Convective stability in the RayleighBenard and directional solidification problems  highfrequency gravity modulation
Wheeler, A.A., McFadden, G.B., Murray, B.T. and Coriell, S.R. (1991) Convective stability in the RayleighBenard and directional solidification problems  highfrequency gravity modulation. Physics of Fluids A, 3, (12), 28472858.
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Description/Abstract
The effect of vertical, sinusoidal, timedependent gravitational acceleration on the onset of solutal convection during directional solidification is analyzed in the limit of large modulation frequencyOMEGA. When the unmodulated state is unstable, the modulation amplitude required to stabilize the system is determined by the method of averaging, and is O(OMEGA). Comparison of the results from the averaged equations with numerical solutions of the full linear stability equations (based on Floquet theory) show that the difference is O(OMEGA1/2). When the unmodulated state is stable, resonant modes of instability occur at large modulation amplitude. These are analyzed using matched asymptotic expansions to elucidate the boundarylayer structure for both the RayleighBenard and directional solidification configurations. The leadingorder term for the modulation amplitude is of O(OMEGA2); the firstorder correction of O(OMEGA3/2) is calculated, and the results are compared with numerical solutions of the full linear stability equations. Based on these analyses, a thorough examination of the dependence of the stability criteria on the unmodulated Rayleigh number, Schmidt number, and distribution coefficient, is carried out.
Item Type:  Article  

Keywords:  Binary alloy, fluid layer, flows, melt.  
Subjects:  Q Science > QA Mathematics  
Divisions:  University Structure  Pre August 2011 > School of Mathematics > Applied Mathematics 

ePrint ID:  816  
Date : 


Date Deposited:  25 Mar 2004  
Last Modified:  31 Mar 2016 11:08  
URI:  http://eprints.soton.ac.uk/id/eprint/816 
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