The departure from mixed-layer similarity during the afternoon decay of turbulence in the free-convective boundary layer: results from Large-Eddy Simulations

We investigate the departure from mixed-layer similarity during the afternoon decay of turbulence. More specifically, we aim to characterize the time-development of the departure of the velocity-variances profiles from their mixed-layer similarity reference state, for vastly-different idealistic shapes and time scales of the prescribed surface heat flux decay. For that purpose, we carry out idealized large-eddy simulations of the homogeneous free-convective boundary layer, where the prescribed surface kinematic heat flux (H) follows a sinusoidal or an exponential decay. The duration between the maximum and the zero surface heat flux, τ_f, is taken equal to 6 h or 2 h. A reference simulation with prescribed constant surface heat flux is also performed in order to derive the mixed-layer similarity profiles (self-similar profiles) for the vertical and horizontal velocity variances. The methodology is based on analyzing the collapse of the normalized velocity-variances profiles from different runs, while they depart from the self-similar profiles. Within the descriptive frames where the time is tracked solely by either one of the forcing time scales τ_f or τ_f _tilde = (1/H.dH/dt)^-1, we find that the velocity-variances profiles from different runs do not collapse while they depart from the self-similar profiles, suggesting that the departure is dependent on the shape of the surface heat flux decay. As the mixed-layer similarity relies on the assumption that the CBL is in a quasi-equilibrium, which is maintained as long as the adjustment time scale of the largest eddies (i.e. the convective eddy-turnover time scale, t_*) is much smaller than the characteristic time scale of the surface heat flux decay, we successively consider the ratios r = τ_f / t_* and r_tilde  = τ_f _tilde / t_* (instead of the forcing time scale alone) for tracking the time and characterizing the departure from mixed-layer similarity. As the velocity-variances profiles from different runs depart from mixed-layer similarity, we find them to collapse in the only case where the parameter r_tilde is used for tracking the time, supporting the independence of the departure from the shape of the surface heat flux decay. As a consequence of this result, the knowledge of r_tilde is sufficient to predict the velocity variances and evaluate their departure from the quasi-steady state, irrespective of the shape of the surface heat flux decay.