Spectral Scaling of Turbulent Static Pressure across Stratification Regimes over Terrains of Increasing Slope

Static pressure fluctuations lie at the core of the equations governing fluid motion and play a key role in Atmospheric Boundary Layer (ABL) dynamics. They regulate pressure transport in the turbulent kinetic energy budget, drive pressure–strain interactions that redistribute energy among velocity components, and provide a physical mechanism for coupling flow regions separated in space and scale. Yet, compared to velocity fluctuations, turbulent static pressure remains one of the least understood variables in atmospheric turbulence. This imbalance largely reflects experimental limitations: accurately measuring high-frequency static pressure fluctuations in the atmosphere is inherently challenging, restricting the availability of high-quality observations and slowing progress toward a unified description of pressure statistics and spectral scaling in the ABL.

From a theoretical perspective, extending Kolmogorov's inertial-range arguments to pressure, the assumption of local isotropy predicts a k^-7/3 scaling for static pressure spectra. Observations under neutral, high–Reynolds-number conditions support this behaviour, while lower frequencies exhibit a transition toward a k^-1regime commonly associated with large-scale, energy-containing motions within Townsend's attached-eddy framework. At the same time, the literature reports a broader range of pressure spectral scalings across stability regimes, indicating departures from the neutral behaviour. The physical origins of these deviations remain unclear.

In this study, we examine how stratification and terrain slope jointly influence the spectral scaling of turbulent static pressure using three observational datasets collected over progressively more complex terrain. These include measurements from M2HATS (Multi-point Monin-Obukhov similarity horizontal array turbulence study), representing perfectly flat and horizontally homogeneous conditions in which turbulent pressure was measured at 4m across 16 towers along a cross-flow transect, and at eight vertical levels (up to 28m) distributed across two additional profiled towers; SCP (Shallow Cold Pools experiment), characterised by gently undulating terrain on a shallow slope that featured pressure observations distributed in space across the terrain; and the recently completed TEAMx winter EOP, conducted over a steep, undulating mountainous slope where pressure was measured at a network of 7 towers installed along and across the slope. The TEAMx wEOP additionally featured varying flow conditions characterized by persistent katabatic periods where low level jet was observed at or below 1m, and foehn periods with flow characterized by more canonical profiles.