136
Land-Ocean Systems in the Siberian Arctic: Dynamics and History
where A=0.56 is an empirical constant. From (13), knowing the mean thickness of the
supercooled water layer L=.35 cm during the June 6 to 11 period, mean salinity difference in
the pycnocline L1S=.18.44 and Ue (given above), and also considering (11), we can determine
the scale of horizontal velocity in the upper freshened layer U. It equals 10-15 cm/s. Hence,
according to (11), U* is about 1.3-1.9 cm/s. The estimated scale of horizontal velocity U in the
upper layer seems to be high, but it has been obtained at the station situated at the traverse of the
Bykovskaya branch (see Figure 1) which is the main channel for the Lena river fresh water
runoff. Hence U value is quite realistic. Such independent evaluation of U and u* confirms our
interpretation of the process of turbulent entrainment at the river/sea water boundary as an
entrainment process at the flat turbulent jet margin.
The above given description of the approach used for determination of the local turbulence
characteristics at the freshened layer-pycnocline boundary does not include evaluation of the
Coriolis force influence, since it is insignificant and can be avoided. Similar approach to
determination of the rate of entrainment at the upper pycnocline boundary (geophysical
application) was used by Turner (1973). Besides this, according to Phillips (1977), at Z< U, /
Q, the influence of the Coriolis force can be neglected. Here Z is depth, Q is angular speed of
the Earth's rotation. The U. / Q value for the above U. estimates is about ",260 m. Sea water
depths in the region investigation (Figure 1) are only 6-20 m. So, it is obvious that during flood
the Coriolis force does not influence the local turbulence patterns at the freshened
layer/pycnocline boundary in the shallow sea area around the Lena river delta.
Estimate of the rate of frazil ice formation
As a result of laboratory experiments of frazil ice formation (Krylov and Zatsepin, 1992), the
expression for estimating the rate of its formation was obtained as:
Vi = B·U.·L1S· Ri.- 1I2 . {( L1T/L1S - (7. alRi,)}
(14),
where B = 3.3.10- 3 (oq-l at the density of frazil ice Pi = 0.1-0.3 g/cm3 (Weeks and Ackley,
1982). An approximately similar, rough estimate of frazil ice density (",0.2 g/cm3) was
obtained by measuring the water volume after melting a sample of frazil ice of known volume
(at st. LN9610b). Here L1 T=T 1-T 2 >0 and L1S=S2 -S I >0 are the temperature and salinity
differences through the pycnocline. Based on the above interpretation of entrainment at the
interface, let us determine from (12) the value of the local Richardson number Ri, for the
pycnocline between river and sea water at st. LN9610, LN9610a and LN9610b for various
values of the external velocity scale in the freshened layer U at actually determined Land L1S.
The estimates are presented in Table 2. According to the classification by Krylov and Zatsepin
(1992), at the local Richardson number Ri. »10 2 the exchange through the pycnocline occurs
at the molecular level. At Ri.",10 2 with the decrease in the density difference in the pycnocline
or the increase in the external velocity scale in the turbulent layers, the "molecular core"
converges. This leads to the molecular-turbulent regime of mass- and heat exchange. At this
regime the exchange of properties through the pycnocline mainly occurs due to sporadic
outbursts of turbulence (eddy formation) in the area of a strongly sharpened density interface.
However, turbulence in the interface area is significantly influenced by buoyancy and is not
pronounced. This is probably the reason for the different effective exchange coefficients
through the pycnocline at this regime. At Ri. <10 there is a purely turbulent exchange regime.
At Ri. < 2 when stratification does not influence turbulence, the regime becomes unsteady
resulting in a rapid mixing of layers.
Land-Ocean Systems in the Siberian Arctic: Dynamics and History
where A=0.56 is an empirical constant. From (13), knowing the mean thickness of the
supercooled water layer L=.35 cm during the June 6 to 11 period, mean salinity difference in
the pycnocline L1S=.18.44 and Ue (given above), and also considering (11), we can determine
the scale of horizontal velocity in the upper freshened layer U. It equals 10-15 cm/s. Hence,
according to (11), U* is about 1.3-1.9 cm/s. The estimated scale of horizontal velocity U in the
upper layer seems to be high, but it has been obtained at the station situated at the traverse of the
Bykovskaya branch (see Figure 1) which is the main channel for the Lena river fresh water
runoff. Hence U value is quite realistic. Such independent evaluation of U and u* confirms our
interpretation of the process of turbulent entrainment at the river/sea water boundary as an
entrainment process at the flat turbulent jet margin.
The above given description of the approach used for determination of the local turbulence
characteristics at the freshened layer-pycnocline boundary does not include evaluation of the
Coriolis force influence, since it is insignificant and can be avoided. Similar approach to
determination of the rate of entrainment at the upper pycnocline boundary (geophysical
application) was used by Turner (1973). Besides this, according to Phillips (1977), at Z< U, /
Q, the influence of the Coriolis force can be neglected. Here Z is depth, Q is angular speed of
the Earth's rotation. The U. / Q value for the above U. estimates is about ",260 m. Sea water
depths in the region investigation (Figure 1) are only 6-20 m. So, it is obvious that during flood
the Coriolis force does not influence the local turbulence patterns at the freshened
layer/pycnocline boundary in the shallow sea area around the Lena river delta.
Estimate of the rate of frazil ice formation
As a result of laboratory experiments of frazil ice formation (Krylov and Zatsepin, 1992), the
expression for estimating the rate of its formation was obtained as:
Vi = B·U.·L1S· Ri.- 1I2 . {( L1T/L1S - (7. alRi,)}
(14),
where B = 3.3.10- 3 (oq-l at the density of frazil ice Pi = 0.1-0.3 g/cm3 (Weeks and Ackley,
1982). An approximately similar, rough estimate of frazil ice density (",0.2 g/cm3) was
obtained by measuring the water volume after melting a sample of frazil ice of known volume
(at st. LN9610b). Here L1 T=T 1-T 2 >0 and L1S=S2 -S I >0 are the temperature and salinity
differences through the pycnocline. Based on the above interpretation of entrainment at the
interface, let us determine from (12) the value of the local Richardson number Ri, for the
pycnocline between river and sea water at st. LN9610, LN9610a and LN9610b for various
values of the external velocity scale in the freshened layer U at actually determined Land L1S.
The estimates are presented in Table 2. According to the classification by Krylov and Zatsepin
(1992), at the local Richardson number Ri. »10 2 the exchange through the pycnocline occurs
at the molecular level. At Ri.",10 2 with the decrease in the density difference in the pycnocline
or the increase in the external velocity scale in the turbulent layers, the "molecular core"
converges. This leads to the molecular-turbulent regime of mass- and heat exchange. At this
regime the exchange of properties through the pycnocline mainly occurs due to sporadic
outbursts of turbulence (eddy formation) in the area of a strongly sharpened density interface.
However, turbulence in the interface area is significantly influenced by buoyancy and is not
pronounced. This is probably the reason for the different effective exchange coefficients
through the pycnocline at this regime. At Ri. <10 there is a purely turbulent exchange regime.
At Ri. < 2 when stratification does not influence turbulence, the regime becomes unsteady
resulting in a rapid mixing of layers.