The atmospheric surface layer - Turbulence in the Atmosphere - page 215

10

The atmospheric surface layer

10.1 The “constant-flux” layer
Near a flat, homo geneo us land surface the turbulent shear stress vector in the hori-
zontal plane,

ρ 0 u i u 3 , is aligned with the mean wind vector U i . † As is traditional
in micrometeorology, we take this as the x -direction. Then integrating the steady
forms of the horizontally homogeneous mean momentum equations (9.22) ,

−

f U g − U ,

∂uw
∂z =

∂vw
∂z =

f(V − V g ), (10.1)

from just above the surface to the mean top of the ABL at height h ,wherethe
turbulence vanishes, gives

f h
0

f h
0

τ 0
ρ 0 =

uw( 0 + ) vw( 0 + )

U g )dz,
(10.2)
with τ 0 the magnitude of the surface shear stress. Equations (10.1) and the integral
constraints (10.2) imply that in the northern he mis p her e (where f is positive) and
with (U g ,V g ) independent of z ,the (U, V ) and (uw, vw) profiles in the near-neutral
case behave qualitatively as sketched in Figure 10.1 (Problem 10.1) .
Equations (10 .1) and F igu re 10.1 indicate that U g and V g are independent of
height and ∂uw/∂z and ∂vw/∂z are largest just above the surface. So why is the
surface layer also called the “constant-flux layer” if momentum-flux gradients can
be largest there?
The answer lies in the behavior of turbulence near a surface, Figure 10.2 . As
shown in the Appendix, the horizontal wavenumber spectrum of w (and, hence, of
turbulent shear stress) peaks at wavenumbers of order 1 /z . Thus distance from the

− = (V − V g )dz, = 0 = (U −

†

This need not be the case over a moving, wavy sea surface (Grachev et al ., 2003 ).

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