Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-05T09:52:11.137Z Has data issue: false hasContentIssue false
  • English
  • Français

Double-diffusive instability in an inclined fluid layer Part 2. Stability analysis

Published online by Cambridge University Press:  19 April 2006

R. C. Paliwal  and
C. F. Chen
R. C. Paliwal
Affiliation:
Department of Mechanical, Industrial and Aerospace Engineering, Rutgers University, New Brunswick, New Jersey 08903 Present address: Electronic Associates, Inc., West Long Branch, N.J. 07764.
C. F. Chen
Affiliation:
Department of Mechanical, Industrial and Aerospace Engineering, Rutgers University, New Brunswick, New Jersey 08903
Get access Rights & Permissions [Opens in a new window]

Abstract

Linear stability analysis is applied to the problem of a density-stratified fluid contained in an inclined slot being subjected to a lateral temperature gradient. Stability equations are solved using the Galerkin technique with 12 terms in the truncated expansion series. Within the range of θ considered, |θ| < 75°, critical instability was found to be of the stationary type. Results of critical thermal Rayleigh numbers and wavenumbers at all inclination angles are in good agreement with the experimental results obtained earlier (Paliwal & Chen 1980). Contrary to intuition, these results show that the system is more stable when the lower wall is heated. This is shown to be the result of the increased vertical solute gradient in the steady state prior to the onset of instabilities when the heating is from below.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 98 , Issue 4 , 26 June 1980 , pp. 769 - 785
Copyright
© 1980 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

Finlayson, B. A. 1972 The Method of Weighted Residuals and Variational Principles, pp. 151–203. Academic.
Hart, J. E. 1970 Thermal convection between sloping parallel boundaries. Ph.D. thesis, Massachusetts Institute of Technology.
Hart, J. E. 1971a Stability of the flow in a differentially heated inclined box. J. Fluid Mech. 47, 547–576.Google Scholar
Hart, J. E. 1971b On sideways diffusive instability. J. Fluid Mech. 49, 279–288.Google Scholar
Hart, J. E. 1973 Finite amplitude sideways diffusive convection. J. Fluid Mech. 59, 47–64.Google Scholar
Paliwal, R. C. 1979 Double-diffusive convective instability in an inclined fluid layer. Ph.D. thesis, Department of Mechanical, Industrial and Aerospace Engineering, Rutgers University.
Paliwal, R. C. & Chen, C. F. 1980 Double-diffusive instability in an inclined fluid layer. Part 1. Experimental investigation. J. Fluid Mech. 98, 755–768.Google Scholar
Shirtcliffe, T. G. L. 1969 An experimental investigation of thermosolutal convection at marginal stability. J. Fluid Mech. 35, 677–688.Google Scholar
Thorpe, S. A., Hutt, P. K. & Soulsby, R. 1969 The effect of horizontal gradients on thermohaline convection. J. Fluid Mech. 38, 375–400.Google Scholar
Veronis, G. 1965 On finite amplitude instability in thermohaline convection. J. Mar. Res. 23, 1–17.Google Scholar