Implicit Large Eddy Simulations (ILES) are deployed to characterize the effect of swirling boundary conditions on vorticity transport as well as on the Lighthill's tensor for a cold, supersonic aerospike nozzle jet. Four jets are simulated at a Nozzle Pressure Ratio (NPR) = 3, one jet without swirl and three jets with swirl numbers S=0.10,0.20,0.30. Swirling boundary conditions lead to an increase in vorticity tilting and stretching downstream of the aerospike bluff body, potentially enhancing sound generation. An exact decomposition of the Lighthill's tensor is undertaken and the magnitude of the obtained source terms is compared. The dominant acoustic source terms are amplified under swirling boundary conditions. Terms describing the interactions between dilatation fields and density gradients balance each other in shock regions. At higher swirl numbers, the convection of density gradients along the flow direction leads to an imbalance that contributes to increased sound generation. Finally, cross-correlations between the near-field pressure and individual source terms reveal that enstrophy correlates more strongly with the near-field acoustics at higher swirl numbers.