  In order to utilize the full potential of tailored flows of electromagnetic
energy at the nanoscale, we need to understand its general behaviour 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 the
topological features in the flow field between 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.
