The hydrocyclone provides an efficient means for solids separation from suspension, dewatering or purification, but there is little detailed understanding of the swirl flow and separation mechanism prevailing within the device. We report on the application of transient three-dimensional computational fluid dynamics incorporating a second-order accurate pressure-strain Reynolds-stress turbulence model. This has led to new understanding of the mechanism that leads to air-core development. Simulations of a water-core development and associated flow and pressure fields are reported. From this, air-core development is demonstrated to be transport-driven as opposed to pressure-driven, for which experimental validation has been acquired. In addition, examination of three-dimensional particle tracking challenges some of the common conceptions of the particle-separation mechanism. A highly asymmetric helical structure of alternating radial velocity, throughout the hydrocyclone, results in stochastic turbulent transport of particles between the wall and core flows to occur principally in regions of favourable radial velocity.