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

CHAPTER 3. IDEALISED TESTCASES 45
z/D
z/D
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 1 2 3 4
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
k [m 2 /s 2 ] ⋅ 10 −4
0
0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
u [m/s]
a)
c)
z/D
z/D
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 0.5 1 1.5 2
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
ε [m 2 /s 3 ] ⋅ 10 −5
0
0 0.005 0.01 0.015
ν [m 2 /s]
eddy viscoity ν t
eddy diffusivity ν’ t
Fig. 3.2.1: Vertical profiles of a) the turbulent kinetic energy k, b) the energy
dissipation rate ε, c) the zonal velocity component u and d) the eddy diffusivity ν ′ t
and viscosity νt.
Depth z [m] CSed,Euler[kg/m 3 ] CSed,Lagrange[kg/m 3 ] CSed,analytical[kg/m 3 ]
−0.5 1.03 · 10 −3 1.07 · 10 −3 1.04 · 10 −3
−1.5 3.69 · 10 −4 3.59 · 10 −4 3.62 · 10 −4
−2.5 2.65 · 10 −4 2.63 · 10 −4 2.59 · 10 −4
−3.5 2.13 · 10 −4 2.14 · 10 −4 2.09 · 10 −4
−4.5 1.78 · 10 −4 1.72 · 10 −4 1.70 · 10 −4
−5.5 1.51 · 10 −4 1.49 · 10 −4 1.47 · 10 −4
−6.5 1.28 · 10 −4 1.23 · 10 −4 1.25 · 10 −4
−7.5 1.07 · 10 −4 1.05 · 10 −4 1.05 · 10 −4
−8.5 8.64 · 10 −5 8.74 · 10 −5 8.40 · 10 −5
−9.5 6.28 · 10 −5 6.41 · 10 −5 6.10 · 10 −5
Table 3.2.1: Sediment concentrations at ten different depths calculated by the
Eulerian scheme, the correct random walk model and the analytical solution.
b)
d)