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Vaid, Kanu
- On Linear Growth Rates in Thermohaline Convection with Viscosity Variations
Authors
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, IN
Source
Research Journal of Science and Technology, Vol 5, No 1 (2013), Pagination: 140-143Abstract
In the present paper it is proved that the complex growth rate (where and are real and imaginary parts of p ) of an arbitrary oscillatory motions of growing amplitude, neutral or unstable, for thermohaline convection configuration of Veronis type (Veronis, G., J. Mar. Res., 23(1965)1), with the viscosity variations must lie inside a semicircle in the right half of the prpiplane whose centre is at the origin and radius equals . A similar theorem is also proved for thermohaline convection of Stern type (Stern, M.E., Tellus 12(1960)172). Furthermore the above results are uniformly valid for all combinations of rigid and free bounding surfaces. The results obtain herein, in particular, also yield sufficient conditions for the validity of the ‘principle of the exchange of the stabilities’ for the respective configurations.Keywords
Thermohaline Instability, Oscillatory Motions, Veronis Type, Stern Type, Variable Viscosity.References
- Banerjee M. B., Katoch D. C., Dube G. S. and Banerjee K., Bounds for growth rate of a perturbation in thermohaline convection, Proc. Roy. Soc. London. A 387(1981)301.
- Banerjee M. B., Gupta J. R. and Shandil R.G., Generalized thermal convection with viscosity variations, J. Math. Phys. Sc. 11(5)(1977)421.
- Brandt A. and Fernando H. J. S., Double Diffusive Convection, Am. Geophys. Union, Washington, (1996).
- Lighthill M. J., Introduction to Boundary Layer Theory in Laminar Boundary Layers, (Ed.: L. Rosenhead), Clarendon Press, Oxford, (1963).
- Prakash J., A Mathematical theorem for thermohaline convection of the Veronis type with viscosity variations, Ind. J. Pure Appl.Math., 26(8)(1995)813.
- Schultz M. H., Spline Analysis, Prentice Hall Ince., Englewood Cliffs. N.J., (1973).
- Stern M. E., The salt fountain and thermohaline convection, Tellus 12 (1960)172.
- Torrance K.E., and. Turcotte D.L., Thermal convection with large viscosity variation, J. Fluid Mech, 47(1971)113.
- Turner J. S., Double diffusive phenomena, Ann. Rev. Fluid mech. 6(1974)37.
- Veronis G., On finite amplitude instability in thermohaline convection, J. Mar. Res., 23(1965)1.
- On Rotatory Hydrodynamic Triply Diffusive Convection in Porous Medium:Darcy Model
Authors
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-5, IN
2 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-5
Source
Research Journal of Engineering and Technology, Vol 6, No 1 (2015), Pagination: 19-22Abstract
Upper bounds for the complex growth rate of an arbitrary oscillatory perturbation, which may be neutral or unstable for triply diffusive convection in porous medium (Darcy model) in the presence of a uniform vertical rotation, are obtained. It is further proved that the result obtained herein is uniformly valid for quite general nature of the bounding surfaces.Keywords
Triply Diffusive Convection, Porous Medium, Taylor Number, Concentration Rayleigh Number, Darcy Model.- Characterization of Magnetorotatory Thermohaline Instability in Porous Medium:Darcy Model
Authors
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, IN
Source
International Journal of Technology, Vol 4, No 1 (2014), Pagination: 32-36Abstract
The present paper prescribes upper bounds for oscillatory motions of neutral or growing amplitude in magnetorotatory thermohaline configurations of Veronis (Veronis, G., J. Mar. Res., 23(1965)1) and Stern types (Stern, M.E., Tellus 12(1960)172) in porous medium (Darcy model) in such a way that also result in sufficient conditions of stability for an initially bottom-heavy as well as initially top-heavy configuration.
Keywords
Thermohaline Instability, Oscillatory Motions, Initially Bottom-Heavy Configuration, Initially Topheavy Configuration, Porous Medium.- A Semi-Circle Theorem in Triply Diffusive Convection
Authors
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, IN
Source
International Journal of Technology, Vol 4, No 1 (2014), Pagination: 1-4Abstract
The paper mathematically establishes that the complex growth rate (Pr, Pi) of an arbitrary neutral or unstable oscillatory perturbation of growing amplitude, in a triply diffusive fluid layer with one of the components as heat with diffusivity k, must lie inside a semicircle in the right- half of the (Pr, Pi)-plane whose centre is origin and radius equals
√(R1+R2)σ-27/4π4τ22
where R1 and R2are the Rayleigh numbers for the two concentration components with diffusivities κ1and κ2(with no loss of generality, κ > κ1> κ2) and σ is the Prandtl number. The bounds obtained herein, in particular, yield a sufficient condition for the validity of 'the principle of the exchange of stability'. Further, it is proved that above result is uniformly valid for quite general nature of the bounding surfaces.