On Thermohaline Convection of the Veronis Type

Thermohaline Convection of Veronis and Stern Types Revisited

“…This result is the characterization theorem of Banerjee et al [4], which we see is built into our characterization Corollary 1. Furthermore, (b) Even when 0 < ≤ 27π 4 /4 1 + τ/σ < s and p i = 0, Corollary 1 implies that p r < 0, a new result that obviously cannot be averred from the characterization theorem of Banerjee et al [4].…”

“…Banerjee et al [4] Furthermore, when the complement of the sufficient condition contained in the characterization theorem of Banerjee et al holds good, oscillatory motions of neutral or growing amplitude can exist, and therefore it is important to derive bounds for the complex growth rate of such motions when both of the boundaries are not dynamically free, since then exact solutions of the problem in closed form are not obtainable. The aim of the present paper is to prescribe upper limits for oscillatory motions of neutral or growing amplitude in thermohaline configurations of Veronis and Stern types in such a way that it also results in sufficient conditions of stability for an initially top-heavy or an initially bottom-heavy configuration.…”

A semi-circle theorem in couple-stress fluid in the presence of rotation

“…We prove the following theorems: Theorem: If R 〉 0, F 〉 0, T A 〉 0, σ r ≥ 0 and σ i ≠ 0 then the necessary condition for the existence of non-trivial solution (W, Θ, Z) of equations (16), (17) and (18) (20) Taking complex conjugate on both sides of equation (18), we get (21) Therefore, using (21), we get (22) Also taking complex conjugate on both sides of equation (17) …”

On the characterization of magnetohydrodynamic triply diffusive convection

“…Thus oscillatory motions of growing amplitude can occur in a multiple component fluid layer wherein the total density field is either gravitationally stable or unstable. Banerjee et al [18] derived a characterization theorem for thermohaline convection which disallow, in certain parameter regime, the existence of oscillatory motions of growing amplitude in an initially bottom configuration and pave the way for further theoretical and experimental investigations. The extension of Banerjee et al's [18] result to triply diffusive convection in the domains of astrophysics and terrestrial physics, wherein the liquid concerned has the property of electrical conduction and the magnetic field is prevalent, is very much sought after in the present context.…”

“…Banerjee et al [18] derived a characterization theorem for thermohaline convection which disallow, in certain parameter regime, the existence of oscillatory motions of growing amplitude in an initially bottom configuration and pave the way for further theoretical and experimental investigations. The extension of Banerjee et al's [18] result to triply diffusive convection in the domains of astrophysics and terrestrial physics, wherein the liquid concerned has the property of electrical conduction and the magnetic field is prevalent, is very much sought after in the present context. As a further step an analogous characterization theorem, in the parameter space of the system alone, is derived for magnetohydrodynamic triply diffusive convection which disallow the existence of oscillatory motions of growing amplitude in an initially bottom heavy magnetohydrodynamic triply diffusive convection, which may be regarded as a first step in this scheme of extended investigations.…”