Energy stability of thermocapillary convection in a model of the float-zone crystal-growth process
Energy stability of thermocapillary convection in a model of the float-zone crystal-growth process
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DOI：
10.1017/s002211209000088x
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发表时间：
1990-08
影响因子：
3.7
通讯作者：
Y. Shen;G. Neitzel;D. Jankowski;H. Mittelmann
中科院分区：
文献类型：
--
作者：
Y. Shen;G. Neitzel;D. Jankowski;H. Mittelmann
将能量稳定理论应用于有限长度圆柱形半区热毛细对流的基本状态，以确定流动稳定的条件。由于区域的长度有限，必须用数值方法确定其基本状态。变分问题不是通过求解相关的欧拉-拉格朗日方程来获得稳定性判据，而是通过利用有限差分对能量恒等式中的积分进行离散化来直接解决。分析的结果是马兰戈尼数（MaE）的值，低于该值，对基本态的轴对称扰动将衰减，对于控制问题的其他参数的不同值。
Energy stability theory has been applied to a basic state of thermocapillary convection occurring in a cylindrical half-zone of finite length to determine conditions under which the flow will be stable. Because of the finite length of the zone, the basic state must be determined numerically. Instead of obtaining stability criteria by solving the related Euler–Lagrange equations, the variational problem is attacked directly by discretization of the integrals in the energy identity using finite differences. Results of the analysis are values of the Marangoni number, MaE, below which axisymmetric disturbances to the basic state will decay, for various values of the other parameters governing the problem.