Three-dimensional Lagrangian Tracer Modelling in Wadden Sea ...

CHAPTER 3. IDEALISED TESTCASES 47
3.3.1 Model setup
The lake covers a length of Lx = 2000 m and has a parabolic depth profile
with a maximum depth of D = 10 m at x = 1000 m. The domain has been
discretised using 101 grid points in x-direction with a grid spacing ∆x = 20 m
and 100 interface layers in the vertical using general vertical coordinates.
The simulations are carried out with a micro time step ∆tm = 1 s and a
macro time step ∆t = 10 s. As a forcing for the model, a constant wind stress
τx = 0.375 N/m 2 is applied. After a simulation time of one hour, the lake is in
steady state equilibrium and a number of ten tracer particles is distributed
equidistantly over depth in the middle of the lake. The simulations are
carried out for another 23 hours and the particle paths are computed. For
the advection and the advection-diffusion simulations, the same starting
positions are used.
3.3.2 Results
In steady state equilibrium, the surface of the lake is slightly inclined to
the west due to wind forcing, and the surface elevation ζ is higher at the
east end of the lake where down-welling occurs (see Fig. 3.3.1a). The windinduced
circulation pattern in the lake consists of a large gyre which causes
particles to move clockwise (see Fig. 3.3.1b). The vertical profiles for the
eddy diffusivity and viscosity are depicted in Fig. 3.3.1c and 3.3.1d for three
different positions along the length of the lake. All profiles have a parabolic
shape and their maximum value increases from both ends towards the middle
of the lake where diffusivity and viscosity have the most distinct profile. The
trajectories of all particles are closed for the pure advection case as shown
in Fig. 3.3.2a - 3.3.2c for three different starting positions. This leads to
the conclusion that the advection algorithm is implemented properly. For
the advection-diffusion case, the particle motions show a strong influence
of turbulence. The drift patterns calculated for the same starting positions
used for the advection case are depicted in Fig. 3.3.2d - 3.3.2f.