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Zeitschrift für Naturforschung A

A Journal of Physical Sciences

Editor-in-Chief: Holthaus, Martin

Editorial Board: Fetecau, Corina / Kiefer, Claus

12 Issues per year


IMPACT FACTOR 2016: 1.432

CiteScore 2017: 1.30

SCImago Journal Rank (SJR) 2017: 0.403
Source Normalized Impact per Paper (SNIP) 2017: 0.632

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1865-7109
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Volume 43, Issue 8-9

Issues

Onset of Turbulence in a Pipe

L. Böberg / U. Brosa
Published Online: 2014-06-02 | DOI: https://doi.org/10.1515/zna-1988-8-901

Abstract

Turbulence in a pipe is derived directly from the Navier-Stokes equation. Analysis of numerical simulations revealed that small disturbances called 'mothers' induce other much stronger disturbances called 'daughters'. Daughters determine the look of turbulence, while mothers control the transfer of energy from the basic flow to the turbulent motion. From a practical point of view, ruling mothers means ruling turbulence. For theory, the mother-daughter process represents a mechanism permitting chaotic motion in a linearly stable system. The mechanism relies on a property of the linearized problem according to which the eigenfunctions become more and more collinear as the Reynolds number increases. The mathematical methods are described, comparisons with experiments are made, mothers and daughters are analyzed, also graphically, with full particulars, and the systematic construction of small systems of differential equations to mimic the non-linear process by means as simple as possible is explained. We suggest that more then 20 but less than 180 essential degrees of freedom take part in the onset of turbulence.

About the article

Received: 1988-06-15

Published Online: 2014-06-02

Published in Print: 1988-09-01


Citation Information: Zeitschrift für Naturforschung A, Volume 43, Issue 8-9, Pages 697–726, ISSN (Online) 1865-7109, ISSN (Print) 0932-0784, DOI: https://doi.org/10.1515/zna-1988-8-901.

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© 1946 – 2014: Verlag der Zeitschrift für Naturforschung. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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