98
?????,?
?
??
= ????????,?? ??? ? ??,?? ? +
????,?
?
??(???)
?
????,?
?
????(???)
? ?????,?? (IV-21)
Here t is time; z is the vertical coordinate directed upwards; ??? = (U, V, W) is water velocity; ?s
is the density of the sediments (kg/m3); i is the index of sediment size class; n is total number
of sediment classes; Sp,i is the concentration of i?th class of suspended sediment (kg/m3); Wp,i
is settling velocity of sediment class i (m/s); Di is sediment deposition rate (kg/m2s); Ei is
sediment erosion rate (kg/m2s); Z? is the thickness of the upper layer of sediment (m); ?i is the
fraction of particles of i?th class in the bottom sediment (??? = 1); ? is porosity; Wwp is water
exchange rate between the water column and pore water (m/s), related with the di?usion
coe?cient ?D and the thickness of upper layer of sediment as Wpw = ?DZ*?1 and ? is the
radioactive decay rate. The total concentration of the particulate phase of radionuclides in water
column is ??? = ???,?? and the total concentration of particulate phase of radionuclide in bottom
sediment is ??? = ?????,?? . The term DIFF presents vertical and horizontal turbulent di?usion.
The phase exchange between dissolved and particulate radionuclides is written in terms of the
desorption rate a12 (s?1) and the distribution coe?cients ??,?? and ??,?? for the water column and
for the bottom deposit, respectively. The dependence of the distribution coe?cient on sediment
particle size can be written for the water column as [IV-9]:
??,?? =
??
?????
(IV-22)
and for bottom sediment as:
??,?? =
???
???????
(IV-23)
where Ri is sediment particle radius (m), ? is an exchange velocity (m/s) and ? is a correction
factor that takes into account that part of the sediment particle surface may be hidden by other
sediment particles.
At the free surface z = ? the boundary conditions for Eqs. IV-18 and IV-19 are:
??
???
?
??
????? = ??? (IV-24)
??
???,?
?
??
+ (? ???,?)??,?? = ???,? (IV-25)
where ? is sea level elevation, and qd and qp,i are atmospheric deposition ?uxes (Bq/m2s) of
dissolved and particulate radionuclide, respectively. The ?uxes into the bottom at z = ?H + zo
are:
??
???
?
??
= ???(??? ? ???) (IV-26)
??
???,?
?
??
+ ?? ???,????,?? = ??,???? ? ??,?? ?? (IV-27)
where zo is roughness height of the seabed.
Assuming that the exchange of the sediment pore water with water column is balanced by
redistribution of activity in bottom sediments, the pore water concentration can be obtained as:
??? =
?????
?(??)????????(???)???
???????????(???)? ??????
(IV-28)
