Solute dispersion in fluid flow results from the interaction between advection and diffusion. The relative contributions of these two mechanisms to mass transport are characterized by the reduced velocity ν, also referred to as the Péclet number. In the absence of diffusion (i.e., when the solute diffusion coefficient D_{m}=0 and ν→∞), divergence-free laminar flow of an incompressible fluid results in a zero-transverse dispersion coefficient (D_{T}=0), both in ordered and random two-dimensional porous media. We demonstrate by numerical simulations that a more realistic realization of the condition ν→∞ using D_{m}≠0 and letting the fluid flow velocity approach infinity leads to completely different results for ordered and random two-dimensional porous media. With increasing reduced velocity, D_{T} approaches an asymptotic value in ordered two-dimensional porous media but grows linearly in disordered (random) structures depending on the geometrical disorder of a structure: a higher degree of heterogeneity results in a stronger growth of D_{T} with ν. The obtained results reveal that disorder in the geometrical structure of a two-dimensional porous medium leads to a growth of D_{T} with ν even in a uniform pore-scale advection field; however, lateral diffusion is a prerequisite for this growth. By contrast, in ordered two-dimensional porous media the presence of lateral diffusion leads to a plateau for the transverse dispersion coefficient with increasing ν.