Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

Turbulent rivers


Author: Björn Birnir
Journal: Quart. Appl. Math. 66 (2008), 565-594
MSC (2000): Primary 35Q30, 35R60, 60H15, 76D06
DOI: https://doi.org/10.1090/S0033-569X-08-01123-8
Published electronically: June 5, 2008
MathSciNet review: 2445529
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Abstract | References | Similar Articles | Additional Information

Abstract: The existence of solutions describing the turbulent flow in rivers is proven. The existence of an associated invariant measure describing the statistical properties of this one-dimensional turbulence is established. The turbulent solutions are not smooth but Hölder continuous with exponent $ 3/4$. The scaling of the solutions' second structure (or width) function gives rise to Hack's law (1957), stating that the length of the main river, in mature river basins, scales with the area of the basin $ l \sim A^{h}$, $ h = 0.568$ being Hack's exponent.


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Additional Information

Björn Birnir
Affiliation: Center for Complex and Nonlinear Science, and Department of Mathematics, University of California, Santa Barbara
Email: birnir@math.ucsb.edu

DOI: https://doi.org/10.1090/S0033-569X-08-01123-8
Received by editor(s): May 15, 2007
Published electronically: June 5, 2008
Article copyright: © Copyright 2008 Brown University
The copyright for this article reverts to public domain 28 years after publication.

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