Parabolic Reynolds-Averaged Navier-Stokes (RANS) approaches offer an attractive compromise between the accuracy of RANS and the efficiency of analytical methods. However, due to neglecting pressure gradients, these models often require near-wake corrections. Moreover, they are typically based on over-simplistic turbulence closures. To address these limitations, this brief proof of concept couples a recently developed analytical pressure-gradient formulation (Bastankhah et al., 2026) with a parabolic RANS framework. It also uses the <em>k</em> − <em>ε</em> − <em>f<sub>p</sub></em> turbulence closure, well suited to strong near-wake velocity gradients (van der Laan et al., 2015). The model closely reproduces RANS results, while reducing per-core computational costs by more than three orders of magnitude.