Turbulence Spectra in the Stable Atmospheric Boundary Layer

TL;DR

This paper proposes a theoretical model for turbulence spectra in the stable atmospheric boundary layer, identifying three regimes and explaining deviations from classical theories due to stratification effects.

Contribution

It introduces a new theoretically-derived shape of turbulence spectra with three regimes at low Froude numbers, supported by observations and discusses DNS limitations.

Findings

Spectra exhibit three regimes: buoyancy subrange, transition, and inertial subrange.

DNS may not accurately model very stable boundary layers at high Reynolds numbers.

Transition regime spectrum explains limitations of Monin-Obukhov similarity theory.

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 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.