parallel to the coordinate axes x and y. In the axially symmetric case the slip lines
are parallel to the coordinate lines r (radial lines) and θ (concentric circles). Since
normal stresses are the same on the slip lines passing through the same point then
σ xx = σ yy , σ rr = σ θθ .
ð6Þ
Therefore, in the plane case σ I = σ xx = σ yy and σ II = jσ xy j, and in the axially
symmetric case σ I = σ rr = σ θθ and σ II = jσ rθ j.
Drag force (F) is equal to a sum of wind (F a ) and water (F w ) drag forces
F = F a + F w , F a = ρ a C a V a V a , F w = − ρ w C w vv,
ð7Þ
where V a = ðV ax , V ay Þ and v = ð0, v y Þ are related to the plane motion, V a = ðV ar , V aθ Þ
and v = ð0, v θ Þ to the axially symmetric motion, V a = jV a j and v = jvj, ρ a and ρ w are
the air and water densities, C a and C w are the air-ice and water-ice drag coefficients.
Representative values of physical constants are given in Table 1.
Ice Drift Induced by Shear Stresses
Equations (1) and (2) in the case when the wind velocity and sea surface tilt are
absent are written as follows:
-5
-4
-3
-2
-1
0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
/ , a
P
k
h
I
σ
/ , a
P
k
h
II
σ
O s
Fig. 6 Yield curve of solid ice cover
Table 1 Representative numerical values of physical constants
ρ i (kg/m
3
)
ρ w (kg/m
3
)
ρ a (kg/m
3
)
C w
C a
f (s
−1
)
920
1020
1.27
0.005
0.002
1.454 × 10
−4
546
A. Marchenko