Employing the Method of Characteristics to Obtain the Solution of Spectral Evolution of Turbulent Kinetic Energy Density Equation in an Isotropic Flow

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.

Keywords

• atmospheric turbulence
• models parameterizations
• characteristic curves
• method of characteristics
• first order pde(s)
• isotropy
• three-dimensional spectrum of turbulent kinetic energy
• dynamic equation of spectral function