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

Limited computer resources lead to a simplified representation of unresolved small-scale processes in weather and climate models, through parameterisation schemes. Among the parameterised processes, turbulent fluxes exert a critical impact on the exchange of heat, water and carbon between the land and the atmosphere. Turbulence theory was, however, developed for homogeneous and flat terrain, with stationary conditions. The theory fails in unsteady flow contexts or with heterogeneous landscapes, but no alternative, viable theory is available. This is not only a source of error in forecasts or climate scenarios, but also a source of model uncertainty which should be characterised and considered when using weather and climate models.

Modelling turbulence is particularly challenging in conditions of stable stratification, which can be associated with intermittent or unsteady turbulence leading to model uncertainty. The study develops a modeling approach to represent unsteady mixing possibly associated with turbulence intermittency and with non-turbulent, sub-mesoscale motions that are typically unresolved by numerical weather prediction or climate models. The approach introduces a stochastic parametrisation of turbulence 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 (RANS) models. Field measurements are processed using a statistical model-based clustering technique, which simultaneously models and classifies the nonstationary stable boundary layer. The obtained stochastic stability correction 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. Its implementation in a single-column RANS model is tested for several numerical examples, demonstrating the effectivity to simulate intermittent mixing, without altering the mean behaviour when compared to a standard RANS model.