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Vaid, Kanu
- 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.