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Transition from shear to sideways diffusive instability in a vertical slot

Published online by Cambridge University Press:  20 April 2006

Sivagnanam Thangam ,
Abdelfattah Zebib  and
C. F. Chen
Sivagnanam Thangam
Affiliation:
Department of Mechanical and Aerospace Engineering, Rutgers University, New Brunswick, New Jersey 08903, U.S.A. Present address: Stevens Institute of Technology, Hoboken, New Jersey 07030.
Abdelfattah Zebib
Affiliation:
Department of Mechanical and Aerospace Engineering, Rutgers University, New Brunswick, New Jersey 08903, U.S.A.
C. F. Chen
Affiliation:
Department of Mechanical and Aerospace Engineering, Rutgers University, New Brunswick, New Jersey 08903, U.S.A. Present address: The University of Arizona, Tucson, Arizona 85721.
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Abstract

Stability of the steady motion of a fluid confined between two differentially heated rigid vertical plates is considered. When a stable, constant vertical salinity gradient is also present, the steady mean velocity in the vertical direction and the mean lateral salinity gradient are characterized by the solute Rayleigh number, Rs. Experimental investigations (Elder 1965; Hart 1970) show that when Rs = 0 the instability is induced by shear and occurs in the form of two-dimensional convection cells. However, at moderate values of Rs, these shear instabilities are replaced by double-diffusive cellular convection (Thorpe, Hutt & Soulsby 1969; Paliwal & Chen 1980a). It is generally believed that the instability is stationary and cellular for all values of Rs (Hart 1971; Paliwal & Chen 1980b). We have solved the general eigenvalue problem, and our results indicate that, during transition from the stationary shear-induced instability to stationary double-diffusive cellular convection, overstable motion occurs. Furthermore, in this transition region, over a range of moderately small values of Rs, there is no preferred wavelength at the onset of instability.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 112 , November 1981 , pp. 151 - 160
Copyright
© 1981 Cambridge University Press

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References

Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Clarendon Press.
Elder, J. W. 1965 Laminar free convection in a vertical slot. J. Fluid Mech. 23, 77–98.Google Scholar
Hart, J. E. 1970 Thermal convection between sloping parallel boundaries. Ph.D. thesis, Massachusetts Institute of Technology.
Hart, J. E. 1971 On sideways diffusive instability. J. Fluid Mech. 49, 279–288.Google Scholar
Khan, A. A. & Zebib, A. 1981 Double-diffusive instability in a vertical layer of porous medium. J. Heat Transfer 103, 179–181.Google Scholar
Martin, R. S. & Wilkinson, J. H. 1968a Similarity reduction of a general matrix to Hessenberg form. Numerische Mathematik 12, 349–368.Google Scholar
Martin, R. S. & Wilkinson, J. H. 1968b The modified LR algorithm for complex Hessenberg matrices. Numerische Mathematik 12, 369–376.Google Scholar
Paliwal, R. C. & Chen, C. F. 1980a Double-diffusive instability in an inclined fluid layer. Part 1. Experimental investigations. J. Fluid Mech. 98, 755–768.Google Scholar
Paliwal, R. C. & Chen, C. F. 1980b Double-diffusive instability in an inclined fluid layer. Part 2. Theoretical investigations. J. Fluid Mech. 98, 769–785.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