Jais, Ibrahim M. and Rees, D. Andrew S. (2017) Horizontal Cellular Oscillations Caused by TimePeriodic Resonant Thermal Forcing in Weakly Nonlinear DarcyBenard Convection. FLUIDS, 2 (4).

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Official URL: http://dx.doi.org/10.3390/fluids2040060
Abstract
The onset of RayleighBenard 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 timeperiodic 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 DarcyRayleigh 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 horizontallythis is a novel form of pattern selection for DarcyBenard convection.
Item Type:  Article 

Uncontrolled Keywords:  porous media, convective instability, weakly nonlinear, resonant forcing, horizontal oscillations 
Subjects:  Q Science > QA Mathematics 
Divisions:  Science 
ID Code:  77289 
Deposited By:  Narimah Nawil 
Deposited On:  28 Jan 2019 04:45 
Last Modified:  28 Jan 2019 04:45 
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