BOUNDARY-LAYER FLOW AND TURBULENCE NEAR POROUS OBSTACLES .1. DERIVATION OF A GENERAL EQUATION SET FOR A POROUS-MEDIUM

We derive a set of governing equations for flow through porous obstacl es by employing a two-step averaging processes. The Navier-Stokes equa tions under the Boussinesq approximation that describe the air space o f the porous obstacle are subjected to high-wavenumber averaging, whic h leads to a set of high-frequency (wake) turbulence equations. We the n use conventional Reynolds-averaging methods to obtain statistically steady mean and turbulence equations that include interactions between wake and shear turbulence. Our method provides a theoretical basis fo r the cascade of turbulent kinetic energy. We use this approach to ana lyze the constants and parameters of simple K-theory and higher-order closure models. We also discuss qualitatively the theory of the turbul ence energy generation process and the significance of interactions be tween different turbulent mechanisms.