Hostname: page-component-8448b6f56d-sxzjt Total loading time: 0 Render date: 2024-04-25T06:40:42.002Z Has data issue: false hasContentIssue false
  • English
  • Français

Spatially growing wave trails of an inviscid fluid discontinuity

Published online by Cambridge University Press:  29 March 2006

Peter Freymuth
Peter Freymuth
Affiliation:
Department of Aerospace Engineering Sciences, University of Colorado
Get access Rights & Permissions [Opens in a new window]

Abstract

The eigenvalue equation for three-dimensional waves in parallel and cross flows parallel to a fluid discontinuity has been considered for spatially growing waves. The discontinuity plane (x, y plane) is perpendicular to the gravitational acceleration and consists in general of a jump in speed, in flow direction and in density. With the assumption of waves which are periodic in time and periodic in the y direction, the eigenvalue equation is solved for the complex wavenumber α in the x direction. These waves are used to Fourier synthesize the wave trails generated by a time-periodic disturbance with a Gaussian amplitude distribution e−δy2 along the y axis. Lines of constant phase and lines of constant amplitude within the wave trail have been illustrated for some examples.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 58 , Issue 4 , 22 May 1973 , pp. 669 - 675
Copyright
© 1973 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

Agrawal, S. C. & Agrawal, G. S. 1969 Proc. Indian Acad. Sci. A 70, 150.
Benjamin, T. B. 1961 J. Fluid Mech. 10, 401.
Criminale, W. O. & Kovasznay, L. S. G. 1962 J. Fluid Mech. 14, 59.
Davey, R. F. & Roshko, A. 1972 J. Fluid Mech. 53, 523.
Freymuth, P. 1966 J. Fluid Mech. 26, 683.
Gaster, M. 1962 J. Fluid Mech. 14, 222.
Gaster, M. 1965 Prog. in Aero. Sci. 8, 251.
Gaster, M. & Davey, A. 1968 J. Fluid Mech. 32, 801.
Kelvin, Lord 1910 Mathematical and Physical Papers, vol. 4, p. 69. Cambridge University Press.
Lamb, H. 1932 Hydrodynamics, 5th edn., § 232. Dover.
Maslowe, C. A. & Thomson, J. M. 1971 Phys. Fluids, 14, 453.
Mattingly, G. E. & Criminale, W. O. 1971 Phys. Fluids, 14, 2258.
Mattingly, G. E. & Criminale, W. O. 1972 J. Fluid Mech. 51, 233.
Michalke, A. 1965 J. Fluid Mech. 23, 521.