Scaling of global momentum transport in Taylor-Couette and pipe flow

  • B. Eckhardt
  • S. Grossmann
  • D. Lohse

Abstract:

We interpret measurements of the Reynolds number dependence of the torque in Taylor-Couette flow by Lewis and Swinney [Phys. Rev. E 59, 5457 (1999)] and of the pressure drop in pipe flow by Smits and Zagarola [Phys. Fluids 10, 1045 (1998)] within the scaling theory of Grossmann and Lohse [J. Fluid Mech. 407, 27 (2000)], developed in the context of thermal convection. The main idea is to split the energy dissipation into contributions from a boundary layer and the turbulent bulk. This ansatz can account for the observed scaling in both cases if it is assumed that the internal wind velocity \(\) introduced through the rotational or pressure forcing is related to the external (imposed) velocity U, by \(\) with \(\) and \(\) for the Taylor-Couette (U inner cylinder velocity) and pipe flow (U mean flow velocity) case, respectively. In contrast to the Rayleigh-Bénard case the scaling exponents cannot (yet) be derived from the dynamical equations.

PACS. 47.27.-i Turbulent flows, convection, and heat transfer 

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Copyright information

© EDP Sciences, Springer-Verlag, Società Italiana di Fisica 2000

Authors and Affiliations

  • B. Eckhardt
    • 1
  • S. Grossmann
    • 1
  • D. Lohse
    • 2
  1. 1.Fachbereich Physik, Philipps-Universität Marburg, Renthof 6, 35032 Marburg, GermanyDE
  2. 2.Department of Applied Physics and J.M. Burgers Centre for Fluid Dynamics, University of Twente, 7500 AE Enschede, The NetherlandsNL

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