50
As can be seen from the tables (see Annex), the transport equation
(see Chapter 1) was solved in different ways. Whereas, in the DHI
model an estimate for the diffusion term is made, the IfMH model re-
stricts itself to the advection term for these si1imulations. The dif-
ference in the treatment of the diffusion in the two models can be
explainded as follows.
Unstable (turbulent) currents are defined as "dif£ffusion”. Its irreg-
ular (stochastic) character can lead to a spreading which, for exam-
ple, is directed transverse to the direction of the mean current.
The separation between advection (transport by the mean current) and
diffusion (transport by the turbulent current) takes place by the
choosing of a spatial and a temporal scale. Both models have the
same horizontal grid distance of about 20 km; for that reason they
can only resolve such spatial structures which have multiples of
that length (scale).
The excursion of a water particle in the North Sea during one day is
of the order of magnitude of the grid distance of the model. Pro-
cesses with spatial scales below the grid distance and temporal
scales between seconds and a day, cannot be efficiently resolved by
the models.
The estimate for the diffusion term in the DHI model consists of two
components. An (isotrope) turbulence part, independent of the cur-
rent direction, simulates a "larger scale” turbulence. Nevertheless,
nixing experiments in the sea have shown that no point symmetrical
but rather deformed, lengthways concentration distribution ensue.
For that reason, moreover, an anisotropic turbulence part - depen-
dent upon the direction of the actual tidal current - enters the
dispersion simulation.
As the first step, the IfMH dispersion model contained no diffusion
term. The wind-induced current varlilability in the IfMH model, howev-
er, include instead the time-dependent part of the "larger scale”
turbulence, and simulate in this manner the spreading of gsubstances.
4 Results of the model simulations
4.1 Mean temporal dispersion of substances
With both model estimates, different rivers as pollutant sources
were investigated here for their effect upon the North Sea. Thereby,
in the DEI model, 1,000 passive tracers entered the model region at
a fixed moment in time. This high number of particles 1s necessary
in order to model the diffusion term in a physically adequate man-
ner. Their further dispersion in the 3-dimensional current field was
computed to concentration lines (after 52, 104, and 155 days)-
In the IfMH model, every day in the simulation period from 1969 to
1982 one particle was placed in the 2-dimensional current field and
every particle position was marked 52, 104 and 155 days after the
introduction. As the model investigations were not carried out espe-
