VELOCITY PROFILE, MEAN WIND
542 Dynamics of atmospheric flight
where W = mean wind, h = height above ground, WG and hQ are the speed and height outside the friction layer, and a and ha depend on surface roughness (see Fig. 9.36).
In the layer below about 300 ft:
о^.Оъ’.Оъ = 1:0.8:0.5
where a12 = (щ2), Xj is in the wind direction, and x3 is vertical. Above this height the a, i tend toward equality at about 1000 ft.
The one-dimensional spectra are given by the von Karman equations (13.2, 16 and 17e), with a in Фй replaced by Thus because of (13.2,20) there are three different one-dimensional spectra.
SHEAR AND CROSS SPECTRA:
The turbulent shearing stress in the boundary layer results in nonvanishing %wз, but symmetry requires = м2мз = 0. The data suggests
uxuz — О-Зп^з
in which a representative value of y0 is 0.5.
For the boundary layer as a whole.
іц = 20 лД
L^i — LZ1 — 0.4Й-
Above about 200 ft, slightly better values are given by
£n = 4.2Г73 L21 = L31 = 2.1A0’73