Published on *METEO 300: Fundamentals of Atmospheric Science* (https://www.e-education.psu.edu/meteo300)

The atmospheric boundary layer has a strong diurnal cycle, which consists of a well-mixed layer that is ~1 km high during the day but collapses down to 10% of that at night, leaving behind a residual layer. The mixing is caused by turbulence, a chaotic mix of swirling eddies ranging in size from the height of the PBL to the size of your fist. Understanding turbulence is the key to understanding the motion of air in the PBL. Taylor’s Hypothesis shows that changes in eddy properties measured by a sensor in time can be used to describe the eddy properties in space.

Equations of motion by turbulent eddies arise from defining all quantities (e.g., wind speed, specific humidity, and potential temperature) in terms of their mean and turbulent parts, then substituting these two parts for each quantity into the appropriate conservation equations, expanding the equations, then taking the Reynolds averages. Terms with two turbulent components arise that are non-zero, and these give rise to turbulent fluxes of temperature, water vapor, and momentum. A key result is that eddies drive vertical transport of these quantities (and others) in the direction of where the mean quantities are the least from where they are the most. Furthermore, changes in the vertical profiles of mean quantities with time are caused by the vertical eddy fluxes of those quantities.

The energy in the PBL is a tale of the turbulent kinetic energy and the energy balance near the surface. Turbulence consists of eddies of all different sizes and lifetimes, ranging from sizes that are the height of the PBL to others as small as your fist. These eddies are related: the largest carrying the most energy, and the smaller ones fracturing off of the larger ones, thus cascading the energy from larger scales to smaller scales, ending eventually with molecular viscosity, which converts all that kinetic energy into heat. The driver of this turbulent kinetic energy is the exchange of energy at Earth’s surface and consists of net radiation, sensible heat flux, latent heat flux, and subsurface ground flux. Depending on the environment and the time of day, the relative values of these fluxes can be quite different, but in every case, the total energy budget must balance.

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