Electrokinetically driven in-plane vortex flows in a microchannel are studied utilizing a patterned surface charge technique requiring both positively and negatively charged regions on the same substrate. In the first part, a periodic flow pattern consisting of counter-rotating vortex pairs is analyzed experimentally and numerically; this is a relatively easy flow to experimentally realize in the lab since no charge-free region is necessary. The good agreement between the measured and computed flow fields demonstrates that: (i) the surface charge patterning technique can be used for driving electrokinetically complex vortex flow patterns in microchannels, and (ii) the applied CFD code can be used for calculating reliably such flow fields. In the second part, the numerical scheme is utilized to study a single, in-plane vortex in order to reveal the proper length and velocity scales as well as the dominant control parameters. This flow field, although simpler, is very difficult to realize experimentally due to the need for a large surface area carrying no charge. The resulting 3D flow field features a coherent vortex with its axis perpendicular to the symmetrically charged regions on the top and bottom surfaces of the microchannel. Three length scales, the active-region length and width as well as the channel height, and a velocity scale, the speed of the electroosmotic flow, have been identified as the relevant variables. The strength of the in-plane vortex along with several flow patterns has been characterized on the basis of these four independent variables.