Hostname: page-component-745bb68f8f-lrblm Total loading time: 0 Render date: 2025-01-14T06:27:50.805Z Has data issue: false hasContentIssue false
  • English
  • Français

Unsteady viscous flow over a wavy wall

Published online by Cambridge University Press:  29 March 2006

W. H. Lyne
W. H. Lyne
Affiliation:
E.C.L.P. and Co. Ltd, St Austell, Cornwall
Get access Rights & Permissions [Opens in a new window]

Abstract

The method of conformal transformation is used to investigate the steady streaming generated by an oscillatory viscous flow over a wavy wall. By assuming that the amplitude of the wall is much smaller than the Stokes layer thickness, the equations are linearized and solved for large and small values of the parameter kR. This parameter is the ratio of the amplitude of oscillation of a fluid particle to the wavelength of the wall. When kR [Lt ] 1, the results due to Schlichting (1932) are recovered, and when kR [Gt ] 1 the equations resemble closely those derived in the theory of stability of plane parallel flows. With the aid of this theory the first-order steady streaming is found.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 50 , Issue 1 , 15 November 1971 , pp. 33 - 48
Copyright
© 1971 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.)

References

Benjamin, T. 1959 J. Fluid Mech. 6, 161.
Hadamard, J. 1923 Lectures on Cauchy's Problem in Linear Partial Differential Equations. Newhaven-London.
Holstein, H. 1950 Z. angew. Math. Mech. 30, 25.
Lighthill, M. J. 1957 J. Fluid Mech. 3, 113.
Lyne, W. H. 1970 Ph.D. Thesis, University of London.
Mangler, K. W. 1952 Aero. Res. Counc. Current Paper, no. 94.
Rayleigh, Lord 1884 Phil. Trans. A 175, 1.
Reid, W. H. 1965 In Basic Developments in Fluid Dynamics (ed. Holt), vol. 1. Academic.
Riley, N. 1965 Mathematika 12, 161.
Schlichting, H. 1932 Phys. Z. 33, 327.
Segel, L. A. 1961 Quart. Appl. Math. 18, 335.
Stuart, J. T. 1963 Laminar Boundary Layers (ed. Rosenhead), chapter 9. Oxford University Press.
Stuart, J. T. 1966 J. Fluid Mech. 24, 673.
Tollmien, W. 1929 W. Nachr. Ges. Wiss. Göttingen, 1, 21. English translation in Nat. Adv. Comm. Aero., Wash., Mem. no. 909.