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Fluids 2017, 2(4), 60; doi:10.3390/fluids2040060

Horizontal Cellular Oscillations Caused by Time-Periodic Resonant Thermal Forcing in Weakly Nonlinear Darcy-Bénard Convection

1
Department of Mathematical Sciences, Universiti Teknologi Malaysia, 81300 Skudai, Malaysia
2
Department of Mechanical Engineering, University of Bath, Bath BA2 7AY, UK
*
Author to whom correspondence should be addressed.
Received: 14 September 2017 / Revised: 25 October 2017 / Accepted: 27 October 2017 / Published: 4 November 2017
(This article belongs to the Special Issue Convective Instability in Porous Media)
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Abstract

The onset of Rayleigh-Bénard convection in a horizontally unbounded saturated porous medium is considered. Particular attention is given to the stability of weakly nonlinear convection between two plane horizontal surfaces heated from below. The primary aim is to study the effects on postcritical convection of having small amplitude time-periodic resonant thermal forcing. Amplitude equations are derived using a weakly nonlinear theory and they are solved in order to understand how the flow evolves with changes in the Darcy-Rayleigh number and the forcing frequency. When convection is stationary in space, it is found to consist of one of two different types depending on its location in parameter space: either a convection pattern where each cell rotates in the same way for all time with a periodic variation in amplitude (Type I) or a pattern where each cell changes direction twice within each forcing period (Type II). Asymptotic analyses are also performed (i) to understand the transition between convection of types I and II; (ii) for large oscillation frequencies and (iii) for small oscillation frequencies. In a large part of parameter space the preferred pattern of convection when the layer is unbounded horizontally is then shown to be one where the cells oscillate horizontally—this is a novel form of pattern selection for Darcy-Bénard convection. View Full-Text
Keywords: porous media; convective instability; weakly nonlinear; resonant forcing; horizontal oscillations porous media; convective instability; weakly nonlinear; resonant forcing; horizontal oscillations
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Jais, I.M.; Rees, D.A.S. Horizontal Cellular Oscillations Caused by Time-Periodic Resonant Thermal Forcing in Weakly Nonlinear Darcy-Bénard Convection. Fluids 2017, 2, 60.

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