A theoretical model for the study of the convective turbulence decay and comparison with LES data

The development of a theoretical model for a decaying convective boundary layer is considered in this paper. The model relies on the dynamical energy spectrum equation in which the buoyancy and inertial transfer terms are retained. A closure assumption is done for these two terms. 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 budget equation for the TKE spectrum is possible just giving the 3-D initial energy spectrum. This is done utilizing a version of Kristensen model valid for a non-isotropic turbulence. During the decay the locus of spectral peak is displaced toward smallest wave-number region indicating the persistence of largest eddies. Comparison of the theoretical model is performed against large eddy simulation data for a decaying convective boundary layer.