The effects of cross-diffusion on linear and weak nonlinear stability of double diffusive convection in an electrically conducting horizontal fluid layer with an imposed vertical magnetic field are investigated. The criterion for the onset of stationary and oscillatory convection is obtained analytically by performing the linear instability analysis. Several noteworthy departures from those of doubly diffusive fluid systems are unveiled under certain parametric conditions. It is shown that (i) disconnected closed convex oscillatory neutral curve separated from the stationary neutral curve exists requiring three critical thermal Rayleigh numbers to completely specify the linear instability criteria instead of a usual single critical value, (ii) an electrically conducting fluid layer in the presence of magnetic field can be destabilized by stable solute concentration gradient, and (iii) a doubly diffusive conducting fluid layer can be destabilized in the presence of magnetic field. It is demonstrated that small variations in the off-diagonal elements enforce discrepancies in the instability criteria. A weak nonlinear stationary stability analysis has been performed using a perturbation method and a cubic Landau equation is derived and the stability of bifurcating equilibrium solution is discussed. It is found that subcritical bifurcation occurs depending on the choices of governing parameters.

研究了交叉扩散对具有垂直磁场的导电水平流体层中双扩散对流的线性和弱非线性稳定性的影响。通过执行线性不稳定性分析，可以解析得出稳态和振荡对流的发生准则。在某些参数条件下，揭示了与双扩散流体系统的一些值得注意的差异。结果表明：（i）与静止中性曲线分离的断开的闭合凸振动中性曲线需要三个临界热瑞利数来完全指定线性不稳定性标准，而不是通常的单个临界值，（ii）在磁场存在下的导电流体层可以通过稳定的溶质浓度梯度而不稳定，并且（iii）在磁场存在下双扩散导电流体层可以不稳定。事实证明，非对角线元素的细微变化会导致不稳定性标准存在差异。利用摄动法进行了非线性非线性平稳稳定性分析，推导了三次Landau方程，并讨论了分叉平衡解的稳定性。发现根据控制参数的选择会发生亚临界分叉。事实证明，非对角线元素的细微变化会导致不稳定性标准存在差异。利用摄动法进行了非线性非线性平稳稳定性分析，推导了三次Landau方程，并讨论了分叉平衡解的稳定性。发现根据控制参数的选择会发生亚临界分叉。事实证明，非对角线元素的细微变化会导致不稳定性标准存在差异。利用摄动法进行了非线性非线性平稳稳定性分析，推导了三次Landau方程，并讨论了分叉平衡解的稳定性。发现根据控制参数的选择会发生亚临界分叉。