Stability-conditioned spectral scaling in the atmospheric surface layer: Field evidence and a deep operator network map

We quantify how thermal stability reshapes velocity and temperature spectra in the atmospheric surface layer (ASL) by combining field observations with neutral, high Reynolds number wind tunnel measurements. In the inertial subrange (nominally 1≲kxz≲10, where kx is the streamwise wavenumber and z is the wall-normal distance), the streamwise spectrum maintains a slope close to the Kolmogorov −5/3 scaling across stability classes. In contrast, the spanwise, wall–normal, and scalar spectra exhibit increasingly negative spectral slopes with increasing instability parameter |z/L| (L is the Obukhov length). Premultiplied streamwise spectra under neutral conditions display a well-defined peak throughout much of the logarithmic region, with a magnitude that decreases gradually with height. Compared to the neutral reference at the same normalized height z/δ, unstable stratification strengthens the premultiplied streamwise spectral peak and slightly shifts it toward lower kxz, indicating enhanced large-scale energy under buoyancy forcing. Building on these trends, we construct a compact stability-conditioned and height-conditioned map from (z/L, z/δ) to the full streamwise spectrum on the kxz abscissa using a deep operator network. The network incorporates a high–wavenumber normalization to enforce physical asymptotic behavior. Applied to held-out cases spanning the observed unstable stability range (−14.5≲z/L≲−0.001), the mapping accurately reproduces measured premultiplied spectra over 10−3≲kxz≲102, capturing the peak magnitude, location, and the inertial-to dissipation-range decay. Parametric evaluations recover smooth, monotonic variations consistent with canonical wall-turbulence phenomenology. The results yield a unified description of buoyancy effects on ASL spectra and a stability-aware parameterization for similarity closures, spectral inflow generation, and large-eddy simulations subgrid modeling.