On a class of Stokes flows inside a corrugated boundary
Author:
W. W. Hackborn
Journal:
Quart. Appl. Math. 51 (1993), 329-341
MSC:
Primary 76D07; Secondary 35Q30
DOI:
https://doi.org/10.1090/qam/1218372
MathSciNet review:
MR1218372
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Abstract: A study is made of a family of steady two-dimensional Stokes flows stirred by an infinitesimal rotating cylinder (a line rotlet) inside a corrugated boundary. Parameters govern the position of the stirrer and the number and sharpness of ridges in the boundary. A solution is found in terms of a finite combination of elementary functions. It is demonstrated that the flow exhibits some interesting dynamical features such as peculiar bifurcations and homoclinic orbits.
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D. E. R. Godfrey, Theoretical elasticity and plasticity for engineers, Thames and Hudson, London, 1959, pp. 58–59
J. H. Michell, On the inversion of plane stress, Proc. London Math. Soc. 34, 142–229 (1901/02)
K. B. Ranger, Eddies in two dimensional Stokes flow, Internat. J. Engrg. Sci. 18, 181–190 (1980)
B. Y. Ballal and R. S. Rivlin, Flow of a Newtonian fluid between eccentric rotating cylinders: inertial effects, Arch. Rational Mech. Anal. 62, 237–294 (1976)
W. W. Hackborn, Asymmetric Stokes flow between parallel planes due to a rotlet, J. Fluid Mech. 218, 531–546 (1990)
W. W. Hackborn, Separation in a two-dimensional Stokes flow inside an elliptic cylinder, J. Engrg. Math. 25, 13–22 (1991)
K. B. Ranger, Separation of streamlines for spatially periodic flow at zero Reynolds numbers, Quart. Appl. Math. 47, 367–373 (1989)
D. W. Pravica and K. B. Ranger, Spatially periodic Stokes flow stirred by a rotlet interior to a closed corrugated boundary, Quart. Appl. Math. (to appear)
H. Aref, Stirring by chaotic advection, J. Fluid Mech. 143, 1–21 (1984)
A. J. Lichtenberg and M. A. Lieberman, Regular and Stochastic Motion, Springer-Verlag, New York, 1983
H. Aref and S. Balachandar, Chaotic advection in a Stokes flow, Phys. Fluids 29, 3515–3521 (1986)
J. Chaiken, R. Chevray, M. Tabor, and Q. M. Tan, Experimental study of Lagrangian turbulence in a Stokes flow, Proc. Roy. Soc. London. Ser. A 408, 165–174 (1986)
P. D. Swanson and J. M. Ottino, A comparative computational and experimental study of chaotic mixing of viscous fluids, J. Fluid Mech. 213, 227–249 (1990)
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Article copyright:
© Copyright 1993
American Mathematical Society