Asymptotic solutions for nonlinear magnetoconvection
Asymptotic solutions for nonlinear magnetoconvection
复制标题
非线性磁对流的渐近解
DOI：
10.1017/s0022112099004966
复制
发表时间：
1999
影响因子：
3.7
通讯作者：
P. Matthews
中科院分区：
文献类型：
--
作者：
P. Matthews
垂直磁场中的对流发生在物理相关极限内的窄网格中，钱德拉塞卡尔数Q变大，对应于强场或小扩散。这使得可以得到完全非线性对流的渐近解，只需要解一个非线性边值问题。得到了定常和振荡磁对流在不同尺度下的解。在定常情况下，热流密度和流体速度在渐近展开中处于领先阶，垂直速度尺度为Q1/6。在振荡情况下，需要继续到二阶，垂直速度为Q1/3量级，并且振荡的频率总是大于线性理论所预测的频率。热流既不取决于波数，也不取决于平面形状。
Convection in a vertical magnetic field occurs in narrow cells in the physically relevant limit where the Chandrasekhar number Q becomes large, corresponding to a strong field or small diffusion. This allows asymptotic solutions to be developed for fully nonlinear convection, requiring only the solution of a nonlinear boundary value problem. Solutions for steady and oscillatory magnetoconvection are obtained, with different scalings. In the steady case, the heat flux and the fluid velocity are found at leading order in the asymptotic expansion and the vertical velocity scales as Q1/6. In the oscillatory case, where it is necessary to continue to second order, the vertical velocity is of order Q1/3 and the frequency of the oscillations is always greater than that predicted by linear theory. The heat flux does not depend on either the wavenumber or the planform.