Electroconvection under injection from cathode and heating from above

We study the electroconvection that appears in a nonuniformly heated, poorly conducting liquid in a parallel-plate horizontal capacitor due to the action of an external static electric field on the charge injected from the cathode. It is shown that the heating of the layer from above prevents steady-state convection and that, unlike the isothermal situation, electroconvection can appear in the oscillatory manner as a result of direct Hopf bifurcation. The effect of the heating intensity, the intensity of charge injection from the cathode, and the charge mobility on the thresholds of oscillatory and monotonic electroconvection is analyzed and the characteristic scales and frequencies of critical perturbations are determined. The nonlinear wave and steady-state regimes of the 2D convective structures formed in the poorly conducting liquid under the action of thermogravitational and injection mechanisms of convection are analyzed. The domains of existence of standing, traveling, and modulated waves are determined.