The linear and weakly nonlinear stability of a doubly diffusive electrically conducting non-Newtonian couple stress fluid layer in the presence of a uniform vertical magnetic field is investigated. The system behaves like a triply diffusive one with the magnetic field as a third diffusing component. Several remarkable departures from those of doubly diffusive couple stress fluid systems are recognized and the implications of couple stresses on the same are explored. By performing the linear stability analysis, it has been recognized that (i) oscillatory convection occurs even if the diffusivity ratios are greater than unity, (ii) the bottom-heavy solute gradient in the presence of magnetic field, as well as magnetic field in the presence of bottom-heavy solute gradient, destabilize the system under certain conditions, (iii) disconnected closed oscillatory neutral curves occur for certain choices of physical parameters indicating the necessity of three critical values of thermal Rayleigh number to specify the linear stability criteria instead of the usual single value. A weakly nonlinear stability analysis has been performed using modified perturbation theory and the steady bifurcating equilibrium solution is found to be subcritical in some parameter space. Heat and mass transports are calculated in terms of Nusselt numbers and the influence of physical parameters on the same is discussed in detail.

中文翻译：

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非牛顿流体层中的线性和弱非线性双扩散磁对流

研究了在均匀垂直磁场下双扩散导电非牛顿耦合应力流体层的线性和弱非线性稳定性。该系统的行为就像一个三重扩散系统，磁场是第三扩散组件。认识到与双重扩散偶应力流体系统的几个显着差异，并探讨了偶应力对相同系统的影响。通过进行线性稳定性分析，我们已经认识到：（i）即使扩散率大于1，也会发生振荡对流；（ii）存在磁场时的底部重溶质梯度，以及底部重溶质梯度的存在会在某些条件下破坏系统的稳定性，（iii）对于某些物理参数选择，会出现断开的闭合振荡中性曲线，表明有必要使用三个热瑞利数临界值来指定线性稳定性标准，而不是通常的单个值。使用修正的扰动理论进行了弱非线性稳定性分析，发现在某些参数空间中稳定的分岔平衡解是次临界的。传热和传质是根据努塞尔数计算的，并详细讨论了物理参数对其的影响。使用修正的扰动理论进行了弱非线性稳定性分析，发现在某些参数空间中稳定的分岔平衡解是次临界的。传热和传质是根据努塞尔数计算的，并详细讨论了物理参数对其的影响。使用修正的扰动理论进行了弱非线性稳定性分析，发现在某些参数空间中稳定的分岔平衡解是次临界的。传热和传质是根据努塞尔数计算的，并详细讨论了物理参数对其的影响。