Consistent Two-Equation Closure Modelling for Atmospheric Research: Buoyancy and Vegetation Implementations

Abstract

A self-consistent two-equation closure treating buoyancy and plant drag effects has been developed, through consideration of the behaviour of the supplementary equation for the length-scale-determining variable in homogeneous turbulent flow. Being consistent with the canonical flow regimes of grid turbulence and wall-bounded flow, the closure is also valid for homogeneous shear flows commonly observed inside tall vegetative canopies and in non-neutral atmospheric conditions. Here we examine the most often used two-equation models, namely ${E - \varepsilon}$ and E − ω (where ${\varepsilon}$ is the dissipation rate of turbulent kinetic energy, E, and ${\omega = \varepsilon/E}$ is the specific dissipation), comparing the suggested buoyancy-modified closure against Monin–Obukhov similarity theory. Assessment of the closure implementing both buoyancy and plant drag together has been done, comparing the results of the two models against each other. It has been found that the E − ω model gives a better reproduction of complex atmospheric boundary-layer flows, including less sensitivity to numerical artefacts, than does the ${E -\varepsilon}$ model. Re-derivation of the ${\varepsilon}$ equation from the ω equation, however, leads to the ${E - \varepsilon}$ model implementation that produces results identical to the E − ω model. Overall, numerical results show that the closure performs well, opening new possibilities for application of such models to tasks related to the atmospheric boundary layer—where it is important to adequately account for the influences of both vegetation and atmospheric stability.