The effect of gravity modulation on thermosolutal convection in an
                        infinite layer of fluid

Saunders, Bonita V.; Murray, Bruce T.; McFadden, Geoffrey B.; Coriell, S. R.; Wheeler, A. A.

doi:10.6028/nist.ir.4679

Cited by 8 publications

(24 citation statements)

References 31 publications

(47 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The result that the critical instability alternates between the synchronous and subharmonic modes as the modulation amplitude is increased at a constant frequency is quite similar to earlier results for convection in a horizontal fluid layer found by Gershuni et al (1970), Gresho & Sani (1970), Saunders et al (1992), and Terrones & Chen (1993). Stability equations for this type of problems can be reduced to the Mathieu equation, which has asymptotic stable solutions in either the synchronous or the subharmonic mode, depending on the modulation frequency and amplitude.…”

Section: Resultssupporting

confidence: 86%

“…More complicated interactions may be expected for fluids with Prandtl numbers near the transition value of 12.5. For these cases, the marginal stability curves may consist of all three branches, synchronous, subharmonic, and quasi-periodic, as in the case of horizontal double-diffusive fluid layers found by Saunders et al (1992) and Terrones & Chen (1993). The instability characteristics of such fluids must be examined individually.…”

Section: Discussionmentioning

confidence: 99%

“…For a case predicted to be stable by Gresho & Sani at a Rayleigh number of 4500, they showed that any initial perturbations in the velocity amplitude vanished in a short time. Saunders et al (1992) studied the effect of gravity modulation on the stability of a double-diffusive layer with stress-free boundaries in both the finger and diffusive cases. They presented stability boundaries in the plane spanned by amplitude and the inverse of modulation frequency for a number of examples.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Effect of gravity modulation on the stability of convection in a vertical slot

Chen

1999

J. Fluid Mech.

View full text Add to dashboard Cite

The nature of instability occurring in a differentially heated infinite slot under steady gravity depends only on the Prandtl number of the contained Boussinesq fluid. For fluids with Pr < 12.5, the instability is shear dominated and onsets in a steady convection mode; for fluids with Pr > 12.5, the instability is buoyancy dominated and onsets in an oscillatory mode. In this paper, we examine the effect of gravity modulation on the stability characteristics of convection in an infinite slot with both kinds of fluids, in particular, Pr = 1 and Pr = 25. Using the method of Sinha & Wu (1991), we are able to obtain accurate results without excessive numerical integration in the linear stability analysis by Floquet theory. Results show that, for Pr = 1, at a non-dimensional oscillation frequency ω = 20, the critical state alternates between the synchronous and subharmonic modes. At higher frequencies, ω > 100, all critical states occur in the synchronous mode. For Pr = 25, with a modulation amplitude ratio of 0.5, resonant interaction occurs in the neighbourhood of ω = 2σc, where σc is the oscillation frequency of the instability at the critical state under steady gravity. This resonant interaction is destabilizing, with the critical Grashof number being reduced by approximately 20% from that at steady gravity. It is due to the presence of a detached subharmonic branch of the marginal stability curve. In frequency ranges where the detached subharmonic branch is absent, the critical state is in the quasi-periodic mode consisting of two waves of different oscillation frequencies whose sum is the forcing frequency. An analysis of the rate of change of the perturbation kinetic energy shows that, for Pr = 1, the instability is shear dominated regardless of the mode of oscillation, synchronous or subharmonic. Similarly, for Pr = 25, the instability is buoyancy dominated whether it is in the quasi-periodic or subharmonic mode. The mode switching is a response to the forcing and is independent of the dominant mechanisms of instability.

show abstract

Section: Resultssupporting

confidence: 86%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Effect of gravity modulation on the stability of convection in a vertical slot

Chen

1999

J. Fluid Mech.

View full text Add to dashboard Cite

show abstract

“…Wadih and Roux (1988) presented a study on instability of the convection in an infinitely long cylinder with gravity modulation oscillating along the vertical axis. Saunders et al (1992) have discussed the effect of gravity modulation on thermosolutal convection in an infinite layer of fluid. performed a detailed non-linear analysis of Rayleigh-Bénard convection under gravity modulation and presented the stability limits to a much wider region of parameter space.…”

Section: Introductionmentioning

confidence: 99%

Weak Nonlinear Double Diffusive Magneto-Convection in a Newtonian Liquid under Gravity Modulation

Bhadauria

Kiran

2015

JAFM

View full text Add to dashboard Cite

A theoretical analysis of thermo-convective instability in an electrically conducting two component fluid layer is carried out when the gravity field vary with time in a sinusoidal manner. Newtonian liquid is considered between two horizontal surfaces, under a constant vertical magnetic field. The disturbance is expanded in terms of power series of amplitude of convection, which is assumed to be small. We use the linear matrix differential operator method to find the Ginzburg-Landau amplitude equation for the modulated problem. Use the solution of the Ginzburg-Landau equation in quantifying the amount of heat and mass transports in terms of Nusselt and Sherwood numbers. It is found that, the effect of magnetic field is to stabilize the system. Effect of various parameters on the heat and mass transport is also discussed. Further, it is found that the heat and mass transports can be controlled by suitably adjusting frequency and amplitude of gravity modulation.

show abstract

“…Murray and colleagues [18] considered the effect of GM on the onset of convection for the unidirectional solidification problem. Saunders and colleagues [19] studied the effect of GM on the stability of a horizontal double-diffusive layer. Clever and colleagues [20] studied the problem of two-dimensional oscillatory convection in a gravitationally modulated fluid layer.…”

Section: Introductionmentioning

confidence: 99%

g-Jitter-Induced Electrothermoconvection in a Dielectric Fluid Saturated Porous Layer

Swamy

2014

Heat Trans. Asian Res.

View full text Add to dashboard Cite

This paper presents linear and nonlinear stability analyses of thermal convection in a dielectric fluid saturated sparsely packed porous layer subject to the combined effect of time-periodic gravity modulation (GM) and an AC electric field. In the domain of linear theory, the critical stability parameters are computed by the regular perturbation method in the form of a perturbation series in powers of frequency of modulation. The local nonlinear theory based on the truncated Fourier series method gives information on convection amplitudes and heat transfer. The principle of the exchange of stabilities is found to be valid and subcritical instability is ruled out. Based on the governing linear autonomous system, several qualitative results on stability are discussed. The sensitive dependence of the solution of a Lorenz system of electrothermal convection subject to the choice of initial conditions points to the possibility of chaos. Low-frequency g-jitter is found to have a significant stabilizing influence, which is in turn diminished by an imposed AC electric field. The role of sparseness of the porous layer, viscosity ratio, and normalized porosity on the stability criterion and on heat transport is determined. C⃝

show abstract

The effect of gravity modulation on thermosolutal convection in an infinite layer of fluid

Cited by 8 publications

References 31 publications

Effect of gravity modulation on the stability of convection in a vertical slot

Effect of gravity modulation on the stability of convection in a vertical slot

Weak Nonlinear Double Diffusive Magneto-Convection in a Newtonian Liquid under Gravity Modulation

g-Jitter-Induced Electrothermoconvection in a Dielectric Fluid Saturated Porous Layer

Contact Info

Product

Resources

About