  The two-dimensional regular and chaotic electro-convective flow states of a
dielectric liquid between two infinite parallel planar electrodes are
investigated using a two-relaxation-time lattice Boltzmann method. Positive
charges injected at the metallic planar electrode located at the bottom of the
dielectric liquid layer are transported towards the grounded upper electrode by
the synergy of the flow and the electric field. The various flow states can be
characterized by a non-dimensional parameter, the electric Rayleigh number.
Gradually increasing the electric Rayleigh number, the flow system sequentially
evolves via quasi-periodic, periodic, and chaotic flow states with five
identified bifurcations. The turbulence kinetic energy spectrum is shown to
follow the -3 law as the flow approaches turbulence. The spectrum is found to
follow a -5 law when the flow is periodic.
