Turbulence Spectra in the Stable Atmospheric Boundary Layer

Stratification causes turbulence spectra to deviate from Kolmogorov’s isotropic -5/3 power-law scaling in the universal equilibrium range at high Reynolds number. However, a consensus has not been reached with regard to the exact shape of the spectra. Here we propose a theoretically-derived shape of the TKE and temperature spectra that consists of three regimes at small Froude number: the buoyancy subrange, a transition region and isotropic inertial subrange separated by the buoyancy scale and Ozmidov scale through derivation. These regimes are confirmed by various observations in the atmospheric boundary layer. We also show that DNS may not apply in the study of very stable boundary layers as they cannot correctly represent the observed spectral regimes seen in actual boundary layers because of the lack of scale separation. In addition, the spectrum in the transition regime explains why Monin-Obukhov similarity theory cannot entirely describe the behavior of the stable atmospheric boundary.