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...
Saved in:
| Main Author: | |
|---|---|
| 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 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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. |
|---|---|
| ISSN: | 0161-1712 1687-0425 |