transverse convective flow in the profile direction are derived from the Navier-Stokes equations. Also the dissipation rates of the advective flows are calculated. Exact relations between the respective currents, the dissipation rates and the external control parameters are presented.
Key words: pipe flow, Rayleigh-Bénard thermal convection, Taylor-Couette flow, dissipation and transport currents, Nusselt number, torque, Skin friction

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