 Eddy fluxes are one of the most important concepts in the planetary boundary layer because they are responsible for most of the vertical transport of everything in the planetary boundary layer, both those things leaving the surface and those things coming back down to Earth. In the horizontal, the mean winds do most of the transporting, but in the vertical, the eddies do most of the transporting. Let's look at the transport of potential temperature, which is the same as the transport of thermal energy or heat. The first is super adiabatic potential temperature profile. That is one in which the potential temperature decreases with height. We get these kinds of profiles on hot sunny days. Usually Eddy cycles some air down and other air up. An air parcel cycled up is warmer than the surrounding air, so the perturbation to the potential temperature, which is just the difference between the potential temperature of the parcel minus the potential temperature of the surrounding air, is positive. The perturbation to the vertical wind is also positive, since the air parcel is being brought up, so that the product of W' and Theta' is positive. The Eddy also moves colder air down into warmer surroundings, so that a negative perturbation to the vertical wind brings a negative perturbation to the potential temperature, and the product of these two perturbations, two negatives, is positive. Taking these two parts of the Eddy together, we see that the cold air has replaced warm air at the lower height, and warmer air has replaced colder air at the greater height, and thus the Eddy flux is upward. Convince yourself that the drawing in figure 11.6 all give downward heat flux.