A Reduced TKE Phase Space for Studying Disturbed Atmospheric Surface Layer Flows: Application to Vertical Velocity Variance over a Forest Canopy

The success of Monin-Obukhov Similarity Theory (MOST) in synthesizing observations elevated the idealized constant-flux surface layer to a status of canonical flow in turbulence textbooks. Given the success of MOST as a predictive model and diagnostic framework, the next clear step was to move to more complex surface layers, such as those that arise in the presence of “disturbances” (e.g., flows over gentle topography or ocean waves, sloping terrain, vegetation and urban canopies, unsteady conditions, surface heterogeneity, etc.). In this work, we refer to this collection of more complex flows near the ground as “disturbed surface layers”, and seek a framework capable of identifying and quantifying differences between disturbed surface layers and the canonical MOST surface layer.

We propose an approach based on a simplified form of the TKE budget equation (the “reduced TKE budget”) which can be represented by a two-dimensional phase space. The phase space provides a visual way to quantify relative contributions of shear and buoyancy production/destruction of TKE, as well as the local imbalance between production and dissipation. In this framework, MOST represents one possible approach to reduce the dimensionality of the phase space. In this sense, the proposed framework is a more general diagnostic tool (but not a predictive model), and can be used to assess whether MOST or any other reduction to one-dimensional representation is reasonable or not. It can also be used to study the larger class of disturbed surface layers, in which MOST is typically assumed not to hold. We apply this framework to study the vertical velocity variance in the canonical surface layer (using data from the AHATS field campaign) and in the canopy roughness sublayer above the Amazon forest (using data from the GoAmazon field campaign). Results reveal interesting insight into the behavior of the vertical velocity variance over forests, linking its magnitude to the imbalance between local production and dissipation of TKE.