University of Illinois Urbana-Champaign

Finite bandwidth long wavelength convection with boundary imperfections near-resonant wavelength excitation

Riahi, Daniel N.

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https://hdl.handle.net/2142/112482

Description

Title
Finite bandwidth long wavelength convection with boundary imperfections near-resonant wavelength excitation
Author(s)
Riahi, Daniel N.
Issue Date
1995-03
Keyword(s)
  • Long Wavelength Convection
  • Near Resonant Wavelength Excitation
Abstract
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 non-uniform temperture 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'.
Publisher
Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report Name or Number
  • TAM R 786
  • 1995-6008
ISSN
0073-5264
Type of Resource
text
Language
eng
Permalink
http://hdl.handle.net/2142/112482
Copyright and License Information
Copyright 1995 Board of Trustees of the University of Illinois

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Technical Reports - Theoretical and Applied Mechanics (TAM) PRIMARY
TAM technical reports include manuscripts intended for publication, theses judged to have general interest, notes prepared for short courses, symposia compiled from outstanding undergraduate projects, and reports prepared for research-sponsoring agencies.