An improved stochastic backscatter parameterisation for large-eddy simulation of the neutral boundary layer

An improved stochastic backscatter parameterisation for large-eddy simulation (LES) of the neutral boundary layer (NBL) is presented. The long-standing ‘overshoot' problem refers to the tendency of LES models to over-predict mean velocity within the surface layer, which in the NBL is seen as a deviation from the expected logarithmic velocity profile. This deficiency has been attributed to the inability of purely dissipative sub-grid scale (SGS) models to account for backscatter; that is, the transfer of energy from sub-grid to resolved scales. Mason and Thomson (1992) successfully reduced the LES overshoot by augmenting the (dissipative) Smagorinsky SGS model with stochastically generated acceleration fields that explicitly inject this missing energy back into the flow at the grid scale. These stochastic fields are constrained by certain conditions; for example they are divergence-free and thus, like the resolved scale flow, satisfy the continuity equation. However, this scheme becomes less effective with increasing refinement of the near-surface vertical grid, due to a dependence on grid geometry that introduces anisotropy into the acceleration fields (Fig. 1, left). In an attempt to overcome this issue, Weinbrecht and Mason (2008) modified the scheme by interpolating the acceleration fields from an isotropic mesh onto the model grid (Fig. 1, middle). However, this interpolation procedure can introduce significant divergences into the acceleration fields when employing a refined vertical grid. Utilising a grid-adaptive discrete filtering technique, we successfully generate stochastic acceleration fields that are both divergence-free and isotropic, irrespective of the grid geometry (Fig. 1, right). Both existing schemes and our new scheme have been implemented in the Regional Atmospheric Modelling System (RAMS) LES model at the University of Birmingham (Cai, 1999), and results indicate that our new scheme is able to most accurately predict a logarithmic velocity profile in the surface layer when using a refined vertical grid. Furthermore, the scheme comes at very little extra computational cost and can thus be beneficial to a wide range of boundary-layer flow modellers. References: Mason, P. J. and D. J. Thomson (1992). "Stochastic Backscatter in Large-Eddy Simulations of Boundary-Layers." Journal of Fluid Mechanics, 242, 51-78. Weinbrecht, S. and P. J. Mason (2008). "Stochastic Backscatter for Cloud-Resolving Models. Part I: Implementation and Testing in a Dry Convective Boundary Layer." Journal of the Atmospheric Sciences, 65(1), 123-139. Cai, X. M. (1999). "Large-Eddy Simulation of the Convective Boundary Layer over an Idealized Patchy Urban Surface." Quarterly Journal of the Royal Meteorological Society, 125, 1427-1444.