The Onset of Resolved Boundary-Layer Turbulence at Grey-Zone Resolutions

Abstract

Numerical weather prediction (NWP) models are now capable of operating at horizontal resolutions in the 100-m to 1-km range, a grid spacing similar in scale to that of the turbulent eddies present in the atmospheric convective boundary layer (CBL). Known as the ‘grey zone’ of turbulence, this regime is characterized by significant contributions from both the resolved and subgrid components to represent the dominant motions of the system. This study examines how the initiation of resolved turbulence – a concept commonly referred to as ‘spin-up’– can be delayed during the evolution of a simulated CBL in the grey zone. We identify the importance of imposed pseudo-random perturbations of potential temperature (theta ) for the development of the resolved fields showing that without such perturbations, resolved turbulence does not become established at all. When the perturbations are organized, spin-up can develop more rapidly, and we find that the earliest spin-up times can be achieved by applying an idealized profile of variance to derive the theta perturbation values. The perturbation structures are shown to be most effective when applied at intervals following the mixed-layer time scale, t_{*}, rather than perturbing only at the initial time. We also propose a modification to the three-dimensional Smagorinsky turbulence closure, in which the Smagorinsky constant is replaced by a scale-dependent coefficient. Both the approaches of: (1) applying structured theta perturbations, and (2) using a dynamically-evolving Smagorinsky coefficient are shown to encourage faster spin-up independently of each other, but the best results clearly emerge when the two methods are applied concurrently.