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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| Format: | Article |
| Language: | English |
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Wiley
1998-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171298000234 |
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| _version_ | 1849306006828351488 |
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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. |
| format | Article |
| id | doaj-art-30ceacdf3bba41a59c6d6231cdaaf73f |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1998-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| 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 |
| work_keys_str_mv | AT dnriahi finitebandwidthlongwavelengthconvectionwithboundaryimperfectonsnearresonantwavelengthexcitation |