# 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).

COMPONENT INTENSITIES:

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.

SPECTRUM SHAPES:

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.

INTEGRAL SCALES:

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