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The atmospheric boundary layer is particularly challenging to model in conditions of stable stratification, which can be associated with intermittent or unsteady turbulence. We develop a modelling approach to represent unsteady mixing possibly associated with turbulence intermittency and with unresolved fluid motions, called sub‐mesoscale motions. This approach introduces a stochastic parametrisation by randomising the stability correction used in the classical Monin–Obhukov similarity theory. This randomisation alters the turbulent momentum diffusion and accounts for sporadic events that cause unsteady mixing. A data‐driven stability correction equation is developed, parametrised, and validated with the goal to be modular and easily combined with existing Reynolds‐averaged Navier–Stokes models. Field measurements are processed using a statistical model‐based clustering technique, which simultaneously models and classifies the non‐stationary stable boundary layer. The stochastic stability correction obtained includes the effect of the static stability of the flow on the resolved flow variables, and additionally includes random perturbations that account for localised intermittent bursts of turbulence. The approach is general and effectively accounts for the stochastic mixing effects of unresolved processes of possibly unknown origin. [ABSTRACT FROM AUTHOR]

Time integration of the unsteady Reynolds-averaged Navier–Stokes (URANS) equations is the principal approach used in numerical weather prediction. This approach represents a balanced compromise between accuracy and computational cost. The URANS equations require the flow to be decomposed into an ensemble mean and excursions that are presumed to be entirely related to turbulence, thereby enabling conventional closure schemes to be used to describe their statistics. Implicit in such a decomposition is the assumption of a spectral gap between the unsteadiness in the mean flow and the scales of turbulence. Modelling challenges arise when some of the unresolved fluctuations are related to non-turbulent, structured motions that can also blur the spectral gap and render conventional closure schemes ineffective. This work seeks to clarify modelling issues that occur when unresolved fluctuations include submesoscale motions and persistent secondary circulations related to surface heterogeneities. Because submeso motions and persistent secondary circulations are not random, new theoretical tactics are discussed to represent their effects on URANS transport. By reviewing the interpretation of fluctuating terms in the URANS equations, we suggest the use of large-eddy simulations, direct numerical simulations and field measurements to guide the development of closure schemes that explicitly include fluxes due to submeso motions and persistent secondary circulations. [ABSTRACT FROM AUTHOR]

The lower nocturnal boundary layer is governed by intermittent turbulence which is thought to be triggered by sporadic activity of so-called sub-mesoscale motions in a complex way. We analyze intermittent turbulence based on an assumed relation between the vertical gradients of the sub-mean scales and turbulence kinetic energy. We analyze high-resolution nocturnal eddy-correlation data from 30-m tower collected during the Fluxes over Snow Surfaces II field program. The non-turbulent velocity signal is decomposed using a discrete wavelet transform into three ranges of scales interpreted as the mean, jet and sub-mesoscales. The vertical gradients of the sub-mean scales are estimated using finite differences. The turbulence kinetic energy is modelled as a discrete-time autoregressive process with exogenous variables, where the latter ones are the vertical gradients of the sub-mean scales. The parameters of the discrete model evolve in time depending on the locally-dominant turbulence-production scales. The three regimes with averaged model parameters are estimated using a subspace-clustering algorithm which illustrates a weak bimodal distribution in the energy phase space of turbulence and sub-mesoscale motions for the very stable boundary layer. One mode indicates turbulence modulated by sub-mesoscale motions. Furthermore, intermittent turbulence appears if the sub-mesoscale intensity exceeds 10 % of the mean kinetic energy in strong stratification. [ABSTRACT FROM AUTHOR]

A combination of methods originating from non-stationary time-series analysis is applied to two datasets of near-surface turbulence in order to gain insights on the non-stationary enhancement mechanism of intermittent turbulence in the stable atmospheric boundary layer (SBL). We identify regimes of SBL turbulence for which the range of time scales of turbulence and submeso motions, and hence their scale separation (or lack of separation), differs. Ubiquitous flow structures, or events, are extracted from the turbulence data in each flow regime. We relate flow regimes characterized by very stable stratification, but differing in the dynamical interactions and in the transport properties of different scales of motion, to a signature of flow structures thought to be submeso motions. [ABSTRACT FROM AUTHOR]

Atmospheric boundary layers with stable stratification include a variety of small-scale nonturbulent motions such as waves, microfronts, and other complex structures. When the thermal stratification becomes strong, the presence of such motions could affect the turbulent mixing to a large extent, and common similarity theory that is used to describe weakly stable conditions may become unreliable. The authors apply a statistical clustering methodology based on a bounded variation, finite-element method (FEM-BV) to characterize the interaction between small-scale nonturbulent motions and turbulence. The clustering methodology achieves a multiscale representation of nonstationary turbulence data by approximating them through an optimal sequence of locally stationary multivariate autoregressive factor model (VARX) processes and some slow hidden process switching between them. The clustering method is used to separate periods with different influence of the nonturbulent motions on the vertical velocity fluctuations. The methodology can be used in a later stage to derive a stochastic parameterization for the interactions between nonturbulent and turbulent motions. [ABSTRACT FROM AUTHOR]