112
5 2D Shallow-Water Modelling
5.9.4 Results
Inclusion of the nonlinear terms modifie the lake’s circulation (Fig. 5.15). A clockwise eddy establishes in the northwestern corner of the lake and the eddy northwest
of the island has largely disappeared. The upstream scheme is highly diffusive and
therefore triggers rapid establishment of a steady-state circulation in the lake. In
contrast to this, less diffusive TVD advection schemes based on either the Superbee
or the Super-C limiters lead to slight oscillations of the circulation pattern presumably triggered by the initial adjustment of the wind field Due to reduced numerical
diffusion, either of these schemes should be applied for the nonlinear terms. Use
of the Lax-Wendroff scheme for the nonlinear terms did not lead to satisfactory
results.
Fig. 5.15 Exercise 13. Same as Fig. 5.8, but with inclusion of nonlinear terms in the momentum
equations using the TVD Superbee scheme
5.10 Exercise 14: Island Wakes
5.10.1 Aim
The aim of this exercise is to simulate turbulent wakes produced by horizontal fl ws
around an island. This includes implementations of both lateral friction and lateral
momentum diffusion in the shallow-water model.
5 2D Shallow-Water Modelling
5.9.4 Results
Inclusion of the nonlinear terms modifie the lake’s circulation (Fig. 5.15). A clockwise eddy establishes in the northwestern corner of the lake and the eddy northwest
of the island has largely disappeared. The upstream scheme is highly diffusive and
therefore triggers rapid establishment of a steady-state circulation in the lake. In
contrast to this, less diffusive TVD advection schemes based on either the Superbee
or the Super-C limiters lead to slight oscillations of the circulation pattern presumably triggered by the initial adjustment of the wind field Due to reduced numerical
diffusion, either of these schemes should be applied for the nonlinear terms. Use
of the Lax-Wendroff scheme for the nonlinear terms did not lead to satisfactory
results.
Fig. 5.15 Exercise 13. Same as Fig. 5.8, but with inclusion of nonlinear terms in the momentum
equations using the TVD Superbee scheme
5.10 Exercise 14: Island Wakes
5.10.1 Aim
The aim of this exercise is to simulate turbulent wakes produced by horizontal fl ws
around an island. This includes implementations of both lateral friction and lateral
momentum diffusion in the shallow-water model.