Electrothermohydrodynamic convection driven by strong unipolar charge injection in the presence of a stabilizing inverse thermal gradient between two parallel electrodes is investigated by a linear stability analysis and a numerical simulation. The generalized Schur decomposition is used to solve for the eigenvalues of the linearized system revealing the critical parameters. The two relaxation time lattice Boltzmann method coupled to a fast Poisson solver is used to resolve the nonlinear system for the spatiotemporal distribution of flow field, electric field, charge density, and temperature. With strong charge injection and high electric Rayleigh number, the system exhibits electrothermoconvective vortices. The interactions between the stabilizing buoyancy force and the destabilizing electric force lead to overstability, where the flow constantly oscillates when instability evolves. A two-stage bifurcation is observed for overstability near the threshold Rayleigh number with a significant change in phase and amplitude. The effects of ion mobility and thermal diffusivity are characterized by the ratio of the counteracting forces.

中文翻译：

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二维电热流体动力流的单调不稳定性和超稳定性

通过线性稳定性分析和数值模拟研究了在两个平行电极之间存在稳定逆热梯度的情况下，由强单极性电荷注入驱动的电热流体对流。广义Schur分解用于求解揭示关键参数的线性化系统的特征值。结合快速泊松求解器的两个弛豫时间格子Boltzmann方法用于求解非线性系统，以求解流场，电场，电荷密度和温度的时空分布。该系统具有强电荷注入和高电瑞利数，显示出电热对流涡流。稳定的浮力和不稳定的电力之间的相互作用会导致过大的稳定性，不稳定演变时，流量不断振荡的地方。观察到两阶段分叉，在阈值瑞利数附近存在过大的稳定性，相位和幅度都有明显变化。离子迁移率和热扩散率的影响以反作用力之比为特征。