Compressible magnetoconvection in three dimensions: planforms and nonlinear behaviour
Compressible magnetoconvection in three dimensions: planforms and nonlinear behaviour
复制标题
三维可压缩磁对流：平面和非线性行为
DOI：
10.1017/s0022112095004630
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发表时间：
1995
影响因子：
3.7
通讯作者：
N. Weiss
中科院分区：
文献类型：
--
作者：
P. Matthews;M. Proctor;N. Weiss
在具有周期性横向边界条件的三维笛卡尔几何中，对施加垂直磁场的可压缩流体中的对流进行了数值研究。注意仅限于轻度非线性状态，参数的选择首先使对流在开始时是稳定的，然后使它是振荡的。当磁场较弱时，稳定对流以二维卷的形式发生。这些卷可以变得不稳定到平均水平剪切流，这在二维上导致平均流动方向相反的脉动波。在三维空间中，发现了辊子对中与剪切流交替的新模式。如果磁场足够强，正方形或六边形在对流开始时是稳定的。正方形和六边形都具有不对称的拓扑结构，向上流动呈羽状，向下流动呈片状。对于方块，这涉及到与盒子对齐的滚动和与盒子对角线对齐的滚动之间的共振。当磁场较强时，偏爱三维流动是层的可压缩性的结果——对于Boussinesq来说，磁对流在开始时总是比方形更受青睐。在对流振荡的情况下，发现中等场的首选平台是交替的滚波，即两个水平方向上的非相位驻波。在强磁场下，交替辊和二维行辊都是稳定的。随着对流振幅的增加，无论是通过降低磁场强度还是通过增加温度对比，开始时看到的规则的平台结构很快被二次不稳定性破坏。
Convection in a compressible fiuid with an imposed vertical magnetic field is studied numerically in a three-dimensional Cartesian geometry with periodic lateral boundary conditions. Attention is restricted to the mildly nonlinear regime, with parameters chosen first so that convection at onset is steady, and then so that it is oscillatory. Steady convection occurs in the form of two-dimensional rolls when the magnetic field is weak. These rolls can become unstable to a mean horizontal shear flow, which in two dimensions leads to a pulsating wave in which the direction of the mean flow reverses. In three dimensions a new pattern is found in which the alignment of the rolls and the shear flow alternates. If the magnetic field is sufficiently strong, squares or hexagons are stable at the onset of convection. Both the squares and the hexagons have an asymmetrical topology, with upflow in plumes and downflow in sheets. For the squares this involves a resonance between rolls aligned with the box and rolls aligned digonally to the box. The preference for three-dimensional flow when the field is strong is a consequence of the compressibility of the layer- for Boussinesq magnetoconvection rolls are always preferred over squares at onset. In the regime where convection is oscillatory, the preferred planform for moderate fields is found to be alternating rolls - standing waves in both horizontal directions which are out of phase. For stronger fields, both alternating rolls and two-dimensional travelling rolls are stable. As the amplitude of convection is increased, either by dcereasing the magnetic field strength or by increasing the temperature contrast, the regular planform structure seen at onset is soon destroyed by secondary instabilities.