6
Land-Ocean Systems in the Siberian Arctic: Dynamics and History
a~
a~
a~
w =-{--+u--+v-)
at ax ay
(5)
Here: 'tx,y - are the vector components of tangential friction stress at sea surface,
l; - is the deviation of sea surface from undisturbed state.
On the bottom: z=H(x,y) the speed vector is assumed to be equal to zero:
u=v=w=O
(6)
To reduce computation time we have used the method of "splitting" the equations into
baroclinic and barotropic components, as suggested in (Killworth et aI., 1987; Marchuk and
Sarkisyan, 1988):
Coefficient of the horizontal turbulent exchange was determined according to the
Smagorinsky formula that was successfully used in the practice of such calculations (Oye et al.,
1985):
2 a 1! 2 1 a v a IT 2 a v 2112
A == C(&) [(--) +-;;-{--+--) +(--)
L
ax
2axay
ay
Where &., represents the grid area interval and the empirical constant C == 0.1.
Let us determine the coefficient of vertical turbulent exchange by momentum using the
following parameterization that is a specific case of solving the turbulent energy balance
equation (Marchuk and Sarkisyan, 1980):
2
a u
l
2
a VI 2
g a pI 112
A == (bh ) [(--) + (--) - - - - ]
z
z
az
az
paz
o
Where: hz - is the thickness of the upper quasistationary layer that was chosen in such a way
that within it Az :::; Icmls.
The empirical constant b was prescribed to be equal to 0.05.
The problem of prescribing tangential stresses at the ocean surface includes two
parameterizations: at ice-free surface and under ice. Let us use in the first case well known
formulas:
1
d p. d p.
't = ---.-(--+ --);
x
2adx dy
1
d p. d Pa
't =--.-(-----)
y 2adx
dy
·fT
where: a = "J"l,;' " ; Pa - atmospheric pressure at sea level.
u' _ coefficient of vertical turbulent air viscosity, the most used value of which is equal to
u' = 10' em 2 Is.
For calculating tangential friction at the ice-water boundary several ways can be used. The
most simple is given in (Pavlov and Kulakov, 1994).
We shall write down the momentum balance equations for the sea ice in the following form:
Land-Ocean Systems in the Siberian Arctic: Dynamics and History
a~
a~
a~
w =-{--+u--+v-)
at ax ay
(5)
Here: 'tx,y - are the vector components of tangential friction stress at sea surface,
l; - is the deviation of sea surface from undisturbed state.
On the bottom: z=H(x,y) the speed vector is assumed to be equal to zero:
u=v=w=O
(6)
To reduce computation time we have used the method of "splitting" the equations into
baroclinic and barotropic components, as suggested in (Killworth et aI., 1987; Marchuk and
Sarkisyan, 1988):
Coefficient of the horizontal turbulent exchange was determined according to the
Smagorinsky formula that was successfully used in the practice of such calculations (Oye et al.,
1985):
2 a 1! 2 1 a v a IT 2 a v 2112
A == C(&) [(--) +-;;-{--+--) +(--)
L
ax
2axay
ay
Where &., represents the grid area interval and the empirical constant C == 0.1.
Let us determine the coefficient of vertical turbulent exchange by momentum using the
following parameterization that is a specific case of solving the turbulent energy balance
equation (Marchuk and Sarkisyan, 1980):
2
a u
l
2
a VI 2
g a pI 112
A == (bh ) [(--) + (--) - - - - ]
z
z
az
az
paz
o
Where: hz - is the thickness of the upper quasistationary layer that was chosen in such a way
that within it Az :::; Icmls.
The empirical constant b was prescribed to be equal to 0.05.
The problem of prescribing tangential stresses at the ocean surface includes two
parameterizations: at ice-free surface and under ice. Let us use in the first case well known
formulas:
1
d p. d p.
't = ---.-(--+ --);
x
2adx dy
1
d p. d Pa
't =--.-(-----)
y 2adx
dy
·fT
where: a = "J"l,;' " ; Pa - atmospheric pressure at sea level.
u' _ coefficient of vertical turbulent air viscosity, the most used value of which is equal to
u' = 10' em 2 Is.
For calculating tangential friction at the ice-water boundary several ways can be used. The
most simple is given in (Pavlov and Kulakov, 1994).
We shall write down the momentum balance equations for the sea ice in the following form: