Turbulent Kinetic Energy Budgets over Gentle Topography Covered by Forests

Abstract: Large-eddy simulations of flow over a “horizontally” uniform model forest are used to investigate the effects of gentle topography on the turbulent kinetic energy (TKE) budget within the canopy roughness sublayer. Despite significant differences between simulations using idealized sinusoidal topography and real topography of the Amazon forest, results indicate that the effects of topography are located predominantly in the upper canopy and above, and are mostly caused by mean advection of TKE. The “horizontally” averaged TKE budget from idealized and real gentle topographies are almost identical to that for flat terrain, including a clear inertial layer above the roughness sublayer in which shear production is balanced by local dissipation. At topography crests, where observational towers are usually located, mean vertical advection of TKE can be as important as horizontal advection. We propose the use on an approximate TKE balance equation to estimate mean advection from single tower measurements, and introduce a new advection index that can be used as a proxy to quantify the importance of the topography on the TKE budget

Effects of Gentle Topography on Forest‐Atmosphere Gas Exchanges and Implications for Eddy‐Covariance Measurements

Abstract: The interpretation of tower‐based eddy‐covariance (EC) turbulent flux measurements above forests hinges on three key assumptions: (1) steadiness in the flow statistics, (2) planar homogeneity of scalar sources or sinks, and (3) planar homogeneity in the flow statistics. Large eddy simulations (LESs) were used to control the first two so as to explore the break‐down of the third for idealized and real gentle topography such as those encountered in Amazonia. The LES runs were conducted using uniformly distributed sources inside homogeneous forests covering complex terrain to link the spatial patterns of scalar turbulent fluxes to topographic features. Results showed strong modulation of the fluxes by flow features induced by topography, including large area with negative fluxes compensating “chimney” regions with fluxes almost an order of magnitude larger than the landscape flux. Significant spatial heterogeneity persisted up to at least two canopy heights, where most eddy‐covariance measurements are performed above tall forests. A heterogeneity index was introduced to characterize and contrast different scenarios, and a topography categorization was shown to have predictive capabilities in identifying regions of negative and enhanced fluxes

A Half-Discrete Reverse Hilbert-type Inequality with a Logarithmic Kernel

Abstract By using the way of weight functions and Hadamard's inequality, a half-discrete reverse Hilbert-type inequality with a logarithmic kernel and a best constant factor is given. A best extension with a parameter as well as the equivalent forms are also considered. Mathematics Subject Classification: 26D1