Scaling properties of temperature spectra in the surface friction layer

Temperature variance and temperature power spectra have always presented a problem to the standard Monin-Obukhov similarity model. Recently that problem has intensified for convective boundary layers with the demonstration by Smedman et al. (2007, Q J Roy. Meteorol. Soc. 133: 37-51) that temperature spectra can have two distinct peaks in slightly unstable conditions, and by McNaughton et al. (2007, Nonlin. Proc. Geophys. 14: 257-271) who showed that the wavenumber of the peak of temperature spectra close above the surface friction layer (SFL) can be sensitive to the depth of the convective boundary layer, z_i. Neither the two-peak form at slight instability nor the dependence of peak position on z_i at large instability are compatible with the Monin-Obukhov model.

Here we examine the properties of temperature spectra from between these extremes, using observations made within unstable surface friction layers over grassland in the Coorong region of South Australia. During our observations the ABL depth, z_i, ranged from 100 to 1300 m, SFL depth, z_s, ranged from 16 to 160 m, and the ABL's convective structure parameter z_i/z_s ranged from 1.9 to 76. We base our analysis on the suggestion by McNaughton et al. (2007) that temperature transport through most of the SFL is by streamwise roll vortices formed by eddies from the outer inertial subrange interacting with the ground, with frictional turbulence being important only very near the ground (z < 0.02 z_s).

The main results are:

1) There is an orderly succession in spectral shape, dependent on z/z_s: the T spectra have an increasingly sharp peak for z approaching z_s; conversely, the spectrum becomes flatter and wider as z/z_s decreases.

2) The low-wavenumber range (production range), the peak region and the high-wavenumber range (inertial subrange) each obey a different scaling, with different combinations of z, z_i and z_s involved. For z approaching z_s, the scaling expressions converge towards those found above the SFL by McNaughton et al. (2007).

3) The dependence of peak position on both z_i and z_s is consistent with the observations of Smedman et al. (2007). This includes the emergence of a second peak for certain combinations of the scaling parameters.