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.

Sensible heating as a potential mechanism for enhanced cloud formation over temperate forest

“…, ; van Heerwaarden and Mellado, 2016; McColl et al. , ). The use of this type of model has several advantages compared to the use of observations.…”

MicroHH 1.0: a computational fluid dynamics code for direct numerical simulation and large-eddy simulation of atmospheric boundary layer flows

“…The work of van Heerwaarden et al (2014) focused on the scaling of flow over heterogeneously heated land surfaces using DNS and LES, Gentine et al (2015) used LES to study the structure of the inversion of a convective boundary layer, van Heerwaarden and Mellado (2016) developed scaling laws for the convective boundary layer over a surface with a constant temperature from DNS data, McColl et al (2017) improved surfacelayer similarity under mildly convective conditions with the help of DNS data, and Umphrey et al (2017) used DNS data produced with MicroHH as a reference for their simulations of slope flow.…”

MicroHH 1.0: a computational fluid dynamics code for direct numerical simulation and large-eddy simulation of atmospheric boundary layer flows

“…The spatial operators are based on finite differences. The code supports second-order and fourth-order accurate discretizations following Morinishi et al (1998) and Vasilyev (2000). From Taylor series, spatial operators can be derived that constitute the building blocks of more advanced operators, such as the advection and diffusion operators.…”

“…MicroHH makes use of ghost cells in order to avoid the need of biased schemes for single interpolation or gradient operators near the wall. The values at the ghost cells are derived making use of the boundary conditions following Morinishi et al (1998). The ghost cells for the Dirichlet boundary conditions in the second-order accurate discretization are…”

“…Here, we set the third derivative equal to zero following Morinishi et al (1998). For the Dirichlet boundary condition we then acquire the following expressions for the ghost cells:…”