Hostname: page-component-669899f699-ggqkh Total loading time: 0 Render date: 2025-04-28T20:49:10.670Z Has data issue: false hasContentIssue false
  • English
  • Français

The asymptotic behaviour of a starting plume

Published online by Cambridge University Press:  29 March 2006

Jason H. Middleton
Jason H. Middleton
Affiliation:
Department of Mathematics, Monash University, Clayton, Victoria 3168, Australia
Get access Rights & Permissions [Opens in a new window]

Abstract

A similarity solution is obtained for a model of the turbulent starting plume comprising a steady plume feeding mass, momentum and buoyancy into a vortex ring. Bulk equations representing the time rate of increase of ring momentum and ring buoyancy, together with equations (dependent on broad features of the ring structure) representing the velocity of propagation and time rate of circulation increase are used to determine the motion of the vortex ring. The similarity solution is found to exist only for diffuse distributions of vorticity and buoyancy within the ring. Further, the ratio of ring velocity to plume velocity, which is assumed to be constant, is found to take a value which agrees with that obtained from experimental observations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 72 , Issue 4 , 23 December 1975 , pp. 753 - 771
Copyright
© 1975 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

Abraham, G. 1965 Entrainment principle and its restrictions to solving problems of jets. J. Hydraul. Res. 3, 1–23.Google Scholar
Kuethe, A. M. 1935 Investigations of the turbulent mixing regions formed by jets. J. Appl. Mech. 2, 87–95.Google Scholar
Lamb, H. 1932 Hydrodynamics, 161–163. Cambridge University Press.
Mcgregor, J. L. 1974 Ph.D. thesis, Monash University.
Morton, B. R. 1959 Forced plumes. J. Fluid Mech. 5, 151–163.Google Scholar
Morton, B. R. 1960 Weak thermal vortex rings. J. Fluid Mech. 9, 107–118.Google Scholar
Morton, B. R. 1971 The structure of vortices. I. Bulk equations. Monash University, Dept. Math. GFDL Paper, no. 39.Google Scholar
Morton, B. R. & Middleton, J. 1973 Scale diagrams for forced plumes. J. Fluid Mech. 58, 165–176.Google Scholar
Morton, B. R., Taylor, G. I. & Turner, J. S. 1956 Turbulent gravitational convection from maintained and instantaneous sources. Proc. Roy. Soc. A 234, 1–23.Google Scholar
Reichardt, H. 1942 VDI-Forsch. no. 414.
Ricou, F. P. & Spalding, D. B. 1961 Measurements of entrainment by axisymmetrical turbulent jets. J. Fluid Mech. 11, 21–32.Google Scholar
Rouse, H., Yih, C. S. & Humphreys, H. W. 1952 Gravitational convection from a boundary source. Tellus, 4, 201–210.Google Scholar
Ruden, P. 1933 Naturwissenschaften 21, 375–378.
Schmidt, W. 1941 Turbulent expansion of a stream of heated air. Z. angew. Math. Mech. 21, 265–278, 351–363.Google Scholar
Squire, H. B. 1950 Aircraft Engng, 22, 62–67.
Turner, J. S. 1957 Buoyant vortex rings. Proc. Roy. Soc. A 239, 61–75.Google Scholar
Turner, J. S. 1962 The starting plume in neutral surroundings. J. Fluid Mech. 13, 356–368.Google Scholar
Turner, J. S. 1969 Buoyant plumes and thermals. Ann. Rev. Fluid Mech. 1, 29–44.Google Scholar