Turbulence Spectra in the Stable Atmospheric Boundary Layer

Stratification can cause turbulence spectra to deviate from Kolmogorov's isotropic -5/3 power-law scaling in the universal equilibrium range at high Reynolds numbers. 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 turbulent kinetic energy (TKE) and temperature spectra in horizontal wavenumber that consists of three regimes at small Froude number: the buoyancy subrange, a transition region and isotropic inertial subrange through derivation based on previous research. 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 atmospheric boundary layers at very high Reynolds numbers as they cannot correctly represent the observed spectral regimes because of the lack of scale separation limited by current computational capacity. In addition, the spectrum in the transition regime explains why Monin-Obukhov similarity theory cannot entirely describe the behavior of the stable atmospheric boundary.