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This work studies the effects of a through-flow on two-dimensionalelectrohydrodynamic (EHD) flows of a dielectric liquid confined between twoplane plates, as a model problem to further our understanding of the fluidmechanics in the presence of an electric field. The liquid is subjected to astrong unipolar charge injection from the bottom plate and a pressure gradientalong the streamwise direction. Highly-accurate numerical simulations andweakly nonlinear stability analyses based on multiple-scale expansion andamplitude expansion methods are used to unravel the nonlinear spatiotemporalinstability mechanisms in this combined flow. We found that the through-flowmakes the hysteresis loop in the EHD flow narrower. In the numerical simulationof an impulse response, the leading and trailing edges of the wavepacket withinthe nonlinear regime are consistent with the linear ones, a result which wealso verified against that in natural convection. In addition, as thebifurcation in EHD-Poiseuille flows is of a subcritical nature, nonlinearfinite-amplitude solutions exist in the subcritical regime, and our calculationindicates that they are convectively unstable. The validity of theGinzburg-Landau equation (GLE), derived from the weakly nonlinear expansion ofNavier-Stokes equations and the Maxwell's equations in the quasi-electrostaticlimit, serving as a physical reduced-order model for probing the spatiotemporaldynamics in this flow, has also been investigated. We found that thecoefficients in the GLE calculated using amplitude expansion method can predictthe absolute growth rates even when the parameters are away from the linearcritical conditions, compared favourably with the local dispersion relation,whereas the validity range of the GLE derived from the multiple-scale expansionmethod is confined to the vicinity of the linear critical conditions.

Nonlinear spatiotemporal instabilities in two-dimensional electroconvective flows