A stochastic stability equation for unsteady turbulence in the stable boundary layer

• Published in: Quarterly journal of the Royal Meteorological Society 2023-07, Vol.149 (755), p.2125-2145
• Main Authors: Boyko, Vyacheslav, Vercauteren, Nikki
• Format: Article
• Language: English
• Subjects: Atmospheric boundary layer; Boundary layers; intermittent turbulence; Mathematical models; Mesoscale motions; Modelling; Momentum; MOST; nocturnal boundary layer; Stable boundary layer; Static stability; Statistical analysis; Statistical models; stochastic parametrisation; Stochasticity; Stratification; Turbulence; turbulence closure; Vertical stability
• ISSN: 0035-9009; 1477-870X
• DOI: 10.1002/qj.4498

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. The stochastic stability equation for predicting the temporal evolution of the momentum stability correction of turbulent diffusion in a stably stratified boundary layer under the influence of unresolved random processes is validated. Comparison of the probability distribution is calculated from the parametrised model (lower panel) and the data (upper panel). The dashed line is the scaling function used in the Meteorological Service of Canada model. The red solid line is the expected value, and the yellow line is the most likely value.