The resistance law for stably stratified atmospheric planetary boundary layers

The resistance law for stably and neutrally stratified atmospheric planetary boundary layers (PBL) entered textbooks on boundary-layer meteorology but, until now, remains practically unused in modelling applications. This is not surprising. The law has been formulated and validated only for idealised cases, such as truly neutral PBL - implying neutral stratification across the entire atmosphere, nocturnal stable PBL - stably stratified near the surface but developed against the neutrally stratified free flow, and (more recently) conventionally neutral PBLs - neutrally stratified near the surface but developed against stable stratification in the free flow. We derive and validate the general formulation of the resistance law accounting for the integral effect on PBL of stable stratifications at the surface and in the free atmosphere. Such long-lived stable PBLs, typical of wintertime at high latitudes, were until recently overlooked in boundary-layer meteorology, not to mention weather and climate models. The proposed general formulation of the resistance law covers long-lived stable PBLs and opens up prospects for their improved modelling.Peer reviewe

Order out of chaos : Shifting paradigm of convective turbulence

Publisher Copyright: © 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).Turbulence is ever produced in the low-viscosity/large-scale fluid flows by velocity shears and, in unstable stratification, by buoyancy forces. It is commonly believed that both mechanisms produce the same type of chaotic motions, namely, the eddies breaking down into smaller ones and producing direct cascade of turbulent kinetic energy and other properties from large to small scales toward viscous dissipation. The conventional theory based on this vision yields a plausible picture of vertical mixing and has remained in use since the middle of the twentieth century in spite of increasing evidence of the fallacy of almost all other predictions. This paper reveals that in fact buoyancy produces chaotic vertical plumes, merging into larger ones and producing an inverse cascade toward their conversion into the self-organized regular motions. Herein, the velocity shears produce usual eddies spreading in all directions and making the direct cascade. This new paradigm is demonstrated and proved empirically; so, the paper launches a comprehensive revision of the theory of unstably stratified turbulence and its numerous geophysical or astrophysical applications.Peer reviewe

Evaluation of Surface Layer Stability Functions and Their Extension to First Order Turbulent Closures for Weakly and Strongly Stratified Stable Boundary Layer

In this study, we utilize a generalization of Monin–Obukhov similarity theory to construct first order turbulent closures for single-column models of the atmospheric boundary layer (ABL). A set of widely used universal functions for dimensionless gradients is evaluated. Two test cases based on Large-Eddy Simulations (LES) experimental setups are considered – weakly stable ABL (GABLS1; Beare et al. in Bound Layer Meteorol 118(2):247–272,2006), and very strongly stratified ABL (van der Linden et al. in Bound Layer Meteorol 173(2):165–192, 2019). The comparison shows that approximations obtained using a linear dimensionless velocity gradient tend to match the LES data more closely. In particular, the EFB (Energy- and Flux- Budget) closure proposed by Zilitinkevich et al. (Bound Layer Meteorol 146(3):341–373, 2013) has the best performance for the tests considered here. We also test surface layer “bulk formulas” based on these universal functions. The same LES data are utilized for comparison. The setup showcases the behavior of surface scheme, when one assumes that the velocity and temperature profiles in ABL are represented correctly. The advantages and disadvantages of different surface schemes are revealed

Dissipation rate of turbulent kinetic energy in stably stratified sheared flows

Over the years, the problem of dissipation rate of turbulent kinetic energy (TKE) in stable stratification remained unclear because of the practical impossibility to directly measure the process of dissipation that takes place at the smallest scales of turbulent motion. Poor representation of dissipation causes intolerable uncertainties in turbulence-closure theory and thus in modelling stably stratified turbulent flows. We obtain a theoretical solution to this problem for the whole range of stratifications from neutral to limiting stable; and validate it via (i) direct numerical simulation (DNS) immediately detecting the dissipation rate and (ii) indirect estimates of dissipation rate retrieved via the TKE budget equation from atmospheric measurements of other components of the TKE budget. The proposed formulation of dissipation rate will be of use in any turbulence-closure models employing the TKE budget equation and in problems requiring precise knowledge of the high-frequency part of turbulence spectra in atmospheric chemistry, aerosol science, and microphysics of clouds.Peer reviewe

Dissipation rate of turbulent kinetic energy in stably stratified sheared flows

Over the years, the problem of dissipation rate of turbulent kinetic energy (TKE) in stable stratification remained unclear because of the practical impossibility to directly measure the process of dissipation that takes place at the smallest scales of turbulent motion. Poor representation of dissipation causes intolerable uncertainties in turbulence-closure theory and thus in modelling stably stratified turbulent flows. We obtain a theoretical solution to this problem for the whole range of stratifications from neutral to limiting stable; and validate it via (i) direct numerical simulation (DNS) immediately detecting the dissipation rate and (ii) indirect estimates of dissipation rate retrieved via the TKE budget equation from atmospheric measurements of other components of the TKE budget. The proposed formulation of dissipation rate will be of use in any turbulence-closure models employing the TKE budget equation and in problems requiring precise knowledge of the high-frequency part of turbulence spectra in atmospheric chemistry, aerosol science, and microphysics of clouds.</p