Finite bandwidth, long wavelength convection with boundary imperfectons: near-resonant wavelength excitation

Finite amplitude thermal convection with continuous finite bandwidth of long wavelength modes in a porous layer between two horizontal poorly conducting walls is studied when spatially nonuniform temperature is prescribed at the lower wall. The weakly nonlinear problem is solved by using multiple sc...

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Main Author: D. N. Riahi
Format: Article
Language:English
Published: Wiley 1998-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Subjects:
Online Access:http://dx.doi.org/10.1155/S0161171298000234
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author D. N. Riahi
author_facet D. N. Riahi
author_sort D. N. Riahi
collection DOAJ
description Finite amplitude thermal convection with continuous finite bandwidth of long wavelength modes in a porous layer between two horizontal poorly conducting walls is studied when spatially nonuniform temperature is prescribed at the lower wall. The weakly nonlinear problem is solved by using multiple scales and perturbation techniques. The preferred long wavelength flow solutions are determined by a stability analysis. The case of near resonant wavelength excitation is considered to determine the non-modal type of solutions. It is found that, under certain conditions on the form of the boundary imperfections, the preferred horizontal structure of the solutions is of the same spatial form as that of the total or some subset of the imperfection shape function. It is composed of a multi-modal pattern with spatial variations over the fast variables and with non-modal amplitudes, which vary over the slow variables. The preferred solutions have unusual properties and, in particular, exhibit kinks in certain vertical planes which are parallel to the wave vectors of the boundary imperfections. Along certain vertical axes, where some of these vertical planes can intersect, the solutions exhibit multiple kinks.
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spelling doaj-art-30ceacdf3bba41a59c6d6231cdaaf73f2025-08-20T03:55:12ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251998-01-0121117118110.1155/S0161171298000234Finite bandwidth, long wavelength convection with boundary imperfectons: near-resonant wavelength excitationD. N. Riahi0Department of Theoretical and Applied Mechanics, University of Illinois at Urbana-Champaign, Urbana 61801, Illinois, USAFinite amplitude thermal convection with continuous finite bandwidth of long wavelength modes in a porous layer between two horizontal poorly conducting walls is studied when spatially nonuniform temperature is prescribed at the lower wall. The weakly nonlinear problem is solved by using multiple scales and perturbation techniques. The preferred long wavelength flow solutions are determined by a stability analysis. The case of near resonant wavelength excitation is considered to determine the non-modal type of solutions. It is found that, under certain conditions on the form of the boundary imperfections, the preferred horizontal structure of the solutions is of the same spatial form as that of the total or some subset of the imperfection shape function. It is composed of a multi-modal pattern with spatial variations over the fast variables and with non-modal amplitudes, which vary over the slow variables. The preferred solutions have unusual properties and, in particular, exhibit kinks in certain vertical planes which are parallel to the wave vectors of the boundary imperfections. Along certain vertical axes, where some of these vertical planes can intersect, the solutions exhibit multiple kinks.http://dx.doi.org/10.1155/S0161171298000234Convectionimperfectionslong wavelengthlong wavelength convectionnear-resonanceboundary imperfectionsfinite-bandwidth.
spellingShingle D. N. Riahi
Finite bandwidth, long wavelength convection with boundary imperfectons: near-resonant wavelength excitation
International Journal of Mathematics and Mathematical Sciences
Convection
imperfections
long wavelength
long wavelength convection
near-resonance
boundary imperfections
finite-bandwidth.
title Finite bandwidth, long wavelength convection with boundary imperfectons: near-resonant wavelength excitation
title_full Finite bandwidth, long wavelength convection with boundary imperfectons: near-resonant wavelength excitation
title_fullStr Finite bandwidth, long wavelength convection with boundary imperfectons: near-resonant wavelength excitation
title_full_unstemmed Finite bandwidth, long wavelength convection with boundary imperfectons: near-resonant wavelength excitation
title_short Finite bandwidth, long wavelength convection with boundary imperfectons: near-resonant wavelength excitation
title_sort finite bandwidth long wavelength convection with boundary imperfectons near resonant wavelength excitation
topic Convection
imperfections
long wavelength
long wavelength convection
near-resonance
boundary imperfections
finite-bandwidth.
url http://dx.doi.org/10.1155/S0161171298000234
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