Manifestation of stationary and oscillatory convection and secondary instabilities due to a chemical reaction in a two-component convective fluid system is reported in the paper by considering idealistic as well as physically realistic boundaries. Using a normal mode solution, analytical expression of the critical Rayleigh number for a stationary and oscillatory disturbances, and the natural frequency are reported. The range of parameters is identified where oscillatory motion happens. Further, the parameters’ range for existence of oscillatory regime is found to be larger for rigid boundaries compared to that of free boundaries. Furthermore, for both the boundaries, parameters’ range for this regime increases when the chemical reaction rate increases, leading to the conclusion that the oscillatory motion emerges as the most preferred mode in the two-component system due to the presence of a chemical reaction and the size of this domain is directly proportional to the chemical reaction rate. The marginal stability plots depict that the oscillatory and stationary regimes respectively correspond to Hopf and direct pitchfork bifurcations. The critical Rayleigh number and the wave number where codimension two bifurcation exists are documented in the paper for fixed values of parameters. It is shown that the codimension two bifurcation that arose in the problem is not a Takens–Bogdanov bifurcation. In a stationary regime, the domain for secondary instabilities of Eckhaus and zigzag is obtained using the spatio-temporal Newell–Whitehead–Segel equation. These instabilities grow with increasing chemical reaction rate. In the oscillatory regime, the complex Ginzburg–Landau equation is used to predict the appearance of the Benjamin–Feir instability.

本文通过考虑理想边界和物理现实边界，报告了由于双组分对流流体系统中的化学反应引起的静止和振荡对流以及二次不稳定性的表现。使用正常模式解，报告了稳态和振荡扰动的临界瑞利数的解析表达式，以及固有频率。确定振荡运动的参数范围发生。此外，发现与自由边界相比，刚性边界存在的振荡状态的参数范围更大。此外，对于这两个边界，当化学反应速率增加时，该状态的参数范围也会增加，从而得出结论，由于化学反应的存在，振荡运动成为双组分系统中最优选的模式，并且该域的大小与化学反应速率成正比。边际稳定性图描绘了振荡和静止状态分别对应于 Hopf 和直接干草叉分叉。对于参数的固定值，论文中记录了存在余维二分岔的临界瑞利数和波数。表明问题中出现的余维二分岔不是Takens-Bogdanov分岔。在静止状态下，使用时空 Newell-Whitehead-Segel 方程获得 Eckhaus 和 zigzag 二次不稳定性的域。这些不稳定性随着化学反应速率的增加而增加。在振荡状态下，复杂的 Ginzburg-Landau 方程用于预测 Benjamin-Feir 不稳定性的出现。