Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



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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  • [1] D. E. R. Godfrey, Theoretical elasticity and plasticity for engineers, Thames and Hudson, London, 1959, pp. 58-59 MR 0105861
  • [2] J. H. Michell, On the inversion of plane stress, Proc. London Math. Soc. 34, 142-229 (1901/02) MR 1575489
  • [3] K. B. Ranger, Eddies in two dimensional Stokes flow, Internat. J. Engrg. Sci. 18, 181-190 (1980)
  • [4] 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) MR 0436773
  • [5] W. W. Hackborn, Asymmetric Stokes flow between parallel planes due to a rotlet, J. Fluid Mech. 218, 531-546 (1990) MR 1071890
  • [6] W. W. Hackborn, Separation in a two-dimensional Stokes flow inside an elliptic cylinder, J. Engrg. Math. 25, 13-22 (1991)
  • [7] K. B. Ranger, Separation of streamlines for spatially periodic flow at zero Reynolds numbers, Quart. Appl. Math. 47, 367-373 (1989) MR 998109
  • [8] 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) MR 1121678
  • [9] H. Aref, Stirring by chaotic advection, J. Fluid Mech. 143, 1-21 (1984) MR 758687
  • [10] A. J. Lichtenberg and M. A. Lieberman, Regular and Stochastic Motion, Springer-Verlag, New York, 1983 MR 681862
  • [11] H. Aref and S. Balachandar, Chaotic advection in a Stokes flow, Phys. Fluids 29, 3515-3521 (1986) MR 865480
  • [12] 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)
  • [13] 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) MR 1051539

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Additional Information

DOI: https://doi.org/10.1090/qam/1218372
Article copyright: © Copyright 1993 American Mathematical Society

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