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Longitudinal profile of channels cut by springs

Published online by Cambridge University Press:  13 December 2010

O. DEVAUCHELLE ,
A. P. PETROFF ,
A. E. LOBKOVSKY  and
D. H. ROTHMAN
O. DEVAUCHELLE*
Affiliation:
Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, USA
A. P. PETROFF
Affiliation:
Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, USA
A. E. LOBKOVSKY
Affiliation:
Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, USA
D. H. ROTHMAN
Affiliation:
Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, USA
*
†Email address for correspondence: [email protected]
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Abstract

We propose a simple theory for the longitudinal profile of channels incised by groundwater flow. The aquifer surrounding the stream is represented in two dimensions through Darcy's law and the Dupuit approximation. The model is based on the assumption that, everywhere in the stream, the shear stress exerted on the sediment by the flow is close to the minimal intensity required to displace a sand grain. Because of the coupling of the stream discharge with the water table elevation in the neighbourhood of the channel head, the stream elevation decreases as the distance from the stream's tip with an exponent of 2/3. Field measurements of steephead ravines in the Florida Panhandle conform well to this prediction.

JFM classification

Interfacial Flows (free surface): Fingering instability Geophysical and Geological Flows: River dynamics Geophysical and Geological Flows: Sediment transport
Type
Papers
Information
Journal of Fluid Mechanics , Volume 667 , 25 January 2011 , pp. 38 - 47
Copyright
Copyright © Cambridge University Press 2010

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References

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