Low-mode model of electroconvection of an ideal dielectric

A three-mode model of electroconvection of an ideal dielectric in the ac electric field of a horizontal capacitor is developed. With the help of this model, hysteretic transitions between different nonlinear regimes of electroconvection of the perfect liquid dielectric are found and investigated. The cases of zero-gravity and of heating from above in the gravitational field are considered. Frequency dependencies of the electroconvection oscillatory regimes are studied. Diagrams of the regimes are constructed. The following scenarios of transition to chaos are explored: through a subharmonic cascade, through quasi-periodicity, and from equilibrium. Behavior of the electroconvecton oscillations in the high-frequency limit is also studied.