https://doi.org/10.1007/s100510070044
Scaling of global momentum transport in Taylor-Couette and pipe flow
1
Fachbereich Physik, Philipps-Universität Marburg,
Renthof 6, 35032 Marburg, Germany
2
Department of Applied Physics and J.M. Burgers Centre for
Fluid Dynamics,
University of Twente, 7500 AE Enschede,
The Netherlands
Corresponding author: a lohse@tn.utwente.nl
Received:
9
September
2000
Published online: 15 December 2000
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 Uw 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
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000
