Global stability of centrifugal filtration convection

• Published in: Journal of mathematical analysis and applications Vol. 367; no. 1; pp. 116 - 128
• Main Authors: Saravanan, S., Brindha, D.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 01-07-2010; Elsevier
• Subjects: Centrifugal force; Darcy's and Brinkman's equations; Exact sciences and technology; Functional analysis; Mathematical analysis; Mathematics; Nonlinear stability; Porous medium; Sciences and techniques of general use; Nonlinear stability; Darcy's and Brinkman's equations; Centrifugal force; Porous medium; Mathematical analysis; Nonlinear analysis; Layered fluid; Instability; Functional analysis; Application; Numerical stability; Non linear stability
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/j.jmaa.2009.12.026

A nonlinear stability analysis is performed to study the onset of convection in a fluid saturated porous layer subject to alternating direction of the centrifugal body force. By introducing a suitable energy functional, the analysis is carried out for the Darcy and the Brinkman models of flow through porous media. The nonlinear result is unconditional and its sharpest limit is determined and is compared with the corresponding linear limit. The failure of linear theory in describing the instability is established in a certain region of the parameter space where possible subcritical instabilities may arise. The stability boundaries are discussed graphically for various values of the Darcy number and comparison is made with the available known results.