Oscillations in double-diffusive convection

1981 ◽  
Vol 109 ◽  
pp. 25-43 ◽  
Author(s):  
L. N. Da Costa ◽  
E. Knobloch ◽  
N. O. Weiss
Keyword(s):  
Rayleigh Number ◽  
Period Doubling ◽  
Thermosolutal Convection ◽  
Two Dimensional ◽  
Double Diffusive Convection ◽  
Dimensional Problem ◽  
Diffusive Convection ◽  
Steady Solutions ◽  
Steady Convection ◽  
Double Diffusive

We have studied the transition between oscillatory and steady convection in a simplified model of two-dimensional thermosolutal convection. This model is exact to second order in the amplitude of the motion and is qualitatively accurate for larger amplitudes. If the ratio of the solutal diffusivity to the thermal diffusivity is sufficiently small and the solutal Rayleigh number, RS, sufficiently large, convection sets in as overstable oscillations, and these oscillations grow in amplitude as the thermal Rayleigh number, RT, is increased. In addition to this oscillatory branch, there is a branch of steady solutions that bifurcates from the static equilibrium towards lower values of RT; this subcritical branch is initially unstable but acquires stability as it turns round towards increasing values of RT. For moderate values of RS the oscillatory branch ends on the unstable (subcritical) portion of the steady branch, where the period of the oscillations becomes infinite. For larger values of RS a birfurcation from symmetrical to asymmetrical oscillations is followed by a succession of bifurcations, at each of which the period doubles, until the motion becomes aperiodic at some finite value of RT. The chaotic solutions persist as RT is further increased but eventually they lose stability and there is a transition to the stable steady branch. These results are consistent with the behaviour of solutions of the full two-dimensional problem and suggest that period-doubling, followed by the appearance of a strange attractor, is a characteristic feature of double-diffusive convection.

Temperature Modulation of Double Diffusive Convection in a Horizontal Fluid Layer

2006 ◽  
Vol 61 (7-8) ◽  
pp. 335-344 ◽  
Author(s):  
Beer Singh Bhadauria
Keyword(s):  
Rayleigh Number ◽  
Fluid Layer ◽  
Thermosolutal Convection ◽  
Periodic Part ◽  
Temperature Modulation ◽  
Double Diffusive Convection ◽  
Diffusive Convection ◽  
Horizontal Fluid Layer ◽  
Double Diffusive ◽  
Diffusivity Ratio

Linear stability analysis is performed for the onset of thermosolutal convection in a horizontal fluid layer with rigid-rigid boundaries. The temperature field between the walls of the fluid layer consists of two parts: a steady part and a time-dependent periodic part that oscillates with time. Only infinitesimal disturbances are considered. The effect of temperature modulation on the onset of thermosolutal convection has been studied using the Galerkin method and Floquet theory. The critical Rayleigh number is calculated as a function of frequency and amplitude of modulation, Prandtl number, diffusivity ratio and solute Rayleigh number. Stabilizing and destabilizing effects of modulation on the onset of double diffusive convection have been obtained. The effects of the diffusivity ratio and solute Rayleigh number on the stability of the system are also discussed.

scholarly journals Double Diffusive Convection in a Layer of Maxwell Viscoelastic Fluid in Porous Medium in the Presence of Soret and Dufour Effects

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Ramesh Chand ◽  
G. C. Rana
Keyword(s):  
Porous Medium ◽  
Rayleigh Number ◽  
Viscoelastic Fluid ◽  
Fluid Layer ◽  
Lewis Number ◽  
Double Diffusive Convection ◽  
Free Boundaries ◽  
Soret And Dufour Effects ◽  
Diffusive Convection ◽  
Double Diffusive

Double diffusive convection in a horizontal layer of Maxwell viscoelastic fluid in a porous medium in the presence of temperature gradient (Soret effects) and concentration gradient (Dufour effects) is investigated. For the porous medium Darcy model is considered. A linear stability analysis based upon normal mode technique is used to study the onset of instabilities of the Maxwell viscolastic fluid layer confined between two free-free boundaries. Rayleigh number on the onset of stationary and oscillatory convection has been derived and graphs have been plotted to study the effects of the Dufour parameter, Soret parameter, Lewis number, and solutal Rayleigh number on stationary convection.

Onset of Double Diffusive Convection in a Thermally Modulated Fluid-Saturated Porous Medium

2008 ◽  
Vol 63 (5-6) ◽  
pp. 291-300 ◽  
Author(s):  
Beer S. Bhadauria ◽  
Aalam Sherani
Keyword(s):  
Porous Medium ◽  
Rayleigh Number ◽  
Saturated Porous Medium ◽  
Critical Rayleigh Number ◽  
Periodic Part ◽  
Double Diffusive Convection ◽  
Diffusive Convection ◽  
Fluid Saturated Porous Medium ◽  
The Galerkin Method ◽  
Double Diffusive

The onset of double diffusive convection in a sparsely packed porous medium was studied under modulated temperature at the boundaries, and a linear stability analysis has been made. The primary temperature field between the walls of the porous layer consisted of a steady part and a timedependent periodic part and the Galerkin method and the Floquet were used. The critical Rayleigh number was found to be a function of frequency and amplitude of modulation, Prandtl number, porous parameter, diffusivity ratio and solute Rayleigh number.

scholarly journals Linear and Nonlinear Stability Analysis of Double Diffusive Convection in a Maxwell Fluid Saturated Porous Layer with Internal Heat Source

