Spectral energy balance in dry convective boundary layers

Abstract

Three-dimensional large-eddy simulations (LES) of the convective boundary layer over a domain of approximately 6 km are performed with the UCLA LES model. Simulations are forced with a constant surface heat flux and prescribed subsidence, and are run to equilibrium. Sub-grid scale fluxes are parameterised with the Smagorinsky–Lilly scheme. A range of grid spacings from 40 down to 5 m are employed. Kinetic energy spectra and the various terms in the kinetic energy spectral budget – heat flux, nonlinear transfer, pressure, and dissipation – are computed using two-dimensional discrete Fourier transforms at every vertical level. Despite the fact that isotropic grid spacings of down to 5 m (grid sizes of 11522×400) were used, an inertial range with a −5/3 spectrum is not obtained. Rather, shallower energy spectral slopes that are closer to −4/3 are found. The shallower spectra are shown to possibly result from the injection of kinetic energy over a wide range of scales via a very broad heat flux spectrum. Only with the highest resolution (Δx = 5 m) does the total heat flux begin to converge and the possibility of local isotropy emerge at small scales. Dependence on surface heat flux and domain size is considered. Preliminary sub-grid scale sensitivity results are obtained through comparison with the turbulent kinetic energy sub-grid scale model.