89
??
??
??
= (1 ? ?) ???
(?)
??
+ ? ???
(?)
??
(III-10)
where ?AW and ?IW are atmospheric stresses directly imposed on water and stresses between ice
and water, respectively. They have to be specified in the x and y directions.
The turbulent heat ?ux through water surface is:
???
??
??
= ??
?????
(III-11)
where FT is the heat ?ux from the water and it includes long wave radiation [III-8], latent and
sensible heat [III-9].
A simple ice dynamic–thermodynamic submodel that is applicable for simulation of the
seasonal cycle of moving ice in the coastal seas is used by THREETOX [III-4, III-10]. The ice
submodel describes momentum balance, ice rheology, mass balance, ice concentration and ice
strength and is described in detail in Ref. [III-3].
III-3. SEDIMENT TRANSPORT
The model simulates the transport of non-cohesive and cohesive sediments, as well as a mixture
of fractions of di?erent sizes of cohesive/non-cohesive sediments. The sediments are
transported in the water layer as suspended sediments. Suspended sediment transport is
described by the advection–di?usion equation, taking into account settling velocity of sediment
grains:
????
?
??
+ ? ????
?
??
+ ? ????
?
??
+ ?? ????)
????
?
??
= ?
??
(???
????
?
??
? + ?
??
???
????
?
??
? + ?
??
???
????
?
??
? (III-12)
where ???? is the concentration of i-th fraction of sediment in the water column, and ??? is the
settling velocity of solid particles. At the free surface z = ?, zero vertical sediment ?ux is
assumed, i.e.:
?? ????????? = ???
????
?
??
(III-13)
The bottom boundary condition describes sediment resuspension or settling down depending
on the ratio between equilibrium and actual near bottom suspended sediment concentration.
The vertical ?ux of suspended sediments at the bottom z = ?H + zb is equal to the di?erence of
the resuspension and sedimentation rates:
???
????
?
??
+??????
? = ??? ? ??? (III-14)
where ??? and ??? are sedimentation and resuspension rates, respectively. They are calculated
according to empirical formulae for non-cohesive sediments [III-11] and cohesive sediments
[III-12, III-13].
