Scaling Properties of Temperature Spectra and Heat-Flux Cospectra in the Surface Friction Layer Beneath an Unstable Outer Layer |
| |
Authors: | Johannes Laubach Keith G McNaughton |
| |
Institution: | (1) Graduate School of Environmental Studies, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8601, Japan;(2) Hydrospheric Atmospheric Research Center, Nagoya University, Nagoya, Japan |
| |
Abstract: | Temperature variance and temperature power spectra in the unstable surface layer have always presented a problem to the standard
Monin-Obukhov similarity model. Recently that problem has intensified with the demonstration by Smedman et al. (2007, Q J
Roy Meteorol Soc 133: 37–51) that temperature spectra and heat-flux cospectra can have two distinct peaks in slightly unstable
conditions, and by McNaughton et al. (2007, Nonlinear Process Geophys 14: 257–271) who showed that the wavenumber of the peak
of temperature spectra in a convective boundary layer (CBL), closely above the surface friction layer (SFL), can be sensitive
to the CBL depth, z
i. Neither the two-peak form at slight instability nor the dependence of peak position on z
i at large instability is compatible with the Monin-Obukhov model. Here we examine the properties of temperature spectra and
heat-flux cospectra from between these extremes, i.e. from within the unstable SFL, in two experiments. The analysis is based
on McNaughton’s model of the turbulence structure in the SFL. According to this model, heat is transported through most of
the SFL by sheet plumes, created by the action of impinging outer eddies. The smallest and most effective of these outer eddies
have sizes that scale on SFL depth, z
s. The z
s-scale eddies and plumes are organised within the overall convection pattern in the CBL, and in turn they organise the motion
of smaller eddies within the SFL, whose sizes scale on height, z. The main experimental results are: (1) the peak amplitudes of the temperature spectra in the SFL are collapsed with a scaling
factor (zsz)1/3eo2/3{(z_{\rm s}z)^{1/3}\varepsilon_{\rm o}^{2/3}} divided by the square of the surface temperature flux, where eo{\varepsilon_{\rm o}} is the dissipation rate of turbulent energy in the outer CBL (above the SFL); (2) the peak wavenumbers of the temperature
spectra are collapsed with the mixed length scale (z
i
z
s)1/2; (3) the peak wavenumbers of the heat-flux cospectra are collapsed with the doubly-mixed length scale (z
i
z
s)1/4
z
1/2; (4) for z/z
s < 0.03, the peak in the cospectrum is replaced by another peak at a wavenumber about a magnitude larger. This peak’s position
scales on z; (5) all these findings are consistent with the observations of Smedman et al. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|