On nonlinear convection in mushy layers. Part 2. Mixed oscillatory and stationary modes of convection
On nonlinear convection in mushy layers. Part 2. Mixed oscillatory and stationary modes of convection
复制标题
糊状层中的非线性对流。
DOI：
--
复制
发表时间：
2004
影响因子：
3.7
通讯作者：
D. N. Riahi
中科院分区：
文献类型：
--
作者：
D. N. Riahi
本文介绍了二元合金凝固过程中水平糊状层中非线性对流的研究的第二部分。第1部分只讨论对流的振荡模式（Riahi， J.流体力学）。第467卷，2002年，第331-359页)。在本文中，我们考虑了振荡和平稳对流起始的标度瑞利数R的临界值彼此接近的特定参数范围，并在这种参数范围内发展和分析了一个非线性理论，该理论考虑了具有共同波数矢量的对流的混合平稳和振荡模式。在近共晶近似下，在大远场温度极限下，我们首先确定了一些弱非线性解，然后研究了这些解的稳定性。最有趣的结果是，在相对较宽的参数值范围内，对于由静止和静止六边形模态组成的混合溶液的偏好，以及在可能对流的最低亚临界值之上的R。这种优选溶液的性质与Tait等人（Nature, vol. 359, 1992, pp. 406-408）的实验结果基本一致，即在细胞中心处水流向下，在细胞边界处水流向上，并且在细胞节点处有一定的通道形成趋势。
This paper presents part 2 of a study of nonlinear convection in horizontal mushy layers during the solidification of binary alloys. Part 1 dealt with only the oscillatory modes of convection (Riahi, J. Fluid Mech. vol. 467, 2002, pp. 331–359). In the present paper we consider the particular range of parameters where the critical values of the scaled Rayleigh number $R$ for the onset of oscillatory and stationary convection are close to each other, and we develop and analyse a nonlinear theory in such a parameter regime which takes into account those mixed stationary and oscillatory modes of convection with common wavenumber vectors. Under a near-eutectic approximation and in the limit of large far-field temperature, we first determine a number of weakly nonlinear solutions, and then the stability of these solutions is investigated. The most interesting result is the preference for a mixed solution composed of standing and stationary hexagonal modes over a relatively wide range of the parameter values and for $R$ just above its lowest subcritical value where convection is possible. Such a preferred solution has properties mostly in agreement with the experimental results due to Tait et al. (Nature, vol. 359, 1992, pp. 406–408) in the sense that the flow is downward at the cell centres, upward at the cell boundaries and there is some tendency for channel formation at the cell nodes.