A universal wind profile for the inversion‐capped neutral atmospheric boundary layer

Abstract

Wind profiles above the atmospheric surface layer are not accurately described by classic similarity theories. Far from the surface, the underlying assumptions of such surface‐layer theories break down due to the stronger influence of buoyancy forces induced by the temperature inversion that caps the atmospheric boundary layer (ABL), as well as the Coriolis force. This paper examines the influence of these forces on the mean flow and presents a new similarity theory to predict mean wind profiles in and above the surface layer for an ABL with zero surface heat flux and capped by an inversion of potential temperature, that is, the conditionally neutral ABL. The analysis here is based on the results of 17 large‐eddy simulations (LES) over a flat homogeneous rough surface, which leads to and supports the new similarity theory. The development is based on two applications of the Buckingham Π theorem. A first application allows determination of the entrainment‐induced heat flux profile through the ABL and into the surface layer, which is then used within a second dimensional argument for the vertical shear of mean wind speed. We subsequently find a new dimensionless group (Π2) depending on the capping inversion strength, the Coriolis parameter, the surface stress and the ABL depth, which is correlated to the dimensionless shear (Π1) through a universal function β. Integrating the functional relation between Π1 and Π2 produces an equation for the mean wind speed profile; it effectively includes an additive “correction” to the log‐law in terms of Π2, analogous to the Monin–Obukhov profile correction function. Unlike surface‐layer similarity, the new form accounts for the influences of both the surface and the ABL top. Relative to the LES, the new profile form exhibits errors in mean wind speed below 5% for heights below 90% of the ABL depth; this is relevant for applications above the surface layer (e.g., wind energy).