The behaviour of an incompressible dielectric liquid subjected to a laminar planar Couette flow with unipolar charge injection is investigated numerically in two dimensions. The computations show new morphological characteristics of roll structures that arise in this forced electro-convection problem. The charge and velocity magnitude distributions between the two parallel electrodes are discussed as a function of the top wall velocity and the EHD Rayleigh number, T for the case of strong charge injection. A wide enough parametric space is investigated such that the observed EHD roll structures progress through three regimes. These regimes are defined by the presence of a single or double-roll free convective structure as observed elsewhere (Vazquez et al 2008 J. Phys. D 41 175303), a sheared or stretched roll structure, and finally by a regime where the perpendicular velocity gradient is sufficient to prevent the generation of a roll. These three regimes have been delineated as a function of the wall to ionic drift velocity UW/κE, and the T number. In the stretched regime, an increase in UW/κE can reduce charge and momentum fluctuations whilst in parallel de-stratify charge in the region between the two electrodes. The stretched roll regime is also characterised by a substantial influence of UW/κE on the steady development time, however in the traditional non-stretched roll structure regime, no influence of UW/κE on the development time is noted.