Pavlov and Pavlov: Features of Seasonal and Interannual Variability ofthe Sea Level
~.1tu ~~tv ~~- fv = -!~~t ~-~t ~-~ ~~t~-~ ~~
at
'ax
'ay
,
p,ax Pihi p,h, ax Lax ay Lay
(7)
dV i
dV,
dVi
gd~ 'tya
'tyw
d
dvi d
dV,
--tu--tv.--tfu =----t---t-~--t-~a t ' d X'd Y , Pi d Y Pih, p,h i d x d x d y Lay
7
here U i' Vi - components of the ice velocity vector by axes x, y - respectively; Pi, hi· ice
density and thickness, f.lL - coefficients of turbulent exchange by momentum along horizontal
axes.
While accepting condition of equal velocities of ice drift and of water at the ice bottom
surface, and Wz=o =0, AL = ilL , we shall subtract the equations (7) from the equations (I).
Then we shall obtain while representing the term describing the vertical turbulent exchange as a
finite difference
d u'
't'+1it = 't'+IitR - pA --R
xw
xa..L'"w
z a z I
dV'
't'+1it = 'tt+IitR - pA --R
yw
ya.l. '"w
z a z I
where:
R = p&
W
POZ+Pi h,
&: - time step, bz - spatial step for vertical coordinate.
As the drift ice occupies only some part of the water area represented by ice concentration
(0 ~ a ~ 1), we shall finally obtain
dU'
't'+1it = 't'+Iit[aR +(l-a)]- apA --R
xO
xa
w
z a z I
d v'
't'M = 't'+Iit[aR + (1- a)]- apA --R
yO
ya
W
Z d Z '
(8)
The formulas (8) allow us to calculate the tangential stress under the drift ice cover with
accuracy of spatial-temporal resolution of the model.
The following boundary condition is accepted under the fast ice:
uz=O = VZ=O = O.
for the barotropic component of current