The onset of convective instability in a triply diffusive fluid layer

Abstract

The onset of instability is investigated in a triply diffusive fluid layer in which the density depends on three stratifying agencies having different diffusivities. It is found that, in some cases, three critical values of the Rayleigh number are required to specify the linear stability criteria. As in the case of another problem requiring three Rayleigh numbers for the specification of linear stability criteria (the rotating doubly diffusive case studied by Pearlstein 1981), the cause is traceable to the existence of disconnected oscillatory neutral curves. The multivalued nature of the stability boundaries is considerably more interesting and complicated than in the previous case, however, owing to the existence of heart-shaped oscillatory neutral curves. An interesting consequence of the heart shape is the possibility of ‘quasi-periodic bifurcation’ to convection from the motionless state when the twin maxima of the heart-shaped oscillatory neutral curve lie below the minimum of the stationary neutral curve. In this case, there are two distinct disturbances, with (generally) incommensurable values of the frequency and wavenumber, that simultaneously become unstable at the same Rayleigh number. This work complements the earlier efforts of Griffiths (1979a), who found none of the interesting results obtained herein.

The Onset of Double-Diffusive Nanofluid Convection in a Layer of a Saturated Porous Medium

“…Indeed, it is well known that the linear stability problem for triply diffusive systems is complex (Pearlstein et al 1989). Numerical values of Ra c can be calculated readily using the Mathematica software package, but it appears even a moderately simple analytical solution can be obtained only in the case Pr → ∞, so we now make this assumption.…”

The onset of convection in a rotating multicomponent fluid layer

“…The presence of more than one salt in fluid mixtures is very often requested for describing natural phenomena such as contaminant transport, acid rain effects, underground water flow and warming of the stratosphere. The subject of more than two stratifying agents has attracted many researchers (Griffiths, 1979a,b;Pearlstein et al, 1989;Rionero, 2013aRionero, ,b, 2014Lopez et al, 1990;Terrones, 1993;Poulikakos, 1985; Shivakumara and Naveen Kumar, 2014). In double diffusive convection (Turner, 1974) or, more generally, in multicomponent convection (Turner, 1985;Griffiths, 1979a) instability may occur in two kinds: first in form of steady (or stationary) convection which is called as 'salt finger' modes and the second in form of oscillatory motions of growing amplitude (or overstability) which is called as 'diffusive convection'.…”

On the characterization of magnetohydrodynamic triply diffusive convection

“…The presence of more than one salt in fluid mixtures is very often requested for describing natural phenomena such as contaminant transport, underground water flow, acid rain effects, warming of the stratosphere. Further a number of technologically important alloys such as nickel-based alloys (Pearlstein et al [12]) used in turbine blades and another highstrength applications, containing significant mass fraction of as many as seven metallic elements. In laboratory experiments on double diffusive convection also, dyes or small temperature anomalies introduce a third property which affects the density of the fluid.…”

“…Griffiths [10], Pearlstein et al [12], Lopez et al [13], Ryzhkov and Shevtsova [14], Salvatore Rionero [15] and [16] have theoretically studied the onset of convection in a triply diffusive fluid layer (where density depends on three independently diffusing agencies with different diffusivities). The summary of the investigations of these researchers is that small concentrations of a third component with a smaller diffusivity can have a significant effect upon the nature of diffusive instabilities and diffusive convection (oscillatory convection) and salt finger (Stationary convection) modes are simultaneously unstable under a wide range of conditions when the density gradients due to components with the greatest and smallest diffusivity are of same signs and further that [11] differential or coupled diffusion can produce convective motions that are associated with a decrease in the gravitational potential energy of the system.…”