Hostname: page-component-54dcc4c588-br6xx Total loading time: 0 Render date: 2025-09-11T23:06:01.780Z Has data issue: false hasContentIssue false
  • English
  • Français

Doubly Diffusive Convection Due to a Point Source at Various Depths in a Stratified Fluid

Published online by Cambridge University Press:  05 May 2011

Chin-Hwa Kong ,
Chi-Min Liu  and
Ray-Yeng Yang
Chin-Hwa Kong*
Affiliation:
Department of Naval Architecture and Ocean Engineering, National Taiwan University, 73 Chow-Shan Rd., Taipei, Taiwan 106, R.O.C
Chi-Min Liu*
Affiliation:
Department of Naval Architecture and Ocean Engineering, National Taiwan University, 73 Chow-Shan Rd., Taipei, Taiwan 106, R.O.C
Ray-Yeng Yang*
Affiliation:
Tainan Hydraulics Laboratory, National Cheng Kung University, Tainan, Taiwan 70101, R.O.C
*
*Professor
**Graduate Student
***Associate Researcher
Get access

Abstract

The problem of a stable stratified fluid heated by a point source of heat at various depths is treated in this paper. A hot plume is formed with a series of layer around and above it. Quantitative estimates for the criterion of onset of doubly diffusive instability are obtained in this work. The linear differential system governing stability is then solved. The results show that the stationary onset of this doubly diffusive problem caused by a point source may be led to a similar form of small-gap Taylor- Couette problem.

Keywords

StabilityDoubly diffusive convectionTemperature gradientSalinity gradient

Information

Type
Articles
Information
Journal of Mechanics , Volume 15 , Issue 1 , March 1999 , pp. 27 - 33
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 1999

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

REFERENCES

1.Kong, C. H. and Liu, I. C, “The Stability of Nonaxisymmetric Circular Couette Flow with a Radial Temperature Gradient,” Phys. Fluids, 6(8), pp. 2617–2622(1994).CrossRefGoogle Scholar
2.Kong, C. H. and Liu, I. C, “Incipient Instability Criterion of Two Confined Superposed Fluids,” ASCE, Feb., Vol. 121, No. 2, pp. 198–202 (1995).Google Scholar
3.Chen, C. F. and Chen, Falin, “Onset of Salt Finger Convection in a Gravity Gradient,” Phys. Fluids, A, Vol. 4, No. 2, pp. 451–452 (1992).CrossRefGoogle Scholar
4.Harris, D. L. and Reid, W. H., “On the Stability of Viscous Flow Between Rotating Cylinders,” Part 1, Asymptotic Analysis, J. FluidMech., 20, 81 (1964).Google Scholar
5.Harris, D. L. and Reid, W. H., “On the Stability of Viscous Flow Between Rotating Cylinders,” Part 1, Asymptotic Analysis, J. Fluid Mech., 20, 95 (1964).CrossRefGoogle Scholar
6.Krueger, E. R., Gross, A. and Di Prima, R. C, “On the Relative Importance of Taylor-Vortex and Nonaxisymmetric Modes in Flow Between Rotating Cylinders,” Fluid Mech., 24, 521 (1966).Google Scholar
7.Huppert, H. E. and Linden, P. F., “On Heating a Salinity Gradient from Below,” J. Fluid Mech., 100, pp. 367–384 (1979).Google Scholar
8.Turner, J. S., “Double-Diffusive Phenomena,” Ann. Rev. Fluid Mech., 6, pp. 37–56 (1974).Google Scholar
9.Turner, J. S., “Double-Diffusive Intrusions into a Density Gradient,” J. Geophys. Res., 83, pp. 2887–2901 (1978).CrossRefGoogle Scholar
10.Pearson, J. R. A., “On Convection Cells Induced by Surface Tension,” J. Fluid Mech., 4, pp. 489–500 (1958).Google Scholar
11.Fox, L.The Numerical Solution of Two-Point Boundary Problems in Ordinary Differential Equations, Oxford University Press (1957).Google Scholar
12.Chandrasekhar, S., “On Characteristic Value Problems in High Order Differential Equations Which Arises in Studies on Hydrodynamic and Hydromagnetic Stability,” American Math. Monthly, 61, pp. 32–45(1954).CrossRefGoogle Scholar
13.Chandrasekhar, S., Hydrodynamic and Hydromagnetic Stability, Clarendon, Oxford (1961).Google Scholar
14.Reid, W. H. and Harris, D. L., “Some Further Results on the Benard Problem,” The Physics of Fluids, l,pp. 102–109(1958).Google Scholar
15.Debler, W. R., “On the Analogy Between Thermal and Rotational Hydrodynamic Stability,” J. Fluid Mech., 24, pp. 65–176 (1966).Google Scholar