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Moli Zhao ◽  
Qiangyong Zhang ◽  
Shaowei Wang
Keyword(s):  
Rayleigh Number ◽  
Heat Source ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Maxwell Fluid ◽  
Double Diffusive Convection ◽  
Diffusive Convection ◽  
Saturated Porous Layer ◽  
Linear And Nonlinear ◽  
Double Diffusive

The onset of double diffusive convection is investigated in a Maxwell fluid saturated porous layer with internal heat source. The modified Darcy law for the Maxwell fluid is used to model the momentum equation of the system, and the criterion for the onset of the convection is established through the linear and nonlinear stability analyses. The linear analysis is obtained using the normal mode technique, and the nonlinear analysis of the system is studied with the help of truncated representation of Fourier series. The effects of internal Rayleigh number, stress relaxation parameter, normalized porosity, Lewis number, Vadasz number and solute Rayleigh number on the stationary, and oscillatory and weak nonlinear convection of the system are shown numerically and graphically. The effects of various parameters on transient heat and mass transfer are also discussed and presented analytically and graphically.

Two-dimensional effects in double-diffusive convection

1974 ◽  
Vol 63 (3) ◽  
pp. 577-592 ◽  
Author(s):  
J. S. Turner ◽  
C. F. Chen
Keyword(s):  
Two Dimensional ◽  
Double Diffusive Convection ◽  
Mechanism Of Formation ◽  
Concentration Gradients ◽  
One Dimensional ◽  
Horizontal Gradients ◽  
Diffusive Convection ◽  
Similar Density ◽  
Double Diffusive ◽  
Vertical Gradients

The limitations of existing one-dimensional experiments on double-diffusive convection are discussed, and a variety of new two-dimensional phenomena are described. We have used the sugar-salt system and shadowgraph photography to make exploratory studies of motions which can arise in a fluid with two smooth, opposing, vertical concentration gradients, with and without horizontal gradients. Many different effects have been observed, the most important of which are the following, (a) In the ‘finger’ case, local disturbances can propagate rapidly as wave motions, which cause a simultaneous breakdown to convection over large horizontal distances. (b) Layers formed in the’ diffusive’ sense overturn locally to produce fingers, but propagate more slowly, as convective rather than wave motions, (c) A series of layers, separated by diffusive interfaces, can become unstable, in the sense that successive layers merge in time as their densities become equal, (d) The presence of horizontally separated sources of water of similar density but differentT,Scharacteristics can lead to the development of strong vertical gradients and extensive quasi-horizontal layering.Most of our results are qualitative, but it is hoped that they will stimulate further quantitive work on each of the new processes described. It is already clear that much more needs to be done before the mechanism of formation of layers observed in the ocean can be regarded as properly understood.

scholarly journals On the Onset of Double-diffusive Convection in a Couple Stress Nanofluid in a Porous Medium

2018 ◽  
Vol 62 (3) ◽  
pp. 233-240
Author(s):  
Gian C. Rana ◽  
Ramesh Chand
Keyword(s):  
Porous Medium ◽  
Rayleigh Number ◽  
Couple Stress ◽  
Lewis Number ◽  
Double Diffusive Convection ◽  
Stationary Convection ◽  
Stress Parameter ◽  
Diffusive Convection ◽  
Double Diffusive ◽  
Solutal Rayleigh Number

Double-diffusive convection in a horizontal layer of nanofluid in a porous medium is studied. The couple-stress fluid model is considered to describe the rheological behavior of the nanofluid and for porous medium Darcy model is employed. The model applied for couple stress nanofluid incorporates the effect of Brownian motion and thermophoresis. We have assumed that the nanoparticle concentration flux is zero on the boundaries which neutralizes the possibility of oscillatory convection and only stationary convection occurs. The dispersion relation describing the effect of various parameters is derived by applying perturbation theory, normal mode analysis method and linear stability theory. The impact of various physical parameters, like the couple stress parameter, medium porosity, solutal Rayleigh Number, thermo-nanofluid Lewis number, thermo-solutal Lewis number, Soret parameter and Dufour parameter have been examined on the stationary convection. It is observed that the couple stress parameter, thermo-nanofluid Lewis number, thermo-solutal Lewis number, Soret parameter and Dufour parameter have stabilizing effects on the stationary convection whereas the solutal Rayleigh number and Dufour parameter have very small effect on the system.

The influence of a third diffusing component upon the onset of convection

1979 ◽  
Vol 92 (4) ◽  
pp. 659-670 ◽  
Author(s):  
R. W. Griffiths
Keyword(s):  
Stability Analysis ◽  
Rayleigh Number ◽  
Small Amplitude ◽  
Double Diffusive Convection ◽  
Onset Of Convection ◽  
Molecular Diffusivity ◽  
Diffusive Convection ◽  
Wide Range ◽  
Straight Lines ◽  
Double Diffusive

The small amplitude stability analysis for the onset of double-diffusive convection when the density gradient is gravitationally stable is extended to include a third diffusing component. Special attention is given to systems with κ1 [Gt ] κ2, κ3 and Pr [Gt ] κ/κ1, where κi is the molecular diffusivity of the ith component and Pr is the Prandtl number based on the largest of the Ki. It is found that the boundary for the onset of overstability is approximated by two straight lines in a Rayleigh number plane. Small concentrations of a third property with a smaller diffusivity can have a significant effect upon the nature of diffusive instabilities, the magnitude of this effect being proportional to κ1/Ki. Oscillatory and direct ‘salt-finger’ modes are found to be simultaneously unstable under a wide range of conditions when the density gradients due to the components with the greatest and smallest diffusivities are of the same sign.

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