Environmental Engineering Reference
In-Depth Information
Fig. 7.1 Schematic demonstration of the stability dependence of the roughness length: ( a )for
stably stratified flows ( b ) for convective flows
In this paper this silence is broken with a proposal of a new z 0 u -model which
accounts for the effect of stratification (7-9). The model is evaluated (Figs. 7.1,
7.2 and 7.3) and the effect and practical importance demonstrated (Fig. 7.1). Rec-
ommendations are given on how to accurately determine z 0 u and thus improve the
formulation of an essential boundary condition in a range of applications such as
numerical weather forecasting, climate and air pollution modelling, or gas exchange
between the Earth's surface and the atmosphere.
To illustrate the physical background of the classical concept and its applicabil-
ity to environmental problems, consider a neutrally stratified atmospheric bound-
ary layer (ABL) over a horizontally homogeneous surface covered with obstacles
(roughness elements) of standard shape, separated by standard distances and having
standard heights, h 0 . At heights, z , much larger than h 0 but much smaller than the
ABL height, h , the locally generated turbulence does not depend on h , h 0 , and other
properties of the surface and, therefore, is fully characterized by z (that serves as the
vertical turbulent length scale: l T
z ) and the vertical flux of momentum per unit
Fig. 7.2 Stable stratification: Bin-average values of z 0 u
z 0 (the actual roughness length, z 0 u , over
its neutral-stability value, z 0 ) versus the roughness-layer stratification parameter, h 0 / L , based on
the Monin-Obukhov turbulent length scale, L , for boreal forest with the typical height of pine
trees h 0
/
=
13.5m ( z 0
=
1.1m). The bars show standard errors. The theoretical curve is z 0 u
/
z 0
=
L ) 1
(1
+
8.13 h 0
/
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