A theoretical model for the study of convective turbulence decay and comparison with large-eddy simulation data

The development of a theoretical model for a decaying convective boundary layer is considered. The model relies on the dynamical energy spectrum equation in which the buoyancy and inertial transfer terms are retained, and a closure assumption made for both. The parameterization for the buoyancy term is given providing a factorization between the energy source term and its temporal decay. Regarding the inertial transfer term a hypothesis of superposition is used to describe the convective energy source and time variation of velocity correlation separately. The solution of the budget equation for the turbulent kinetic energy spectrum is possible, given the three-dimensional initial energy spectrum. This is done utilizing a version of the Kristensen et al. (see Boundary-Layer Meteorol. 47, 149-193) model valid for non-isotropic turbulence. During the decay the locus of the spectral peak remains at about the same position as the heat flux decreases. Comparison of the theoretical model is performed against large-eddy simulation data for a decaying convective boundary layer.