旋转层中自由磁流体对流弱非线性双尺度扰动的振幅方程
Amplitude equations for weakly nonlinear two-scale perturbations of free hydromagnetic convective regimes in a rotating layer
摘要：
在Boussinesq近似下，研究了具有自由导电边界的旋转水平层中自由磁流体热对流的弱非线性稳定性。扰动应该涉及大的空间和时间尺度。应用均匀化的抛物方程的方法，我们推导出系统的振幅方程的扰动的演变的假设下，α-效应是微不足道的领导秩序。振幅方程包含各向异性涡动扩散系数修正和平流算子。该系统是定性不同的平均场方程组的强迫对流磁流体制度的大尺度扰动。它是混合的：平均磁扰动的方程是演化的，其余的方程既不涉及时间导数，也不涉及分子扩散率算子。
英文摘要：
Weakly non-linear stability of regimes of free hydromagnetic thermal convection in a rotating horizontal layer with free electrically conducting boundaries is considered in the Boussinesq approximation. Perturbations are supposed to involve large spatial and temporal scales. Applying methods for homogenisation of parabolic equations, we derive the system of amplitude equations governing the evolution of perturbations under the assumption that the alpha-effect is insignificant in the leading order. The amplitude equations involve the operators of anisotropic combined eddy diffusivity correction and advection. The system is qualitatively different from the system of mean-field equations for large-scale perturbations of forced convective hydromagnetic regimes. It is mixed: equations for the mean magnetic perturbation are evolutionary, all the rest involve neither time derivatives, nor the molecular diffusivity operator.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
