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Observations of solitary waves in a viscously deformable pipe

Scott, David R. and Stevenson, David J. and Whitehead , John A., Jr. (1986) Observations of solitary waves in a viscously deformable pipe. Nature, 319 (6056). pp. 759-761. ISSN 0028-0836. https://resolver.caltech.edu/CaltechAUTHORS:20140311-131625761

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Abstract

We have made simple observations of the ascent of a buoyant fluid through a pipe formed in a denser and more viscous fluid that can deform viscously and allow the pipe radius to change. There is no wall between the two fluids, and the Reynolds number is small in both fluids. If the buoyant fluid is supplied at a uniform rate, the system exhibits uniform Poiseuille flow. The response of the system to fluctuations in the rate of supply of the buoyant fluid is to form local maxima in the pipe radius that ascend as solitary waves. Larger-amplitude waves can catch up and collide with smaller waves and, to a good approximation, both waves recover their original form and amplitude after such a collision. Periodic wavetrains are formed when the supply of fluid to the pipe is increased and sustained at a higher rate. These observations gain significance because the system is analogous to that of one-dimensional buoyancy-driven porous flow in a viscous matrix. The experiment may be regarded as a laboratory analogue for studying some aspects of the equations governing porous flow. The observed behaviour is consistent with recent theoretical and computational studies, which have focused on the problem of magma migration in the Earth. The behaviour we observe will, however, arise in other systems governed by the same mechanics. The existence of solitary waves in such systems means that the responses to transient changes in the porosity or the supply of fluid could be long-lived.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://www.nature.com/nature/journal/v319/n6056/abs/319759a0.htmlPublisherArticle
http://dx.doi.org/10.1038/319759a0DOIArticle
ORCID:
AuthorORCID
Stevenson, David J.0000-0001-9432-7159
Additional Information:© 1986 Nature Publishing Group. Received 29 September; accepted 30 December 1985. We thank Robert E. Frazel at Woods Hole, and various members of the Division of Geological and Planetary Sciences at Caltech, for experimental assistance. Peter Olson and Uli Christensen have independently performed experiments similar to those described here, and have shared their results This work was supported by NSF grant EAR-8418353, and by Geodynamics program of the Center for the Analysis of Marine Systems at Woods Hole Oceanographic Institution. Contribution number 4271, Division of Geological and Planetary Sciences, California Institute of Technology.
Funders:
Funding AgencyGrant Number
NSFEAR-8418353
Woods Hole Oceanographic InstitutionUNSPECIFIED
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Other Numbering System NameOther Numbering System ID
Caltech Division of Geological and Planetary Sciences 4271
Issue or Number:6056
Record Number:CaltechAUTHORS:20140311-131625761
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20140311-131625761
Official Citation:Observations of solitary waves in a viscously deformable pipe 759 David R. Scott, David J. Stevenson & John A. Whitehead Jr doi:10.1038/319759a0
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:44249
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:11 Mar 2014 21:24
Last Modified:03 Oct 2019 06:15

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