Hostname: page-component-7dd5485656-dk7s8 Total loading time: 0 Render date: 2025-10-31T01:57:10.261Z Has data issue: false hasContentIssue false
  • English
  • Français

The eddy structure in Stokes flow in a cavity

Published online by Cambridge University Press:  26 April 2006

P. N. Shankar
P. N. Shankar
Affiliation:
Computational and Theoretical Fluid Dynamics Division, National Aeronautical Laboratory, Bangalore 560017, India
Get access Rights & Permissions [Opens in a new window]

Abstract

Stokes flow in a two-dimensional cavity of rectangular section, induced by the motion of one of the walls, is considered. A direct, efficient calculational procedure, based on an eigenfunction expansion, is used to study the eddy structure in the cavity. It is shown that some of the results of earlier studies are quantitatively in error. More importantly, two interesting questions, namely the extent of the symmetry of the corner eddies and their relationship to the large-eddy structure are settled. By carefully examining the rather sudden change in the main eddy structure for cavities of depth around 1.629, it is shown that the main eddies are formed by the merger of the primary corner eddies; the secondary corner eddies then become the primary corner eddies and so on. Thus, in the evolution of the large-eddy structure the corner eddies, in some sense, play the role of progenitors. This explicit prediction should be experimentally verifiable.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 250 , May 1993 , pp. 371 - 383
Copyright
© 1993 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Gregory, R. D. 1980 The semi-infinite strip x [ges ] 0, -1 [les ] y [les ] 1; completeness of the Papkovich–Fadle eigenfunctions when øxx (0, y), øyy (0, y) are prescribed. J. Elast. 10, 57.Google Scholar
Jeffrey, D. J. & Sherwood, J. D. 1980 Streamline patterns and eddies in low-Reynolds-number flow. J. Fluid Mech. 96, 315.Google Scholar
Johnson, M. W. & Little, R. W. 1965 The semi-infinite elastic strip. Q. Appl. Maths 22, 335.Google Scholar
Joseph, D. D. & Sturges, L. 1978 The convergence of biorthogonal series for biharmonic and Stokes flow edge problems: Part II. SIAM J. Appl. Maths 34, 7.Google Scholar
Joseph, D. D., Sturges, L. D. & Warner, W. H. 1982 Convergence of biorthogonal series of biharmonic eigenfunctions by the method of Titchmarsh. Arch. Rat. Mech. Anal. 78, 223.Google Scholar
Moffatt, H. K. 1964 Viscous and resistive eddies near a sharp corner. J. Fluid Mech. 18, 1.Google Scholar
Pan, F. & Acrivos, A. 1967 Steady flows in rectangular cavities. J. Fluid Mech. 28, 643 (referred to herein as PA.)Google Scholar
Robbins, C. I. & Smith, R. C. T. 1948 A table of roots of sin z = -z. Phil. Mag 39, 1004.Google Scholar