In order to utilize the full potential of tailored flows of electromagnetic energy at the nanoscale, we need to understand its general behavior given by its generic representation of interfering random waves. For applications in on-chip photonics as well as particle trapping, it is important to discern between the topological features in the flow-field of the commonly investigated cases of fully vectorial light fields and their 2D equivalents. We demonstrate the distinct difference between these cases in both the allowed topology of the flow-field and the spatial distribution of its singularities, given by their pair correlation function g(r). Specifically, we show that a random field confined to a 2D plane has a divergence-free flow-field and exhibits a liquid-like correlation, whereas its freely propagating counterpart has no clear correlation and features a transverse flow-field with the full range of possible 2D topologies around its singularities.