论文标题
磁性泰勒 - 库特流动中的完全非线性模式竞赛
Fully nonlinear mode competitions in magnetised Taylor-Couette flow
论文作者
论文摘要
我们研究了磁性泰勒 - 库特流动中各种螺旋不稳定性的非线性模式竞争。使用Deguchi＆Altmeyer（2013）开发的环形平行周期域方法跟踪所得的有限振幅混合模式解分支。在反环境和旋风瑞利稳定的方案中都研究了模式竞争现象。在抗环绕式亚旋转状态下，内部气缸的旋转速度比外部旋转速度快，而Hollerbach，Teeluck＆Rudiger（2010）在实验范围内发现了竞争性的轴对称性和非轴对称磁电磁性线性不稳定模式，而实验范围内实验研究是可行的。在这里，我们确认了模式竞争的存在，并计算了由此产生的非线性混合模式解决方案。在旋风超旋转状态下，内部圆柱体旋转的旋转速度比外部速度慢，Deguchi（2017）最近发现了一种非轴对称性纯流体动力线性不稳定性，与非轴对称磁性磁通型 - 旋转不稳定相交，鲁达（Rudiger）稍早地发现了Rudiger，Schultz，Gellert＆Stefani＆Stefani（2016）。我们表明，这些不稳定性的非线性相互作用导致了丰富的模式形成现象，从而导致角动量转运增强/还原。
We study the nonlinear mode competition of various spiral instabilities in magnetised Taylor-Couette flow. The resulting finite-amplitude mixed-mode solution branches are tracked using the annular-parallelogram periodic domain approach developed by Deguchi & Altmeyer (2013). Mode competition phenomena are studied in both the anti-cyclonic and cyclonic Rayleigh-stable regimes. In the anti-cyclonic sub-rotation regime, with the inner cylinder rotating faster than the outer, Hollerbach, Teeluck & Rudiger (2010) found competing axisymmetric and non-axisymmetric magneto-rotational linearly unstable modes within the parameter range where experimental investigation is feasible. Here we confirm the existence of mode competition and compute the nonlinear mixed-mode solutions that result from it. In the cyclonic super-rotating regime, with the inner cylinder rotating slower than the outer, Deguchi (2017) recently found a non-axisymmetric purely hydrodynamic linear instability that coexists with the non-axisymmetric magneto-rotational instability discovered a little earlier by Rudiger, Schultz, Gellert & Stefani (2016). We show that nonlinear interactions of these instabilities give rise to rich pattern-formation phenomena leading to drastic angular momentum transport enhancement/reduction.
