EM 1110-2-1100 (Part II)
(Change 1) 31 July 2003
than the air, the atmosphere becomes stably stratified and turbulent transfers are suppressed. If the surface
is warmer than the air, the atmosphere becomes unstably stratified and turbulent transfers are enhanced. In
this more general case, the form of the near-surface wind profile can be approximated as
U(
z
z
ln
&φ
Uz '
(II-2-6)
k
z0
L
where
φ = universal similarity function characterizing the effects of thermal stratification
L = parameter with dimensions of length that represent the relative strength of thermal stratification
effects (Obukov stability length)
(6) L is positive for stable stratification, negative for unstable stratification, and infinite for neutral
stratification. Algebraic forms for φ and additional details on the specification of near-surface flow
characteristics can be found in Resio and Vincent (1977), Hsu (1988), and the ACES Technical Reference
(Leenhnecht, Szuwalski, and Sherlock 1992; Sec. 1-1).
(7) Transfer of momentum into water from the atmosphere can be markedly influenced by stability
effects. For example, at the 10-m reference level, Equations II-2-4 through II-2-6 give
2
U(
CD '
U
2
k
(II-2-7)
'
z
z
&φ
ln
z0
L
(8) The system of equations representing the boundary layer is readily solved via a number of numerical
techniques. However, a relationship between z0 and U* must also be specified.
(9) Since φ is negative for stable conditions and positive for unstable conditions, stratification clearly
reduces the coefficient of drag for stable conditions and increases the coefficient of drag for unstable
conditions (Figure II-2-5). Consequently, for the same wind speed at a reference level, the momentum
transfer rate is lower in a stable atmosphere than in an unstable atmosphere.
(10) Studies by Hsu (1974); Geernaert, Katsaros, and Richter (1986); Huang et al. (1986); Janssen (1989,
1991); and Geernaert (1990) suggest that the coefficient of drag depends not only on wind speed but also on
the stage of wave development. The physical mechanism responsible for this appears to be related to the
phase speed of the waves in the vicinity of the spectral peak relative to the wind speed. At present, there does
not appear to be sufficient information to establish this behavior definitively. Future studies may shed more
light on these effects and their importance to marine and coastal winds.
II-2-10
Meteorology and Wave Climate
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