Scaling laws and space–time characteristics of wall pressure fluctuations in an axisymmetric boundary layer with varying pressure gradient

Wall-resolved large-eddy simulations of flow over an axisymmetric body of revolution (DARPA SUBOFF bare model) at ReL=1.1× 10⁶ are performed to investigate wall pressure fluctuations under the combined effects of transverse curvature and varying pressure gradients. Due to the coexistence of convex and concave streamwise curvatures, the flow in the stern region features alternating zones of favourable and adverse pressure gradients (APGs). The simulation validates experimental findings by Balantrapu et al. (2023, J. Fluid Mech., vol. 960, A28), confirming that in APG-dominant axisymmetric boundary layers without streamwise curvatures, the root mean square wall pressure fluctuations ( pw,rms ) decrease downstream alongside the wall shear stress ( τ w ), maintaining a constant ratio pw,rms/τ w . This study further finds that when streamwise curvatures and strong streamwise pressure gradient variations present, this relationship breaks down, suggesting that τ w is not the dominant contributor to wall pressure fluctuations. Instead, the local maximum Reynolds shear stress -ρ uₛuₙ ₘₐₓ emerges as a more robust pressure scaling parameter. Normalising the wall pressure spectra by -ρ uₛuₙ ₘₐₓ yields better collapse across the entire stern region compared to conventional inner or mixed scaling methods. The magnitude and location of -ρ uₛuₙ ₘₐₓ significantly influence the spectral levels of wall pressure fluctuations across different frequency bands. As the turbulence intensity and -ρ uₛuₙ ₘₐₓ shift away from the wall, outer-layer structures – with larger spatial and temporal scales – dominate the coherence of wall pressure fluctuations. This mechanism drives sustained attenuation of high-frequency pressure fluctuations and a simultaneous increase in both the streamwise and transverse correlation lengths of wall pressure fluctuations over the stern region.