Velocity selection and the Saffman-Taylor problem

A new approach to the velocity selection problem is presented. It establishes a relation between the existence of propagating steady states as a function of a parameter and a certain inhomogeneous linear problem, the solvability of which determines the set of allowed velocities. The method is illust...

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Bibliographic Details
Published in:Physical review letters 1986-05, Vol.56 (19), p.2028-2031
Main Author: SHRAIMAN, B. I
Format: Article
Language:English
Subjects:
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Nonhomogeneous flows
Physics
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Summary:A new approach to the velocity selection problem is presented. It establishes a relation between the existence of propagating steady states as a function of a parameter and a certain inhomogeneous linear problem, the solvability of which determines the set of allowed velocities. The method is illustrated on the example of a geometrical model of solidification. It is used to explain analytically the fact that at large velocity the Saffman-Taylor 'fingers' have width close to 1/2 and to predict the scaling exponent for the dependence of the finger width on velocity. (Author)
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.56.2028