A stochastic perturbation method to generate inflow turbulence in large-eddy simulation models: Application to neutrally stratified atmospheric boundary layers

Abstract

Despite the variety of existing methods, efficient generation of turbulent inflow conditions for large-eddy simulation (LES) models remains a challenging and active research area. Herein, we extend our previous research on the cell perturbation method, which uses a novel stochastic approach based upon finite amplitude perturbations of the potential temperature field applied within a region near the inflow boundaries of the LES domain [Muñoz-Esparza et al., “Bridging the transition from mesoscale to microscale turbulence in numerical weather prediction models,” Boundary-Layer Meteorol., 153, 409–440 (2014)]. The objective was twofold: (i) to identify the governing parameters of the method and their optimum values and (ii) to generalize the results over a broad range of atmospheric large-scale forcing conditions, Ug = 5 − 25 m s−1, where Ug is the geostrophic wind. We identified the perturbation Eckert number, Ec=Ug2/ρcpθ̃pm, to be the parameter governing the flow transition to turbulence in neutrally stratified boundary layers. Here, θ̃pm is the maximum perturbation amplitude applied, cp is the specific heat capacity at constant pressure, and ρ is the density. The optimal Eckert number was found for nonlinear perturbations allowed by Ec ≈ 0.16, which instigate formation of hairpin-like vortices that most rapidly transition to a developed turbulent state. Larger Ec numbers (linear small-amplitude perturbations) result in streaky structures requiring larger fetches to reach the quasi-equilibrium solution, while smaller Ec numbers lead to buoyancy dominated perturbations exhibiting difficulties for hairpin-like vortices to emerge. Cell perturbations with wavelengths within the inertial range of three-dimensional turbulence achieved identical quasi-equilibrium values of resolved turbulent kinetic energy, q, and Reynolds-shear stress, 〈w′u′〉. In contrast, large-scale perturbations acting at the production range exhibited reduced levels of 〈w′u′〉, due to the formation of coherent streamwise structures, while q was maintained, requiring larger fetches for the turbulent solution to stabilize. Additionally, the cell perturbation method was compared to a synthetic turbulence generator. The proposed stochastic approach provided at least the same efficiency in developing realistic turbulence, while accelerating the formation of large-scales associated with production of turbulent kinetic energy. Also, it is computationally inexpensive and does not require any turbulent information.