Effect of gravity modulation on the stability of a horizontal double-diffusive layer

Persistent Link:
http://hdl.handle.net/10150/279848
Title:
Effect of gravity modulation on the stability of a horizontal double-diffusive layer
Author:
Chen, Wen-Yau
Issue Date:
2001
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
The effect of gravity modulation on the instability onset in an infinite horizontal layer of double-diffusive fluid is investigated in this dissertation. The spectral-Galerkin method is used to transform the linearized perturbation equations to the system of time-periodic ordinary differentiate equations. The Chebyshev expansion method (Sinha and Wu, 1991) is applied to calculate the foundamental matrix which is used to determine the stability of the system according to the Floquet theory. Fluids of Prandtl number Pr = 0.01, 1, and 7 are investigated. The instability onsets in one of three modes, synchronous, subharmonic, and quasi periodic mode. In the synchronous mode, the instability oscillates at the same frequency as the gravity modulation O, in the subharmonic mode, the instability oscillates at O/2, while in the quasi-periodic mode, the oscillation frequency of the instability is different from the above two. The quasi-periodic mode onsets at the same thermal Rayleigh number, RT as that of instability onset under steady gravity. The subharmonic mode onsets with wave numbers in the neighboring region of k where the oscillation frequency of the instability onset in the steady-g case, o, equals to half of the modulation frequency, O/2. Similarly, the synchronous mode onsets at the neighboring of k where the o equals to O. The onset RT for quasi-periodic mode is not changed by the modulation frequency O and the relative amplitude of the modulation, h. For the synchronous and subharmonic modes, destabilization increases with increasing h. If h is large enough, the subharmonic mode will be more unstable than the synchronous and quasi periodic mode, so the instability mode will be switched by increasing h. For a given h with varying O, the resonance effect occurs in the neighborhood of O ≈ 2o cr, i.e, twice the critical oscillation frequency of the instability in the steady-g case associated with the critical RT. The resonant phenomena is found for fluids with Pr = 0.01, 1, and 7, and the effect diminishes as the Prandtl number increases. The effect of gravity modulation is asymptotic to zero when the modulated frequency O approaches zero and infinitely large. For the case of Prandtl number, Pr, = 0.01, it is found that the critical thermal Rayleigh number RT is reduced from the steady-g value of 2183 by 4%, 41%, and 86% as h is increased from 0.01, 0.1 and 0.2. In fact when h = 0.22737, the layer of fluid is destabilized at O = 9.1 with RT = 0, i.e., without heating from below. This is analogous to the case in the research of Gresho and Sani (1970) that a horizontal layer being heated from above can be destabilized by the oscillation of the layer. In this dissertation the stabilization effect caused by the modulation is found at some cases of O, which is analogous to the stability of motion of the pendulum with pivot in oscillation as discussed in Gresho and Sani (1970).
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Engineering, Mechanical.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Aerospace and Mechanical Engineering
Degree Grantor:
University of Arizona
Advisor:
Chen, Chuan F.

Full metadata record

DC FieldValue Language
dc.language.isoen_USen_US
dc.titleEffect of gravity modulation on the stability of a horizontal double-diffusive layeren_US
dc.creatorChen, Wen-Yauen_US
dc.contributor.authorChen, Wen-Yauen_US
dc.date.issued2001en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractThe effect of gravity modulation on the instability onset in an infinite horizontal layer of double-diffusive fluid is investigated in this dissertation. The spectral-Galerkin method is used to transform the linearized perturbation equations to the system of time-periodic ordinary differentiate equations. The Chebyshev expansion method (Sinha and Wu, 1991) is applied to calculate the foundamental matrix which is used to determine the stability of the system according to the Floquet theory. Fluids of Prandtl number Pr = 0.01, 1, and 7 are investigated. The instability onsets in one of three modes, synchronous, subharmonic, and quasi periodic mode. In the synchronous mode, the instability oscillates at the same frequency as the gravity modulation O, in the subharmonic mode, the instability oscillates at O/2, while in the quasi-periodic mode, the oscillation frequency of the instability is different from the above two. The quasi-periodic mode onsets at the same thermal Rayleigh number, RT as that of instability onset under steady gravity. The subharmonic mode onsets with wave numbers in the neighboring region of k where the oscillation frequency of the instability onset in the steady-g case, o, equals to half of the modulation frequency, O/2. Similarly, the synchronous mode onsets at the neighboring of k where the o equals to O. The onset RT for quasi-periodic mode is not changed by the modulation frequency O and the relative amplitude of the modulation, h. For the synchronous and subharmonic modes, destabilization increases with increasing h. If h is large enough, the subharmonic mode will be more unstable than the synchronous and quasi periodic mode, so the instability mode will be switched by increasing h. For a given h with varying O, the resonance effect occurs in the neighborhood of O ≈ 2o cr, i.e, twice the critical oscillation frequency of the instability in the steady-g case associated with the critical RT. The resonant phenomena is found for fluids with Pr = 0.01, 1, and 7, and the effect diminishes as the Prandtl number increases. The effect of gravity modulation is asymptotic to zero when the modulated frequency O approaches zero and infinitely large. For the case of Prandtl number, Pr, = 0.01, it is found that the critical thermal Rayleigh number RT is reduced from the steady-g value of 2183 by 4%, 41%, and 86% as h is increased from 0.01, 0.1 and 0.2. In fact when h = 0.22737, the layer of fluid is destabilized at O = 9.1 with RT = 0, i.e., without heating from below. This is analogous to the case in the research of Gresho and Sani (1970) that a horizontal layer being heated from above can be destabilized by the oscillation of the layer. In this dissertation the stabilization effect caused by the modulation is found at some cases of O, which is analogous to the stability of motion of the pendulum with pivot in oscillation as discussed in Gresho and Sani (1970).en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectEngineering, Mechanical.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineAerospace and Mechanical Engineeringen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorChen, Chuan F.en_US
dc.identifier.proquest3031353en_US
dc.identifier.bibrecord.b4228322xen_US
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