Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2000-09-25
Eur. Phys. J. B 18, 541-544 (2000).
Nonlinear Sciences
Chaotic Dynamics
7 pages, 4 ps figures with 4 program files included in the source. European Physical Journal B, accepted
Scientific paper
10.1007/s100510070044
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 $U_w$ introduced through the rotational or pressure forcing is related to the the external (imposed) velocity U, by $U_w/U \propto Re^\xi$ with xi = -0.051 and xi = -0.041 for the Taylor-Couette (U inner cylinder velocity) and pipe flow (U mean flow velocity) case, respectively. In contrast to the Rayleigh-Benard case the scaling exponents cannot (yet) be derived from the dynamical equations.
Eckhardt Bruno
Grossmann Siegfried
Lohse Detlef
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