The Momentum Flux Budget in the Roughness Sublayer Closed by Turbulent Structural Models

Abstract:

The momentum flux is key to understanding and modeling turbulence effects on land-atmosphere exchange. Experimentally, there has been a long tradition of using quadrant analysis to characterize the roles of sweeps and ejection events in momentum transport for both rough and smooth surfaces. Yet there has been limited success in converting this knowledge to closure models for the momentum flux. The traditional first-order closure model of the momentum flux budget, known as gradient diffusion or K-theory, assumes a linear relation between the momentum flux and its vertical gradient such that it is analogous to a “stress diffusion”. In this presentation, turbulence measurements from a field experiment, wind tunnel experiments, and a simulation are used to assess the performance of gradient diffusion and develop a structural model to improve closure of the stress budget.

Gradient diffusion performs well in the inertial region of the atmospheric surface layer, where there is an approximate balance between sweep and ejection contributions to the flux and probability distributions of velocity are nearly symmetric. However, in the roughness sublayer close to the surface, the vertical transport of momentum flux is non-negligible to the overall flux budget. Cumulant expansion is used here to derive a quantitative relation between this transport term and the imbalance between sweeps and ejections. The coefficients in this relation are shown to be independent of roughness geometry among the evaluated cases, suggesting the roughness effects are entirely captured by the sweep and ejection properties. The derived relation leads to a structural model for the transport of momentum flux to complement, in an additive manner, the gradient diffusion term. The findings also provide a promising pathway to parameterizing roughness effects in turbulence models of the roughness sublayer.