To obtain *C*DN10 from *C*Dh, we must match the

Notice, from eq 19, 20 and 23

profile laws, eq 29 and 30, at *z*w. From eq 29 and

λ(Φ)CR (Φ)

^

τR

32, we have the following results for *z *≥ *z*w

=

.

(44)

τ

^

= ln

/

(35)

1

R92 then related *d*R to *h*. Following his argu-

*

ments but applying them to the specific geome-

and

try of my model, I get

[

]1/ 2

+ ln(cw ) (36)

= ln

/

/2

(45)

*

in which *c*d is a constant that R92 took to be 0.6.

where *h*, *d*, *z*0 and *z*w must be in meters. Subtract-

Inserting eq 5 in this and combining it with eq 43

ing eq 35 from 36, we get

yields

[

].

1 *h*-*d *

ln 10 - *d * + ln(cw ) .

1/ 2

/

/2

/

(37)

(46)

1

Thus, it is easy to find τR/τ from eq 44; and once

From eq 3033, for *h *≤ *z *≤ *z*w

my model yields *C*Dh, it is simple to compute *d*.

Using this value in eq 41 finally gives the quan-

tity we seek, *C*DN10.

+ ψh

= ln

/

(38)

I pointed out in the previous section that we

*

need to convert *C*S10 to *C*Sh before we can begin

and

computations. Equation 41 also makes this con-

version. Unfortunately, we need *C*Sh before we

+ ln(cw ) .

have obtained *d*. I could handle this problem by

= ln

/2

(39)

iterating the entire set of equations on *d*. But, as I

*

will show in the next section, *d*/*h *≈ 0.3, a result

Subtracting eq 38 from 39 yields

also consistent with eq 46. At this step in the

computations, this simple approximation is rea-

[

]

1

ln(cw ) - ψ h .

sonable--especially in light of uncertainties in

/2

/

(40)

the other model parameters--because *C*DN10 is

not very sensitive to *C*S10 for the range of values

On equating eq 37 and 40, we finally can relate

that this parameter can realistically assume.

1 10 - *d *

- ψh .

ln

/

/

(41)

1

I have not yet discussed the value of γ, the

fractional coverage of sastrugi-like roughness el-

We still do not know the displacement height *d*,

ements. Vladimir Churun* tried to quantify the

however.

roughness of the ISW floe using the radar on the

Thom (1971) identified *d *as the effective level

at which the roughness elements absorb the mo-

ployed. His survey suggested that hummock

mentum being transferred to the surface. R92

coverage varied over the floe from 10 to 30%.

used this definition to derive *d*. That is, if *d*R is the

While hummock coverage is not the same as sas-

centroid of the form drag on the roughness ele-

trugi coverage, my personal experience on ISW

ments and if *d*S is the centroid at which the skin

suggests that 1030% sastrugi coverage is also

friction acts

about right. Notice, because of the geometry of

the sastrugi that I am modeling (Fig. 3), the tight-

(42)

est possible packing of roughness elements will

yield a γ value of only 0.5. Thus, my first guess,

because *d*S = 0 by definition. Thus

* Personal communication (Arctic and Antarctic Research

(43)

Institute, St. Petersburg, Russia).

7

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