The evolution of atmospheric surface layer heat and momentum flux co-spectra with increasing flux Richardson number

Abstract:

Co-spectral budgets of turbulent sensible heat and momentum fluxes were recently combined to develop models that explain the variation of the turbulent Prandtl number with several forms of the Richardson number in stable atmospheric surface layers. The shapes of the vertical velocity and air temperature spectra, as well as a wave-number dependent relaxation time scale assumed to be the same for momentum and heat, are required in such budgets. Guided by these theoretical approaches, the shapes of the vertical velocity and temperature spectra are first examined with increasing flux Richardson number (Ri) using data from two field experiments. The focus is on the relation between spectral and co-spectral behavior in the vicinity of the so-called critical flux Richardson number (Ri_cr ≈ 0.2−0.25). In addition, the wave-number dependent relaxation time scales for momentum and heat fluxes are inferred and examined. Using the data and extensions to the co-spectral budgets, results pertaining to how the shapes of the vertical velocity and temperature spectra impact the relative importance of turbulent kinetic energy (in the vertical direction) and potential energy, as well as the origin of any dissimilarity between relaxation time scales for momentum and heat fluxes are presented. The findings here offer a new perspective on how to bridge the micro-states of the energy distribution of eddies (kinetic and potential) with macroscopic relations needed in practical problems such as determination of stability correction functions to the mean flow.