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

B. Eckhardt, S. Grossmann, Detlef Lohse

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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.
Original languageUndefined
Pages (from-to)541-544
Number of pages4
JournalEuropean physical journal B
Volume18
Issue number3
DOIs
Publication statusPublished - 2000

Keywords

  • METIS-129622
  • IR-24821

Cite this

Eckhardt, B. ; Grossmann, S. ; Lohse, Detlef. / Scaling of global momentum transport in Taylor-Couette and pipe flow. In: European physical journal B. 2000 ; Vol. 18, No. 3. pp. 541-544.
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Scaling of global momentum transport in Taylor-Couette and pipe flow. / Eckhardt, B.; Grossmann, S.; Lohse, Detlef.

In: European physical journal B, Vol. 18, No. 3, 2000, p. 541-544.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Scaling of global momentum transport in Taylor-Couette and pipe flow

AU - Eckhardt, B.

AU - Grossmann, S.

AU - Lohse, Detlef

PY - 2000

Y1 - 2000

N2 - 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.

AB - 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.

KW - METIS-129622

KW - IR-24821

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JO - European physical journal B

JF - European physical journal B

SN - 1434-6028

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