Nonlocal boundary layer: The pure buoyancy‐driven and the buoyancy‐shear‐driven cases

Abstract

A Reynolds‐averaged Navier‐Stokes (RANS) model including nonlocality was developed and tested. The aim of this paper was to investigate different boundary layer conditions with the RANS model. In particular we focused our attention on boundary layers where convection plays a major role: the shear‐free buoyancy‐driven boundary layer and the buoyancy‐shear‐driven one. We presented a new model which solves dynamical equations for all the turbulence moments up to the third order. The model assumes the fourth‐order moments to be Gaussian‐distributed according to the quasi‐normal approximation. A new approach to avoid the unphysical growth of the third‐order moments, connected to the quasi‐normal hypothesis, is suggested. The new physical ingredient of this method is in essence the parameterization of the relaxation and dissipation time scales related to the return to isotropy terms in the triple‐pressure correlations and to the dissipation rate of the potential temperature variance, respectively. This new parameterization takes into account the dependence of the third‐order moments on the integral length scale of the dissipation rate, a quantity related to the eddy size variation across the boundary layer. The time scales are reduced as the integral length increases, and these reductions provide the proper damping of the turbulent vertical transport. In order to test our model, we carried out large eddy simulations (LESs) of boundary layers with shear and buoyancy. We present the results of the comparison with LESs, aircraft measurements, and DNS, which show that the model performs rather well in all the stability conditions and that the proposed damping gives reliable third‐order moments that satisfy the realizability constraints.