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Linear and nonlinear convection in porous media between coaxial cylinders

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10.1063/1.3637642

### Abstract

We uncover novel features of three-dimensional natural convection in porous media by investigating convection in an annular porous cavity contained between two vertical coaxial cylinders. The investigations are made using a linear stability analysis, together with high-order numerical simulations using pseudospectral methods to model the nonlinear regime. The onset of convection cells and their preferred planform are studied, and the stability of the modes with respect to different types of perturbation is investigated. We also examine how variations in the Rayleigh number affect the convection modes and their stability regimes. Compared with previously published data, we show how the problem inherits an increased complexity regarding which modes will be obtained. Some stable secondary modes or mixed modes have been identified and some overlapping stability regions for different convective modes are determined.

© 2011 American Institute of Physics

Received 02 May 2011
Accepted 18 August 2011
Published online 16 September 2011

Article outline:

I. INTRODUCTION

II. MATHEMATICAL FORMULATION

III. LINEAR STABILITY ANALYSIS AND MODE MAPS

A. Linearization about the basic state

B. The critical Rayleigh number

C. Mode maps

D. Results and discussion

1. Critical Rayleigh number

2. Mode maps

3. The limiting case when R_{w} goes to zero

IV. NUMERICAL SIMULATIONS AND THE NONLINEAR REGIME

A. Pseudospectral discretization

B. Solution strategy

C. Results and discussion

V. CONCLUSION

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2011-09-16

2014-04-19

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