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

(6a)

concentration of blowing and drifting snow is too

low to affect the dynamics of the flow.

(6b)

R92 modeled the stress on the underlying sur-

face as

λ(Φ) = (γ/*n*) cosΦ .

(6c)

τS (λ) =

exp-*c*1λ(Φ)

ρ*C*ShUh

2

(11)

.

*

Here the wind sees both the front triangular

face and the side ridge. Thus

Here, *C*Sh is the drag coefficient of the underlying

surface referenced to a height *h*, which is where

(7a)

the wind speed *U*h is evaluated. Also in eq 11, ρ is

(7b)

*

*

and *c*1, an empirical constant. The exponential

λ(Φ) = γ[*m*1 sinΦ + (2*n*)1 cosΦ] .

term in eq 11 accounts for the sheltering of the

(7c)

underlying surface by the roughness elements.

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

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

(8b)

approaches zero. In this case, the roughness ele-

λ(Φ) = γ[*m*1 sinΦ (2*n*)1 cosΦ] .

ments completely shelter the surface; thus, skin

(8c)

friction can provide none of the stress.

We can infer the value of *C*Sh 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-

wa (1986). The lowest value for *C*DN10 reported by

(9a)

Overland and Kondo and Yamazawa is roughly

1.1 103. Coincidentally, Figure 4 in Banke et al.

(9b)

implies that the value of *C*DN10 for completely

smooth sea ice is 1.10 103. Call this minimum

λ(Φ) = (γ/*n*) cosΦ .

(9c)

Converting *C*S10 to *C*Sh, however, is not straight-

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)

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 .

(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-

2

(12)

tum from the air because of their inertia. Neither

τR nor τS reflects this momentum exchange. That

where *C*R 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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