Geoscience Reference
In-Depth Information
ft =
π
/2
M
ss
=
τ
0
/f
f t = (0,2
π
)
ft =
π
ft = 3
π
/2
Fig. 2.1
Sketch of the solution to (2-22) for τ
0
=
i
τ
0
. The circle repeats for each inertial period
t
p
=
2π
/
f
The advent of practical satellite navigation showed that inertial oscillations su-
perimposed as cycloidal loops in the trajectories of wind-driven ice drift are ubiq-
uitous,especiallyduringsummerwheniceis relativelystressfreeandmixedlayers
tendtobeshallow.Anexamplefromanunmannedbuoyinitiallydeployednearthe
North Pole in 2002 (Fig. 2.2) shows a well behaved series of inertial oscillations
excited by a rapid increase in wind and drift velocity during the last half of day
269.By integratinga simple combinationof mean velocitywith a clockwise circu-
larrotationfromastartingpointattime270.0,thetrajectoryoverthenexttwodays
can be reproduced reasonably well. The mean ice velocity is dominated by shear
between the ice cover and the upper mixed layer in the direction of surface stress
(Chapter3),soinfacttheactualvelocityinthemixedlayerwasprobablynotmuch
different from the highly idealized situation depicted in Fig. 2.1, at least for about
fourinertialperiods.
AmorecomplicateddriftobservedneartheendoftheSHEBAproject(Fig.2.3)
illustratesatechniquecalledcomplexdemodulationappliedtoseaicedrift(McPhee
1988). The procedure uses least-squares error minimization to fit a differentiable
function to observed positions over a suitable time interval, in order to isolate the
inertial and diurnal tidal components of drift velocity. It also provides a rational
estimateofdriftvelocity,whennavigationfixesare notevenlyspacedintime.
Expanding on concepts introduced by Perkins (1970), the drift velocity over a
time interval comparable to the inertial and/or diurnal tidal period, is expressed as
thesumofameanpart
,plusoscillationsfromacombinationofclockwiseand
counterclockwiserotatingcomponents:
(
V
0
)
