Geoscience Reference
In-Depth Information
7.3
Circulation Variability and Deformation
7.3.1
The Momentum Balance
Detailed reviews of sea ice dynamics and kinematics are given by A. Thorndike
( 1986 ) and W. Hibler ( 1986 ). The motion of sea ice can be described by a momen-
tum balance:
m∂ u /∂t = mf k x u + T a + T w + F - mg∇ H
(7.4)
The term on the left side is the time change in momentum (i.e., acceleration), where
m is the ice mass per unit area and u is the ice velocity. The first term on the right
side is the stress attributed to the Coriolis force, where f is the Coriolis parameter
and k is a unit vector normal to the surface. T a and T w are air and water stresses, and
F is the internal ice stress, which describes floe-to-floe (ice) interaction. The final
term, mg∇ H describes ocean tilt, where H is the height of the sea surface and g is
gravitational acceleration (because of regional density variations in the ocean and
other factors, the height of the ocean surface is not the same everywhere, meaning
that there are slopes, and this has to be accounted for in the momentum balance).
The relative magnitudes of the momentum balance terms vary seasonally and spa-
tially. The dominant terms, however, are the air and water stresses, the Coriolis
force, and ice interaction (Hibler, 1986 ). Whereas ice interaction can be large in
winter and near coasts, the term is often small in summer and away from coasts.
In these situations, it is appropriate to consider the pack ice to be in a state of “free
drift” (McPhee, 1980 ).
F. Nansen ( 1902 ) was the first to observe that on a day-to-day basis, the pack ice
generally moves at about 2 percent of the surface wind speed and 30° to the right
of the wind velocity vector. N. Zubov ( 1945 ) made similar observations. Using data
from the Arctic Ice Dynamics Joint Experiment and the IABP, Thorndike and R.
Colony ( 1982 ) developed a linear regression model to show that away from coasts,
typically 70 percent of the variance in ice motion at daily to monthly time scales
is explained by the local surface geostrophic wind. On average, the ice moves 8°
to the right of the geostrophic wind direction and at 0.008 of its speed. However,
strong seasonality occurs in the mean drift angle, ranging from 5° in winter to 18°
in summer, in response to the ice compactness. In turn, the wintertime scaling factor
is approximately 0.007, increasing in summer to about 0.011. Using a longer data
record, Serreze, Barry, and McLaren ( 1989 ) obtained similar results.
Seasonal variations in the characteristics of ice drift are in part attributable to
changes in the magnitude of the internal ice stress term. While the inclusion of inter-
nal stresses does not generally destroy the linear relationship between ice velocity
(U) and the geostrophic wind (G), it is manifested by a change in the ratio |U|/|G|
and the turning angle (Moritz, 1988 ). Typically, both are reduced. The stability of
the atmosphere also has an impact (Thorndike and Colony, 1982 ). Given the same
geostrophic wind, increased low-level stability in winter acts to reduce the surface
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