In this article, we aim to study the stability and dynamic transition of an electrically conducting fluid in the presence of an external uniform horizontal magnetic field and rotation based on a Boussinesq approximation model. By analyzing the spectrum of the linear part of the model and verifying the validity of the principle of exchange of stability, we take a hybrid approach combining theoretical analysis with numerical computation to study the transition from a simple real eigenvalue, a pair of complex conjugate eigenvalues and a real eigenvalue of multiplicity two, respectively. The center manifold reduction theory is applied to reduce the infinite dimensional system to the corresponding finite dimensional one together with one or several non-dimensional transition numbers that determine the dynamic transition types. Careful numerical computations are performed to determine these transition numbers as well as related temporal and flow patterns etc. Our results indicate that both continuous and jump transitions can occur at certain parameter region.
翻译:在本篇文章中,我们的目标是研究在外部统一的水平磁场和基于Bussinesq近似模型的旋转下进行电导流流的稳定性和动态转换。通过分析模型线性部分的频谱和核实稳定交换原则的有效性,我们采取了一种混合方法,将理论分析与数字计算结合起来,研究从简单的真实值、一对复杂的同源值和一对复杂的二倍的二倍的正电子值的过渡。中位数减少理论用于将无限维系系统减少到相应的有限维度一,同时使用一个或数个非维的过渡数字来确定动态过渡类型。我们进行了仔细的数字计算,以确定这些过渡数字以及相关的时间和流模式等。我们的结果显示,连续和跳跃的过渡可以在某些参数区域发生。