On two-dimensional finite amplitude electro-convection in a dielectric liquid induced by a strong unipolar injection

• The relationship between the finite amplitude criterion and the mobility parameter has been revealed.
• The reason for the discrepancy of numerical and analytical values of the finite amplitude criterion is explained.
• We have determined a new subcritical bifurcation with high values of the driving parameter.

The hydrodynamic stability of a dielectric liquid subjected to strong unipolar injection is numerically investigated. We determined the linear criterion Tc (T being the electric Rayleigh number) and finite amplitude one Tf over a wide range of the mobility parameter M. A noticeable discrepancy is shown for Tf between our numerical prediction and the value predicted by stability analysis, which is due to the velocity field used in stability analysis. Recent studies revealed a transition of the flow structure from one cell to two with an increase in T. We demonstrate that this transition results in a new subcritical bifurcation.