论文标题
在存在垂直磁场的情况下，麦克斯韦 - 卡塔内诺流体的对流不稳定
The convective instability of a Maxwell-Cattaneo fluid in the presence of a vertical magnetic field
论文作者
论文摘要
我们研究了受垂直均匀磁场的贝纳德层的不稳定性，其中流体遵守麦克斯韦 - 卡塔内诺（MC）热通量温度关系。我们将Bissell（Proc。R.Soc。A，472：20160649，2016）的工作扩展到磁性prandtl Number $ p_m $的非零值。随着非零$ p_m $，分散关系的顺序增加，导致行为更加丰富。 Chandrasekhar Number $ Q $的大价值的渐近分析证实，当$ C Q Q^{1/2} $为$ O（1）$时，MC效应变得很重要，其中$ c $是Maxwell-Cattaneo编号。在此制度中，我们得出了一个独立于$ Q $的缩放系统。当$ cq^{1/2} $很大时，结果与prandtl Number $ p \ to \ infty $的限制中的管理方程衍生的结果一致，with $ p_m $ $ pinite;在这里，我们确定了一种新的不稳定性模式，这既不是由于惯性和诱导效应。在大型$ p_m $制度中，我们展示了如何在不同水平尺度的振荡模式之间发生过渡。对于$ q \ gg 1 $，小额值为$ p $，我们表明关键的瑞利号码在$ p $中是非单调的，前提是$ c> 1/6 $。尽管对无应力边界进行了对本文的分析，但可以证明其他类型的机械边界条件给出了相同的领先顺序结果。
We study the instability of a Bénard layer subject to a vertical uniform magnetic field, in which the fluid obeys the Maxwell-Cattaneo (MC) heat flux-temperature relation. We extend the work of Bissell (Proc. R. Soc. A, 472: 20160649, 2016) to non-zero values of the magnetic Prandtl number $p_m$. With non-zero $p_m$, the order of the dispersion relation is increased, leading to considerably richer behaviour. An asymptotic analysis at large values of the Chandrasekhar number $Q$ confirms that the MC effect becomes important when $C Q^{1/2}$ is $O(1)$, where $C$ is the Maxwell-Cattaneo number. In this regime, we derive a scaled system that is independent of $Q$. When $CQ^{1/2}$ is large, the results are consistent with those derived from the governing equations in the limit of Prandtl number $p\to \infty$ with $p_m$ finite; here we identify a new mode of instability, which is due neither to inertial nor induction effects. In the large $p_m$ regime, we show how a transition can occur between oscillatory modes of different horizontal scale. For $Q \gg 1$ and small values of $p$, we show that the critical Rayleigh number is non-monotonic in $p$ provided that $C>1/6$. While the analysis of this paper is performed for stress-free boundaries, it can be shown that other types of mechanical boundary conditions give the same leading order results.
