Progress in the extension of a second-moment closure for turbulent environmental flows

An advanced second-moment closure for the double-averaged turbulence equations of porous medium and vegetation flows is proposed. It treats three kinds of second moments which appear in the double-averaged momentum equation. They are the dispersive covariance, the volume averaged (total) Reynolds stress and the micro-scale Reynolds stress. The two-component-limit pressure–strain correlation model is applied to model the total Reynolds stress equation whilst a novel scale-similarity non-linear $k''–''\epsilon$ two-equation eddy viscosity model is employed for the micro-scale turbulence. For the dispersive covariance, an algebraic relation is applied. Model validation in several fully developed homogeneous porous medium flows, porous channel flows and aquatic vegetation canopy flows is performed with satisfactory agreement with the data.