Abstract
This study aims to review the physical theory and parametrizations associated to Turbulent Kinetic Energy Density Function (STKE). The bibliographic references bring a broad view of the physical problem, mathematical techniques and modeling of turbulent kinetic energy dynamics in the convective boundary layer. A simplified model based on the dynamical equation for the STKE, in an isotropic and homogeneous turbulent flow regime, is done by formulating and considering the isotropic inertial energy transfer and viscous dissipation terms. This model is described by the Cauchy Problem and solved employing the Method of Characteristics. Therefore, a discussion on Linear First Order Partial Differential Equation, its existence, and uniqueness of solution has been presented. The spectral function solution obtained from its associated characteristic curves and initial condition (Method of Characteristics) reproduces the main features of a modeled physical system. In addition, this modeling allows us to obtain the scaling parameters, which are frequently employed in parameterizations for turbulent dispersion.
Highlights
The model that describes the dynamics of Turbulent Kinetic Energy (TKE) under the hypothesis of regime fully developed turbulence covers several arguments associated with the phenomenology of the physical system [1]
Is based on a system of Partial Differential Equations (PDE) known as Navier-Stokes Equations [1], in which the predicted TKE evolution in the Convective Boundary Layer (CBL) is admitted from the parameterization of the forms of production, dissipation, and energy transfer
The theoretical framework applied in the formulation of the 3D-Spectral Density Turbulent Kinetic Energy Function (STKE) and relevant processes that describe the dynamics of the TKE in the CBL are presented here
Summary
The model that describes the dynamics of Turbulent Kinetic Energy (TKE) under the hypothesis of regime fully developed turbulence covers several arguments associated with the phenomenology of the physical system [1]. We must begin with the conception of the autocorrelation functions and 1D spectral density function by the Fourier transform [2], until its representation in the three-dimensional form [3] and later synthesis in a descriptive equation of the dynamic spectral function [1] At this point, the importance of the parameterization process of the constituent terms of the model is emphasized, as it will indicate the reliability of the model through the realistic description of the involved processes and reproduction of observed properties in the phenomenon, and influence the choice of mathematical methods (analytical and/or numerical) to obtain the solution [4].
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