On oscillatory modes of nonlinear compositional convection in mushy layers

✍ Scribed by D.N. Riahi

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 801 KB
• Volume: 10
• Category: Article
• ISSN: 1468-1218
• DOI: 10.1016/j.nonrwa.2007.08.028

✦ Synopsis

We consider the problem of nonlinear compositional convection in horizontal mushy layers during the solidification of binary alloys. Under a near-eutectic approximation and the limit of large far-field temperature, we determine a number of weakly nonlinear oscillatory solutions, and the stability of these solutions with respect to arbitrary disturbances is then investigated. The present investigation is an extension of the problem of the oscillatory modes of convection, which was investigated by [D.N. Riahi, On nonlinear convection in mushy layers. Part 1. Oscillatory modes of convection, J. Fluid Mech. 467 (2002) 331-359] in the absence of the main permeability parameter K 1 and very recently by [P. Guba, M.G. Worster, Nonlinear oscillatory convection in mushy layers, J. Fluid Mech. 553 (2006) 419-443] for two-dimensional cases in the presence of K 1 , to include the effects of K 1 , over a range of values of the other parameters, and for both two-and three-dimensional motion. It was found, in particular, that the results reported in [D.N. Riahi, On nonlinear convection in mushy layers.