Hostname: page-component-7b7567c8c-wxvwp Total loading time: 0 Render date: 2026-11-15T20:25:13.387Z Has data issue: false hasContentIssue false
  • English
  • Français

On high-frequency oscillatory viscous flows

Published online by Cambridge University Press:  28 March 2006

Chang-Yi Wang
Chang-Yi Wang
Affiliation:
Department of Applied Mathematics, California Institute of TechnologyNow at the Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91103. Pasadena, California 91109
Get accessRights & Permissions [Opens in a new window]

Abstract

The equations governing high-frequency oscillatory viscous flows are investigated through the separation of the steady and the unsteady parts. All Reynolds number ranges are studied and the orders of magnitude of the steady streaming produced by the Reynolds stresses are established.

The oscillating circular cylinder at low Reynolds numbers is studied through the method of inner and outer expansions. Steady recirculating cells exist near the cylinder. The results compare very well with experiments. Analytic expressions for the streamfunction and the drag coefficient are obtained.

The oscillating flow towards an infinite plate is investigated in detail. The steady streaming is caused by the steady component of the Reynolds stress. The pressure gradient always causes reverse flow near the solid boundary.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 32 , Issue 1 , 9 April 1968, pp. 55 - 68
Copyright
© 1968 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

Andrade, E. N. DA C. 1931 On the circulations caused by the vibration of air in a tube. Proc. Roy. Soc A 134, 445–470.Google Scholar
Benney, D. J. 1964 The flow induced by a disk oscillating in its own plane J. Fluid Mech. 18, 385–391.Google Scholar
Faraday, M. 1831 On a peculiar class of acoustical figures, and on certain forms assumed by groups of particles upon vibrating elastic surfaces Phil. Trans. 121, 299–340.Google Scholar
Fettis, H. E. 1955 On the integration of a class of differential equations occuring in boundary layer and other hydrodynamic problems. Proc. 4th Midwestern Conf. on Fluid Mech., Purdue Univ. pp. 93–114.Google Scholar
Holtsmark, J., Johnsen, I., Sikkeland, T. & Skavlem, S. 1954 Boundary layer flow near a cylindrical obstacle in an oscillating incompressible fluid J. Acoust. Soc. Am. 26, 26–39.Google Scholar
Lane, C. A. 1955 Acoustic streaming in the vicinity of a sphere J. Acoust. Soc. Am. 27, 1082–1086.Google Scholar
Nyborg, W. L. 1953 Acoustic streaming due to attenuated plane waves J. Acoust. Soc. Am. 25, 68–75.Google Scholar
Rayleigh, LORD 1883 On the circulation of air observed in Kundt's tubes, and on some allied acoustical problems Phil. Trans. 175, 1–21. Scientific Papers, 2, 239–257.Google Scholar
Riley, N. 1965 Oscillating viscous flows Mathematika, 12, 161–175.Google Scholar
Riley, N. 1966 On a sphere oscillating in a viscous fluid Quart. J. Mech. Appl. Math. 19, 461–472.Google Scholar
Rosenblat, S. 1959 Torsional oscillations of a plane in a viscous fluid J. Fluid Mech. 6, 206–220.Google Scholar
Schlichting, H. 1932 Berechnung ebener periodischer Grenzschichtströmungen Physikalische Zeit. 33, 327–335.Google Scholar
Stuart, J. T. 1966 Double boundary layers in oscillatory viscous flow J. Fluid Mech. 24, 673–687.Google Scholar
Wang, C.-Y. 1965 The flow field induced by an oscillating sphere J. Sound Vib. 2, 257–269.Google Scholar
Wang, C.-Y. 1966 The resistance on a circular cylinder in an oscillating stream Quart. Appl. Math. 23, 305–312.Google Scholar
Westervelt, P. J. 1953 The theory of steady rotational flow generated by a sound field J. Acoust. Soc. Am. 25, 60–67.Google Scholar