A convection-driven dynamo I. The weak field case
A convection-driven dynamo I. The weak field case
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对流驱动发电机 I. 弱场情况
DOI：
10.1098/rsta.1974.0003
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发表时间：
1974
期刊：
影响因子：
--
通讯作者：
A. Soward
中科院分区：
文献类型：
--
作者：
A. Soward
考虑了磁流体发电机模型。Boussinesq导电流体被限制在两个水平面之间，并从下面加热。该系统以恒定的角速度绕垂直轴快速旋转。据推测，不稳定性首先设置为一个小的水平长度尺度的特征的静止对流。在初步计算中，忽略洛伦兹力，使磁感应方程和运动方程解耦。因此，不稳定性开始时发生的运动可能维持磁场的可能性被简化为运动发电机问题。此外，两个长度尺度的存在引入了简化，这使得该问题能够通过众所周知的技术来研究。研究了洛仑兹力对系统有限振幅动力学的影响。由于只考虑了弱磁场，运动的动能由其他因素决定，只有流动的精细结构受磁场的影响。一组非线性方程，其中管理的演变的磁流体发电机，来自渐近分析。方程进行了详细的研究分析和数值。尽管严重怀疑是否存在足够复杂的稳定运动，稳定的周期发电机被证明存在。这些方程的一个有趣的解析解，这可能是相关的有限振幅贝纳德对流所产生的其他问题，在最后一节。
A hydromagnetic dynamo model is considered. A Boussinesq, electrically conducting fluid is confined between two horizontal planes and is heated from below. The system rotates rapidly about the vertical axis with constant angular velocity. It is supposed that instability first sets in as stationary convection characterized by a small horizontal length scale. In preliminary calculations the Lorentz force is neglected so that the magnetic induction equation and the equation of motion are decoupled. The possibility that motions occurring at the onset of instability may sustain magnetic fields is thus reduced to a kinematic dynamo problem. Moreover, the existence of two length scales introduces simplifications which enable the problem to be studied by well-known techniques. The effect of the Lorentz force on the finite amplitude dynamics of the system is investigated also. Since only weak magnetic fields are considered the kinetic energy of the motion is fixed by other considerations and it is only the fine structure of the flow that is influenced by the magnetic field. A set of nonlinear equations, which govern the evolution of the hydromagnetic dynamo, are derived from an asymptotic analysis. The equations are investigated in detail both analytically and numerically. In spite of serious doubts concerning the existence of sufficiently complex stable motions, stable periodic dynamos are shown to exist. An interesting analytic solution of these equations, which may be pertinent to other problems arising from finite-amplitude Benard convection, is presented in the final section.