A Model for Turbulence Spectra in the Equilibrium Range of the Stable Atmospheric Boundary Layer. Issue 5 (2nd March 2020) - Cheng, Yu; Li, Qi; Argentini, Stefania; Sayde, Chadi; Gentine, Pierre
Abstract: 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 shape of the turbulent kinetic energy and temperature spectra in horizontal wavenumber for the equilibrium range that consists of three regimes at small Froude number: the buoyancy subrange, a transition region, and the isotropic inertial subrange through dimensional analysis and substantial revision of previous theoretical approximation. These spectral regimes are confirmed by various observations in the atmospheric boundary layer. The representation of the transition region in direct numerical simulations will require large‐scale separation between the Dougherty‐Ozmidov scale and the Kolmogorov scale for strongly stratified turbulence at high Reynolds numbers, which is still challenging computationally. In addition, we suggest that the failure of Monin‐Obukhov similarity theory in the very stable atmospheric boundary layer is due to the fact that it does not consider the buoyancy scale that characterizes the transition region. Key Points: Turbulent kinetic energy and temperature spectra in horizontal wavenumber consist of three regions in the stable ABL Large‐scale separation is required for numerical simulations to resolve the transition region Monin‐Obukhov similarity theory may not apply in the very stable ABL as the buoyancy scale is not considered