Logarithmic Wind Profile: A Stability Wind Shear Term

Abstract: A stability wind shear term of logarithmic wind profile based on the terms of turbulent kinetic energy equation is proposed. The fraction influenced by thermal stratification is considered in the shear production term. This thermally affected shear is compared with buoyant term resulting in a stability wind shear term. It is also considered Reynolds stress as a sum of two components associated with wind shear from mechanical and thermal stratification process. The stability wind shear is responsible to Reynolds stress of thermal stratification term, and also to Reynolds stress of mechanical term at no neutral condition. The wind profile and its derivative are validated with data from Pedra do Sal experiment in a flat terrain and 300m from shoreline located in northeast coast of Brazil. It is close to the Equator line, so the meteorological condition are strongly influenced by trade winds and sea breeze. The site has one 100m tower with five instrumented levels, one 3D sonic anemometer, and a medium-range wind lidar profiler up 500m. The dataset are processed and filter from September to November of 2013 which results in about 550 hours of data available. The results show the derivative of wind profile with R^2 of 0.87 and RMSE of 0.08 m/s. The calculated wind profile performances well up to 400m at unstable condition and up to 280m at stable condition with R^2 better than 0.89. The proposed equation is valid for this specific site and is limited to a stead state condition with constant turbulent fluxes in the surface layer.