On the departure from Monin-Obukhov surface similarity and transition to the convective mixed layer

TL;DR

This study uses large-eddy simulations to examine the limits of Monin-Obukhov similarity in the convective boundary layer, proposing an exponential correction to better model the transition to the mixed layer.

Contribution

It introduces a modified Businger-Dyer relation with an exponential cutoff to improve similarity in the convective boundary layer.

Findings

Monin-Obukhov similarity generally holds but with a steeper slope.

Exponential correction improves similarity from 0.05$z_i$ to above 0.3$z_i$.

Departure from similarity becomes significant below 0.1$z_i$.

Abstract

Large-eddy simulations are used to evaluate mean profile similarity in the convective boundary layer (CBL). Particular care is taken regarding the grid sensitivity of the profiles and the mitigation of inertial oscillations in the simulation spin-up. The nondimensional gradients $\phi$ for wind speed and air temperature generally align with Monin-Obukhov similarity across cases but have a steeper slope than predicted within each profile. The same trend has been noted in several other recent studies. The Businger-Dyer relations are modified here with an exponential cutoff term to account for the decay in $\phi$ to first-order approximation, yielding improved similarity from approximately 0.05$z_i$ to above 0.3$z_i$, where $z_i$ is the CBL depth. The necessity for the exponential correction is attributed to an extended transition from surface scaling to zero gradient in the mixed layer, where the departure from Monin-Obukhov similarity may be negligible at the surface but becomes substantial well below the conventional surface layer height of 0.1$z_i$.