Role of large eddies in the breakdown of the Reynolds analogy in an idealized mildly unstable atmospheric surface layer

Abstract

While the breakdown in similarity between turbulent transport of heat and momentum (or Reynolds analogy) is not disputed in the atmospheric surface layer (ASL) under unstably stratified conditions, the causes of this breakdown are still debated. One reason for the breakdown is differences between how coherent structures transport heat and momentum, and their differing responses to increasing instability. Monin-Obukhov Similarity Theory (MOST), which hypothesizes that only local length-scales play a role in ASL turbulent transport, implicitly assumes that large-scale structures are inactive, despite their large energy content. Widely adopted mixing-length models also rest on this assumption in the ASL. The difficulty of characterizing low-wavenumber turbulent motions with field measurements motivates the use of high-resolution Direct Numerical Simulation (DNS), which is free from subgrid-scale parametrizations and adhoc assumptions near the boundary. Despite the low Reynolds number and idealized geometry of the DNS, DNS-estimated MOST functions are consistent with ASL field experiments, as are low-frequency features of the spectra. Parsimonious spectral models for MO stability correction functions for momentum (ϕm) and heat (ϕh) are derived, based on idealized vertical velocity variance and buoyancy variance spectra fit to the corresponding DNS spectra. For ϕm, a spectral model, based only on local length-scales, matches DNS and field measurements well. In contrast, for ϕh, the model is substantially biased unless contributions from larger length-scales are also included. These results are supported by sensitivity analyses based on field measurements that are independent of the DNS. They show that ASL heat transport is not MO-similar, even under mild stratification, and in the absence of entrainment, non-stationarity and canopy effects. It further suggests that the breakdown of the Reynolds analogy is at least partially caused by the influence of large eddies on turbulent heat transport