A. Goulart

A THEORETICAL MODEL FOR THE STUDY OF CONVECTIVE TURBULENCE DECAY AND COMPARISON WITH LARGE-EDDY SIMULATION DATA

The development of a theoretical model fora decaying convective boundary layeris considered. The model relies on thedynamical energy spectrumequation in which the buoyancy andinertial transfer terms are retained,and a closure assumptionmade for both. The parameterization for thebuoyancy term is given providing a factorizationbetween the energy source termand its temporal decay. Regarding the inertialtransfer term a hypothesis ofsuperposition is used to describe theconvective energy source and time variationof velocity correlation separately.The solution of the budget equation for theturbulent kinetic energy spectrum is possible,given the three-dimensional initial energyspectrum. This is doneutilizing a version of the Kristensen et al.(see Boundary-Layer Meteorol.47, 149–193)model valid for non-isotropic turbulence. During thedecay the locus of the spectralpeak remains at about the sameposition as the heat flux decreases.Comparison of the theoretical modelis performed against large-eddy simulationdata for a decaying convectiveboundary layer.

An analytical solution for the nonlinear energy spectrum equation by the decomposition method

We discuss the isotropic turbulence decay and solve the energy density spectrum (EDS) equation considering the inertial transfer energy and viscosity terms, using the Heisenberg parameterization. In the present approach, buoyant and shear terms are neglected and turbulence is assumed to be homogeneous and isotropic. The nonlinear integro-differential equation is solved by Adomians generic decomposition method, which yields an analytical recursive expression and upon truncation gives an approximate solution. We show the resulting EDS and the time-dependent decay of the intensity of the turbulent kinetic energy. Our results prove consistent the Heisenberg parameterization for the transfer term of the inertial energy. The analytical character of the solution permits a validation of the nonlinear details of the physical model.

A global analysis of the atmospheric pollutant modeling

In this article is carried out a comparison between Lagrangian and Eulerian modelling of the turbulent transport of pollutants within the Planetary Boundary Layer (PBL). The Lagrangian model is based on a three-dimensional form of the Langevin equation for the random velocity. The Eulerian analytical model is based on a discretization of the PBL in N sub-layers; in each of the sub-layers the advection-diffusion equation is solved by the Laplace transform technique. In the Eulerian numerical model the advective terms are solved using the cubic spline method while a Crank-Nicholson scheme is used for the diffusive terms. The models use a turbulence parameterization that considers a spectrum model, which is given by a linear superposition of the buoyancy and mechanical effects. Observed ground-level concentrations measured in a dispersion field experiment are used to evaluate the simulations.