This paper examines the connection between photonic band-gap formation in two types of two-dimensional photonic crystals and the emergence of reverse electromagnetic energy flows generated by linearly polarized plane waves incident on a photonic-crystal slab. We show that these reverse energy flows, observed in both transmitted and reflected fields, originate from vortex structures in the Poynting vector. The resulting energy-flow patterns exhibit striking analogies to vortex formation in fluid motion past obstacles. The geometry and dynamics of the Poynting-vector vortices determine whether the incident electromagnetic energy is impeded, leading to the formation of photonic band gaps, or instead guided through the structure, enabling transmission.