In this paper, we investigate electroconvective ion transport at cation exchange membranes with different geometry square-wave structures (line undulations) experimentally and numerically. Electroconvective microvortices are induced by strong concentration polarization once a threshold potential difference is applied. The applied potential required to start and sustain electroconvection is strongly affected by the geometry of the membrane. A reduction in the resistance of approximately 50% can be obtained when the structure size is similar to the mixing layer (ML) thickness, resulting in confined vortices with less lateral motion compared to the case of flat membranes. From electrical, flow, and concentration measurements, ion migration, advection, and diffusion are quantified, respectively. Advection and migration are dominant in the vortex ML, whereas diffusion and migration are dominant in the stagnant diffusion layer. Numerical simulations, based on Poisson-Nernst-Planck and Navier-Stokes equations, show similar ion transport and flow characteristics, highlighting the importance of membrane topology on the resulting electrokinetic and electrohydrodynamic behavior.