Jökull - 01.12.1969, Side 59

where
1
Si = ice density
h = ice thickness
= displacement vector o£ the ice.
Most studies of ice motion have assumed
steady state conditions for which the left hand
side of (1) is set equal to zero. In the central
Arctic the ice acceferation is probably so small
that it may be neglected. Weather conditions
]n the area are comparatively steady and the
assumption of zero acceleration is probably a
fairly good one. In the area east o£ Greenland,
on the other hand, it is known that weather
conditions are extremely unsteady and this has
tts influence on the ice movement. With this
in mind the left hand side of (1) will be re-
tained in the formulation of the problem.
All studies of ice movement include the ef-
fects of wind on the surface of the ice. In fact,
in certain areas o£ the Arctic this is considered
to be the main factor contributing to the
movement (Gordienko 1958, Dunbar and Witt-
man 1963). For a turbulent boundary layer the
shear stress at a boundary is given by the Bous-
sinesq equation (Rouse 1938).
Ta = Oaea
3v
ar
3z
(2)
where
ea = kinematic eddy viscosity
V„ =; wind velocity vector relative to ice
(Fig. 1)
z = vertical Cartesian coordinate, positive
upward.
Introducing the concept of a mixing lengtli
ancl assuming a constant shearing stress within
the boundary layer, Prandtl (1925) obtained the
expression
Fig'. 1. Velocity vectors (absolute and relative)
í°r sea, air and ice.
3|Va,
3z
- a/Ja
K V o„
9a Z + Za
which gives by integration
v,„. |
C V
z+ za
Oa
ln
(3)
(4)
where
k0 = von Kármán coefficient ~ 0.42
zao = roughness parameter for the air-ice in-
terface.
Solving (4) with respect to ra gives the famx-
liar expression
Ta =OaCa|var|vai. (5)
where the friction coefficient Ca is given by
7 -J- 7 T “2
k+

(6)
in which z may be regardecl as the height at
which the wind is measured.
The water stress at the ice-sea interface is
obtained in a manner analogous to the wind
stress discussed above, resulting in the expres-
sion
ts —ö.C.|v„|v„ (7)
where subscript s refers to the sea.
The force D in Equation (I) denotes the
horizontal component of the Coriolis force,
given by the equation
D = Qjhf V; x k (8)
where
f = 2<u sinij> = Coriolis coefficient
m = eartli’s angular velocity
$ = latitude
k = unit vector in z-direction.
It is seen that the Coriolis force is directed
perpendicular to the velocity vector of the ice
and acting to the right. In the southern hemi-
sphere this force acts in the opposite direction,
i.e. to the left of the velocity vector.
The pressure gradient force G is caused by
a sloping sea surface on which the ice floats.
This is the cause of socalled gradient currents
JÖKULL 19. ÁR 55