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首页> 外文期刊>The European physical journal, B. Condensed matter physics >Thermal convection in a rotating layer of a magnetic fluid
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Thermal convection in a rotating layer of a magnetic fluid

机译：磁性流体旋转层中的热对流

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Thermal convection in magnetic fluids can be driven by buoyancy or by magnetic forces (due to the thermomagnetic effect). Depending on the direction of the applied temperature gradient, buoyancy effects can be stabilizing (heating from above) or destabilizing (heating from below), whereas the magnetic forces always play a destabilizing role for magnetic fields perpendicular to the interface. We investigate the influence of rotations using both linear and weakly non-linear analyses of the governing hydrodynamic equations in the Boussinesq approximation. With a linear stability analysis we determine the values of the wavelength and the temperature gradient at the onset of convection (critical values). These are calculated analytically in the case of stress free boundaries and numerically for rigid boundaries. We discuss the validity of the assumptions entering the calculations for stress free boundaries. In the cased of free boundary conditions, asymptotic expressions of the critical values for high rotation rates are derived. When the system is heated from above and the magnetic forces only slightly exceed the buoyancy forces, linear results show that both the critical wavelength and the critical temperature gradient diverge. Again, this behavior is described by asymptotic expressions. We derive envelope equations for convection patterns characterized by both: one wave vector and two competing wave vectors of equal length but different directions. These equations show that the system always exhibits a forward bifurcation. The well-known Kuppers-Lortz instability is also present in magnetic fluids. This instability sets in at critical values for a sufficiently high rotation rate. In simple fluids the angle α depends only on the Prandtl number of the fluid. We show that for magnetic fluids this angle can be changed by changing the ratio of the the buoyancy forces to the magnetic forces (i. e. by changing the magnetic field). There is also a weak dependence on the other magnetic parameters of the system. For a commercially available magnetic fluid this angle can be increased by approximately 10° - 15° compared to the simple fluid case.
机译：磁性流体中的热对流可以通过浮力或磁力（由于热磁效应）来驱动。根据所施加的温度梯度的方向，浮力作用可能稳定（从上方加热）或不稳定（从下方加热），而磁力始终对垂直于界面的磁场起不稳定作用。我们使用Boussinesq近似中的控制流体力学方程的线性和弱非线性分析来研究旋转的影响。通过线性稳定性分析，我们确定了对流开始时的波长和温度梯度值（临界值）。在无应力边界的情况下通过解析计算得出，在刚性边界的情况下通过数值计算得出。我们讨论了进入无应力边界计算的假设的有效性。在自由边界条件的情况下，导出了高旋转速率的临界值的渐近表达式。当系统从上方加热时，磁力仅略高于浮力，线性结果表明临界波长和临界温度梯度均发生了变化。同样，此行为由渐近表达式描述。我们导出了对流模式的包络方程，其特征是：一个波矢和两个长度相等但方向不同的竞争波矢。这些方程式表明，系统始终表现出正向分歧。磁性流体中也存在众所周知的Kuppers-Lortz不稳定性。对于足够高的转速，这种不稳定性设定在临界值上。在简单流体中，角度α仅取决于流体的普朗特数。我们表明对于磁性流体，该角度可以通过改变浮力与磁力的比率来改变（即，通过改变磁场）。对系统其他磁参数的依赖性也很弱。对于市售的磁性流体，与简单的流体情况相比，该角度可以增加大约10°-15°。

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