Dispersive Fluxes and Flow Structure of Thermally Forced Atmospheric Boundary Layer Flows

Accurate numerical weather predictions are essential for many applications including: transportation, agriculture, wind energy, hydrology and military (Katz et al.,1997). For these applications, it is crucial that the atmospheric surface layer (ASL) is well captured numerically. Within the ASL, land-atmosphere forcings are transmitted to the rest of the atmosphere via turbulent exchanges of momentum and heat. These processes are characterized by short time scales and limited spatial extent, making it difficult for traditional weather forecast models to capture them. Most numerical weather prediction models make use of similarity theory to compute surface fluxes. Similarity flux-profile methods analytically prescribe the mean surface momentum flux as well as the mean latent and sensible heat fluxes as a function of the corresponding averaged velocity, temperature and specific humidity at a height, from a fixed reference roughness length, relating second-order moments to first-order moments (Brutsaert, 1982). Strictly speaking, flux-profile techniques were originally developed for ensemble averages of statistically stationary and horizontally homogeneous surface layer flows (Monin & Yaglom, 1971). However, it is impossible to realize true ensemble averages in real field experiments. Hence, to test flux-profile similarity, temporal averages are used, summoning the principle of Ergodicity (Katul, 2004; Wyngaard, 2010; Higgins et al., 2013). Furthermore, as modern numerical methods rarely rely on the mean equations anymore, they need more detailed information about the fluxes than simply a mean behavior, as boundary conditions. Therefore, to be able to model real flows over heterogeneous surfaces, theory and application must be reconciled under the principle of “local” homogeneity and statistical stationarity. Meaning, that over small enough regions, sampled long enough, what a-priori might resemble a heterogeneous surface, can ultimately be interpreted otherwise. However, recent thermal imagery and moisture measurements show that even over a perfectly homogeneous rough surface, large heterogeneities in surface temperature and moisture can persist in time that can generate important buoyancy effects into the airflow above, altering the development of the atmospheric flow and therefore requiring a differentiated, scale-similar formulation that corrects traditional similarity parameterizations.

In this work we present a suite of large-eddy simulation cases that characterize the effect of surface thermal heterogeneities on the atmospheric flow using the concept of dispersive fluxes (Finnigan, 2000). General results illustrate a regime in which the flow is mostly driven by the surface thermal heterogeneities, in which the contribution of the dispersive fluxes can account for more than 40% of the total sensible heat flux. Results also illustrate an alternative regime in which the effect of the surface thermal heterogeneities is quickly blended, and the dispersive fluxes provide, instead, a quantification of the flow spatial heterogeneities produced by coherent turbulent structures result of the surface shear stress. Specifically, a threshold flow-dynamics parameter is introduced to differentiate dispersive fluxes driven by surface thermal heterogeneities from those induced by surface shear. This new threshold parameter is dependent on the Roll factor (Salesky et al. 2016) and an adjustment of the friction Richardson number. We believe that this threshold factor could be used to decide when to correct traditional atmospheric surface layer (ASL) parameterizations for the non-blended effect of the surface thermal heterogeneities.