Temperature profiles, plumes, and spectra in the surface layer of convective boundary layers

We survey temperature patterns and heat transport in convective atmospheric boundary layers (CBLs). We use the word “plumes” to describe the emergent temperature patterns, in much the same way that “eddies” describe patterns of motion in turbulent flows. We introduce a two-temperature (2T) toy model to connect the cross-sectional areas of plumes to the scaling properties of temperature gradients, temperature spectra, and heat transport. We find that the half power law (z−1/2, where z is the height above the surface) form of the temperature profile reflects the change in plume cross-sectional area with height and that this is consistent with the mixed length scale required to collapse the peak regions of temperature spectra above the surface friction layer (SFL). We introduce new scaling results for temperature spectra and heat flux cospectra that extend this relationship to most of the SFLs. The spectral properties change in the bottom tenth of the SFL, where the temperature profile becomes logarithmic and temperature fluctuations increasingly display Gaussian statistics. At such small heights, the self-similarity property of the plumes reflects their randomness rather than self-similarity in the order observed above. We conclude with a general discussion, contrasting our interpretation of the role of buoyancy, as being associated with the largest structures in CBL flows, with that of Richardson [Proc. R. Soc. A 87, 354–373 (1920)], who neglected large structures and assumed that it acts locally, on the small eddies. Richardson’s ideas still inform the currently accepted, statistical fluid mechanics model of boundary-layer flows.