Scaling properties of velocity and temperature spectra above the surface friction layer in a convective atmospheric boundary layer
Abstract. We report velocity and temperature spectra measured at nine levels from 1.42 meters up to 25.7 m over a smooth playa in Western Utah. Data are from highly convective conditions when the magnitude of the Obukhov length (our proxy for the depth of the surface friction layer) was less than 2 m. Our results are somewhat similar to the results reported from the Minnesota experiment of Kaimal et al. (1976), but show significant differences in detail. Our velocity spectra show no evidence of buoyant production of kinetic energy at at the scale of the thermal structures. We interpret our velocity spectra to be the result of outer eddies interacting with the ground, not "local free convection".
We observe that velocity spectra represent the spectral distribution of the kinetic energy of the turbulence, so we use energy scales based on total turbulence energy in the convective boundary layer (CBL) to collapse our spectra. For the horizontal velocity spectra this scale is (zi εo)2/3, where zi is inversion height and εo is the dissipation rate in the bulk CBL. This scale functionally replaces the Deardorff convective velocity scale. Vertical motions are blocked by the ground, so the outer eddies most effective in creating vertical motions come from the inertial subrange of the outer turbulence. We deduce that the appropriate scale for the peak region of the vertical velocity spectra is (z εo)2/3 where z is height above ground. Deviations from perfect spectral collapse under these scalings at large and small wavenumbers are explained in terms of the energy transport and the eddy structures of the flow.
We find that the peaks of the temperature spectra collapse when wavenumbers are scaled using (z1/2 zi1/2). That is, the lengths of the thermal structures depend on both the lengths of the transporting eddies, ~9z, and the progressive aggregation of the plumes with height into the larger-scale structures of the CBL. This aggregation depends, in top-down fashion, on zi. The whole system is therefore highly organized, with even the smallest structures conforming to the overall requirements of the whole flow.
