Abstract

We have analyzed the magnetic convection regime (Rayleigh–Bénard problem) in a nonuniformly rotating electroconducting liquid in an external periodic magnetic field. In the linear theory of oscillatory convection, the critical value of Rayleigh number Ra_c is obtained as a function on the nonuniform rotation profile (Rossby number Ro). It is shown that the Kepler profile of rotation with Rossby number Ro = –3/4 produces a destabilizing effect. Using the method of perturbation theory in small supercriticality parameter of the Rayleigh number, we have derived the Ginzburg–Landau nonlinear complex equation. The numerical solution of this equation has enabled us to determine heat transfer (from the Nusselt number Nu) in the layer of the liquid for different values of amplitudes δ and modulation frequencies ω_B. Using the Galerkin method, we have obtained a linear dynamic system of nonautonomous Lorenz-type equations. Numerical analysis of these equations has revealed the possibility of controlling the chaotic behavior of convective flows in a nonuniformly rotating (Ro = –3/4) liquid by varying the modulation parameters of the external magnetic field.

中文翻译：

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外部磁场调制作用下非均匀旋转导电介质中的对流

摘要

我们已经分析了外部周期性磁场中非均匀旋转的导电液体中的磁对流状态（瑞利-贝纳德问题）。在振荡对流的线性理论中，瑞利数Ra _c的临界值是根据非均匀旋转轮廓（罗斯比数Ro）得出的函数得出的。结果表明，Rossby数Ro = –3/4的开普勒旋转轮廓产生了不稳定作用。使用微扰理论中的瑞利数的小超临界参数，我们导出了Ginzburg-Landau非线性复方程。该方程的数值解使我们能够确定振幅δ和调制频率ω的不同值时液体层中的传热（根据努塞尔数Nu）。_乙。使用Galerkin方法，我们获得了非自治Lorenz型方程的线性动力学系统。这些方程的数值分析表明，可以通过改变外部磁场的调制参数来控制非均匀旋转（Ro = –3/4）液体中对流的混沌行为。