Non-local Second Order Closure Scheme for Boundary Layer Turbulence

Atmospheric boundary layer (BL) processes, such as turbulent fluxes of moisture and entropy or the dynamics of clouds, happen on a scale of few meters to kilometers, whereas general climate models (GCMs) have a resolution of order 100km. Thus, BL processes cannot be resolved explicitly in GCMs but need to be approximated by parameterization schemes. State-of-the art GCMs usually represent BL turbulence and convection by using two separate schemes, which are based on first order closures of the moment equations. Second-order moments enter these first-order equations as truncation parameters that are determined semi-empirically, e.g., in local diffusive or non-local mass flux closures. The (computational) simplicity of such schemes is achieved at the expense of lower accuracy and the loss of spatially non-local information about the fields of interest. Here we demonstrate the viability of a spatially non-local second-order closure (CE2), obtained by truncating the hierarchy of cumulant equations at second order and neglecting cumulants of 3rd order and higher. To explore the applicability of the CE2 closure, we study characteristics of different turbulence regimes through LES, comparing fully nonlinear LES with quasi-linear LES in which interactions among turbulent eddies are suppressed but nonlinear eddy—mean flow interactions are retained, as they are in the CE2 closure. In physical terms, suppressing eddy—eddy interactions amounts to suppressing, e.g., interactions among plumes, while retaining interactions between plumes and the environment (e.g., entrainment and detrainment). That is, the CE2 closure explicitly resolves entrainment and detrainment, obviating the need to parameterize them. First results show that a QL simulation is able to capture important properties of the dry convective boundary layer: Although interactions among fluctuations are suppressed, QL simulations appear to be similarly turbulent as the fully non-linear simulation. The characteristic coherent structures of the vertical updrafts and the horizontal convective cells are well represented, albeit with diminished intensity. Furthermore, the mean field statistics reveal that the QL dynamics captures the well-mixed nature and the rate of growth of the deepening boundary layer. A computational disadvantage is that solving the resulting equations for the second-order cumulants numerically in general is costly. We will be discussing ways in which additional assumptions (e.g., about horizontal correlation structures among turbulent fields) may lead to closures that are computationally efficient, yet more accurate than existing closures.