A sharp nonlinear stability threshold in rotating porous convection

By B. Straughan. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 2001

139 citations recorded by the source corpus.

A nonlinear stability analysis is performed for the Darcy equations of thermal convection in a fluid‐saturated porous medium when the medium is rotating about an axis orthogonal to the layer in the direction of gravity. A best possible result is established in that we show that the global nonlinear stability Rayleigh number is exactly the same as that for linear instability. It is important to realize that the nonlinear stability boundary holds unconditionally, i.e. for all initial data, and thus for the rotating porous convection problem governed by the Darcy equations, subcritical instabilities are not possible.

Subfields: Applied Mathematics, Biomedical Engineering, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/9504fa98d1dd386ab9df2be7991155551ef5ba40

How researchers see this paper

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In Applied Mathematics

1. F. Franchi
2. Brian Straughan

In Biomedical Engineering

1. F. Franchi
2. Brian Straughan

In Computational Mechanics

1. F. Franchi
2. Brian Straughan
3. Siyu Lin
4. Bixiang Wang
5. Varga K. Kalantarov
6. Sergey Zelik

Citations in the corpus

• Continuous dependence and decay for the Forchheimer equations (2003, methodology): “Our goal is to derive upper and lower bounds for ‖u(t)‖ and we follow the method of Payne & Straughan (1999), mutatis mutandis.”