Region I: 0 ≤ Φ ≤ β
AC95). Thus, since R92 models eq 10 for heights of
Here the wind sees only the front triangular
order h and higher--well above the saltation
face. Thus
layer--eq 10 need not include a term to account
for particle inertia. Above the saltation layer, the
L(Φ) = mh cosΦ
(6a)
concentration of blowing and drifting snow is too
low to affect the dynamics of the flow.
A(Φ) = (mh2/2) cosΦ
(6b)
R92 modeled the stress on the underlying sur-
face as
λ(Φ) = (γ/n) cosΦ .
(6c)
Uh
τS (λ) =
exp-c1λ(Φ)
ρCShUh
2
Region II: β ≤ Φ ≤ 90
(11)
.
u
*
Here the wind sees both the front triangular
face and the side ridge. Thus
Here, CSh is the drag coefficient of the underlying
L(Φ) = nh sinΦ + (mh/2) cosΦ
surface referenced to a height h, which is where
(7a)
the wind speed Uh is evaluated. Also in eq 11, ρ is
A(Φ) = (h2/2)[n sinΦ + (m/2) cosΦ]
(7b)
*
*
and c1, an empirical constant. The exponential
λ(Φ) = γ[m1 sinΦ + (2n)1 cosΦ] .
term in eq 11 accounts for the sheltering of the
(7c)
underlying surface by the roughness elements.
Region III: 90 ≤ Φ ≤ 180β
That is, when the roughness elements are small or
sparse and λ(Φ), thus, is small, eq 11 reduces to
Here the wind sees only the side ridge. Thus
2
L(Φ) = nh sinΦ (mh/2) cosΦ
tion over a smooth surface. On the other hand,
(8a)
when the roughness elements have a large frontal
area or are densely packed, λ(Φ) is large, and τS
A(Φ) = (h2/2) [n sinΦ (m/2) cosΦ]
(8b)
approaches zero. In this case, the roughness ele-
λ(Φ) = γ[m1 sinΦ (2n)1 cosΦ] .
ments completely shelter the surface; thus, skin
(8c)
friction can provide none of the stress.
Region IV: 180 β ≤ Φ ≤ 180
We can infer the value of CSh appropriate for
smooth, snow-covered surfaces from Overland's
Here the flow sees both side ridges as it
(1985) review and from the measurements report-
approaches from the rear of the drift. Thus
ed by Banke et al. (1980) and Kondo and Yamaza-
L(Φ) = mh cosΦ
wa (1986). The lowest value for CDN10 reported by
(9a)
Overland and Kondo and Yamazawa is roughly
1.1 103. Coincidentally, Figure 4 in Banke et al.
A(Φ) = (mh2/2) cosΦ
(9b)
implies that the value of CDN10 for completely
smooth sea ice is 1.10 103. Call this minimum
λ(Φ) = (γ/n) cosΦ .
(9c)
Converting CS10 to CSh, however, is not straight-
Partitioning the stress
forward: We do not know the displacement height
R92's intent was to partition the total surface
stress (τ) into contributions from form drag (τR)
d a priori; and near the tops of the roughness ele-
ments, the semi-logarithmic profile law (see eq 2)
and from stress on the underlying surface (the
skin friction, τS). In general
is not accurate. I will explain how I deal with these
complications later; here, suffice it to say, I obtain
τ = τR + τS .
CSh from CS10.
(10)
R92 wrote a general expression for the force
caused by form drag on an isolated roughness ele-
There is another potential sink for the momen-
ment as
tum in eq 10 that R92 did not treat. Over erodible
surfaces, saltating particles may extract momen-
FD = ρCR AUh
2
(12)
tum from the air because of their inertia. Neither
τR nor τS reflects this momentum exchange. That
where CR is the drag coefficient of the obstacle,
saltation layer, however, is quite thin--on the
and A is its silhouette area. Here, I must modify
order of a centimeter (Owen 1964, Radok 1968,
4
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