Applied model for the growth of the daytime mixed layer

A slab model is proposed for developing the height of the mixed layer capped by stable air aloft. The model equations are closed by relating the consumption of energy (potential and kinetic) at the top of the mixed layer to the production of convective and mechanical turbulent kinetic energy within the mixed layer.

By assuming that the temperature difference at the top of the mixed layer instantaneously adjusts to the actual meteorological conditions without regard to the initial temperature difference that prevailed, the model is reduced to a single differential equation which easily can be solved numerically.

When the mixed layer is shallow or the atmosphere nearly neutrally stratified, the growth is controlled mainly by mechanical turbulence. When the layer is deep, its growth is controlled mainly by convective turbulence. The model is applied on a data set of the evolution of the height of the mixed layer in the morning hours, when both mechanical and convective turbulence contribute to the growth process.

Realistic mixed-layer developments are obtained.