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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

**[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**

Retrieve articles in *Quarterly of Applied Mathematics*
with MSC:
76D07,
35Q30

Retrieve articles in all journals with MSC: 76D07, 35Q30

Additional Information

DOI:
https://doi.org/10.1090/qam/1218372

Article copyright:
© Copyright 1993
American Mathematical Society