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

Abstract

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.