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Morphology of a stream flowing down an inclined plane. Part 2. Meandering

Published online by Cambridge University Press:  30 June 2008

B. BIRNIR ,
K. MERTENS ,
V. PUTKARADZE  and
P. VOROBIEFF
B. BIRNIR
Affiliation:
Department of Mathematics, University of California, Santa Barbara, CA 93106, USA
K. MERTENS
Affiliation:
Department of Mathematics, Colorado State University, Fort Collins, CO 80235, USA
V. PUTKARADZE
Affiliation:
Department of Mathematics, Colorado State University, Fort Collins, CO 80235, USA Department of Mechanical Engineering, The University of New Mexico, Albuquerque, NM 87131, USA
P. VOROBIEFF
Affiliation:
Department of Mechanical Engineering, The University of New Mexico, Albuquerque, NM 87131, USA
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Abstract

A stream of fluid flowing down a partially wetting inclined plane usually meanders, unless the volume flow rate is maintained at a highly constant value. Here we investigate whether the meandering of this stream is an inherent instability. In our experiment, we eliminate meandering on several partially wetting substrates by reducing perturbations entering the flow. By re-introducing controlled fluctuations, we show that they are responsible for the onset of the meandering. We derive a theoretical model for the stream shape, %from first principles which includes stream dynamics and forcing by external noise. The deviation h(x) from a straight linear stream h(x)=0 shows considerable variability as a function of downstream distance x. However, for an ensemble average of stream shapes acquired at different times, the power spectrum S(k) as a function of wavenumber k has a power-law scaling S(k) ~ k5/2. Moreover, the area A(x) swept by the stream at the distance x grows as A(x) ~ x1.75.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 607 , 25 July 2008 , pp. 401 - 411
Copyright
Copyright © Cambridge University Press 2008

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