A simple approach to modeling spectra in unstable atmospheric surface
layers is presented. The authors use a single form for the two-dimensi
onal spectrum of horizontal velocity, vertical velocity, and a scalar
in the horizontal plane; it has two free constants, a length scale, an
d an intensity scale. Continuity is used to relate the vertical and ho
rizontal velocity spectra. The two free constants are determined by ma
tching the variance and the inertial-subrange spectral level with obse
rvations. The scales are chosen so that the spectra follow law of the
wall and mixed-layer scaling in the neutral and free-convection limits
, respectively. The authors model the stability dependence of the spec
tra by combining these two limiting forms. The one-dimensional spectra
, obtained by integration over one wavenumber component, and their var
iances agree well with observations. Near the surface the vertical vel
ocity variance follows Monin-Obukhov (M-O) similarity and shows a real
istic local free-convection asymptote; at greater heights it shows dep
artures from M-O similarity that also agree well with observations. Fi
nally, the two-dimensional spectra are used to calculate the variances
of the resolvable and subgrid-scale components of large eddy simulati
ons and their dependence on grid mesh size, distance from the surface,
boundary layer depth, and stability.