Direct numerical simulation (DNS) of a turbulent flow in an elevated jet in crossflow has been carried out at a Reynolds number (Re) of 3500 based on the outer width of the stack and crossflow velocity. The jet to crossflow velocity ratio is kept constant at V R = 2. Second order spatial and temporal discretization have been used to solve the Navier-Stokes equations employing a high-resolution grid to determine the essential characteristics of the coherent and the incoherent flow fields accurately. The large-scale coherent and small-scale incoherent flow fields are extracted using a reference signal-based phase-averaged method that uses a reference signal against which the phases are identified in each cycle to minimize the phase jitter. The rate of decay of circulation of the stack-wake vortices is observed to be more than that of the jet-wake which has a lower circulation value. The contribution of the incoherent fluctuations to the total turbulent kinetic energy is more compared to its coherent counterpart in the wake as well as jet region, except for the near-wake of the stack. The normal and shear stresses of both coherent and incoherent fields reveal a relatively higher contribution in the near-wake of both stack-wake and jet-wake, while the far-wake shows the opposite trend. The anisotropy factor of both the large-scale coherent and the small-scale fluctuating fields provides the evidence of total anisotropy of the stack-wake. The characterization of both types of fluctuating fields is also carried out using the anisotropy-invariant-map which displays the one-component limit for the coherent fluctuating field in most of the regions, but the anisotropy state of the incoherent fluctuating field is found to switch among various limits, namely, the axisymmetric contraction, the axisymmetric expansion, and isotropic limits. © 2023 Author(s).