Emprego da parametrização de heisenberg e do método de adomian no decaimento da camada limite convectiva

Abstract

In this paper we present a spectral model to describe the decay of turbulent kinetic energy in the Convective Boundary Layer (CLC) of the earths surface, where the physical processes that occur generate turbulence of convective origin and mechanics in the air. Using the equations of conservation of time, which describe the dynamics of an element of fluid in a flow, you get an equation for the spectrum of kinetic energy in a homogeneous turbulent flow, but not isotropic. The spectrum of energy is expressed in terms of number of wave vector kappa and time. Each term in this equation of energy balance, describing different physical processes that generate the turbulence. The terms of production or loss of energy by the effect of heat and friction, are written according to the number of Richardson, which is a dimensionless quantity that expresses a relationship between potential energy and kinetic energy of a fluid. The term transfer of kinetic energy by inertial effect between eddies of different wave numbers is parameterized from the Heisenberg model which, based on intuitive arguments, assume that the transfer of energy between eddies with small number of wave for the large number of wavelength is similar to conversion of mechanical energy into heat energy, the effect of molecular viscosity. The number of eddies with wave absorbing higher energy of eddies of wave number with lower. The dynamic equation for the three-dimensional spectrum of kinetic energy obtained was solved by the Adomian decomposition method for the analytical solution of ordinary differential equations or partial, linear or nonlinear, deterministic or stochastic. This technique is to decompose a given equation into a linear part and one non-linear, isolating the operator linear, easily inverted of higher order. The nonlinear term is written as a sum of a special class of polynomials called Adomian polynomials of, and unknown function as a series whose terms are calculated on recursively. The application of the Adomian decomposition method for the solution of differential equation integrated non linear due to the spectrum of kinetic energy, has an analytical solution without linearization, commonly used for simplicity, in problems where processes are highly nonlinear. Moreover, due to rapid convergence of the solution in terms of the Adomian polynomials, the spectrum of kinetic energy was obtained without a large computational effort. From the calculation of the energy spectrum could be determined the variation of turbulent kinetic energy in the CLC and compared with results of numerical simulation in the literature.%%%%No presente trabalho e apresentado um modelo espectral para descrever o decaimento da energia cinetica turbulenta na Camada Limite Convectiva (CLC) da superficie terrestre, onde acontecem os processos fisicos que geram turbulencia de origem mecânica e convectiva no ar. Partindo das equacoes de conservacao de momento, que descrevem a dinâmica de um elemento de fluido em um escoamento, se obtem uma equacao para o espectro de energia…