Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-19T04:54:06.498Z Has data issue: false hasContentIssue false
  • English
  • Français

The emission of internal waves by vibrating cylinders

Published online by Cambridge University Press:  29 March 2006

D. G. Hurley
D. G. Hurley
Affiliation:
University of Western Australia, Nedlands, Western Australia
Get access Rights & Permissions [Opens in a new window]

Abstract

The paper describes an investigation of the internal waves that are produced in a stratified fluid having constant Brunt—Väisälä frequency by a cylinder which executes small vibrations at a lower frequency. Explicit solutions are found for slender cylinders having arbitrary cross-sections. When the cross-sectional area of the cylinder varies with time it is found necessary in calculating the surface pressures and power output to take account of terms in the governing equations that are significant only at distances from the cylinder comparable to or larger than the scale height of the density variations. For this case a simple expression for the power output is obtained in terms of the rate of change of the cross-sectional area of the cylinder.

When the vibrating cylinder is rigid its cross-sectional area is independent of time and then the expression for the power output is very similar to von Kármán's expression for the drag of a body of revolution in supersonic flow.

In both the above cases it is found that one quarter of the power is radiated in each of the four directions that are inclined at a particular angle to the horizontal.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 36 , Issue 4 , 19 May 1969 , pp. 657 - 672
Copyright
© 1969 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

Carrier, G. F., Krook, M. & Pearson, C. E. 1966 Functions of a Complex Variable. New York: McGraw-Hill.
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics. London: Pergamon.
Mowbray, D. E. & Rarity, B. S. H. 1967 J. Fluid Mech. 28, 1.
Phillips, O. M. 1966 The Dynamics of the Upper Ocean. Cambridge University Press.
Sears, W. R. (ed.) 1954 General Theory of High Speed Aerodynamics. Princeton University Press.
Tolstoy, I. 1963 Rev. Mod. Phys. 35, 216.
Townsend, A. A. 1966 J. Fluid Mech. 24, 307.