Towards dynamic closures for higher-order turbulence schemes

Starting from the spatially filtered equations in the large-eddy simulation (LES) regime,
commonly used turbulence closures assume a local equilibrium between turbulence
production and dissipation, with the closure parameters representing the continuous
cascade of energy from the resolved to the subgrid scales. However, away from grid
resolutions that adequately resolve the inertial subrange of turbulence, this equilibrium
assumption breaks down. Moreover, at such resolutions, the dominant turbulent eddies
are only partially resolved, and the appropriate values of the closure parameters are
generally unknown.
In this study, we explore a dynamic closure for a prognostic turbulent kinetic energy
(TKE) scheme in a quasi-steady convective boundary layer (CBL) case, spanning
resolutions from LES toward the grey zone. The dynamic approach optimises the
closure parameters using information from the resolved small-scale turbulence,
exploiting the assumed similarity between resolved and unresolved scales. Preliminary
results show that the dynamically derived length scales exhibit the desired scale
dependency across resolutions, leading to improved agreement with LES.