5.5 Exercise 10: Wind-Driven Flow in a Lake
101
5.5 Exercise 10: Wind-Driven Flow in a Lake
5.5.1 Aim
The aim of this exercise is to simulate the wind-driven water circulation in a shallow
lake with variable bottom topography.
5.5.2 Creation of Variable Bathymetry
Before simulating the wind-driven circulation in a shallow lake, I want to show the
reader a simple way to create variable bottom topography without using complex
analytical functions. The trick is to start with a coarse block-type bathymetry and to
employ the diffusion equation for subsequent smoothing. The diffusion equation is
given by:
∂h
∂t
= A h
∂
2 h
∂x 2 +
∂
2 h
∂y 2
(5.19)
where the diffusion coefficien A h and the duration of smoothing are adjusted such
that the result is acceptable. Coastlines and land should not disappear during the process. This can be implemented in the code via the choice of zero-gradient conditions
at the borders between dry and wet grid cells.
5.5.3 Sample Code
The FORTRAN 95 bathymetry creator, named “BathCreator.f95” is included in the
folder “Miscellaneous/2D Bathymetry Creator” of the CD-ROM. The result is written to a f le named “topo.dat”. This fil is required as input fil for the simulation
code. Included is also a SciLab script, called “Bath.sce”, creating Figure 5.7.
5.5.4 Task Description
Consider a lake of 5 km×5 km in horizontal extent, being resolved by equidistant horizontal grid spacings of Δx = Δy = 100 m, and variable bathymetry.
Figure 5.7 shows the lake’s bathymetry used by the author. Consider a uniform
southerly wind stress of τ
wind
y
= 0.2 Pa in strength being linearly adjusted from zero
to its fina value over 2 days to avoid unwanted inertial and gravity waves. Simulate the steady-state circulation resulting from the wind-stress forcing applied. Five
days of simulation should be sufficien for this. Set the bottom-friction coefficien
to r = 0.001. I used a time step of Δt = 3 s, which satisfie the CFL stability
criterion.
101
5.5 Exercise 10: Wind-Driven Flow in a Lake
5.5.1 Aim
The aim of this exercise is to simulate the wind-driven water circulation in a shallow
lake with variable bottom topography.
5.5.2 Creation of Variable Bathymetry
Before simulating the wind-driven circulation in a shallow lake, I want to show the
reader a simple way to create variable bottom topography without using complex
analytical functions. The trick is to start with a coarse block-type bathymetry and to
employ the diffusion equation for subsequent smoothing. The diffusion equation is
given by:
∂h
∂t
= A h
∂
2 h
∂x 2 +
∂
2 h
∂y 2
(5.19)
where the diffusion coefficien A h and the duration of smoothing are adjusted such
that the result is acceptable. Coastlines and land should not disappear during the process. This can be implemented in the code via the choice of zero-gradient conditions
at the borders between dry and wet grid cells.
5.5.3 Sample Code
The FORTRAN 95 bathymetry creator, named “BathCreator.f95” is included in the
folder “Miscellaneous/2D Bathymetry Creator” of the CD-ROM. The result is written to a f le named “topo.dat”. This fil is required as input fil for the simulation
code. Included is also a SciLab script, called “Bath.sce”, creating Figure 5.7.
5.5.4 Task Description
Consider a lake of 5 km×5 km in horizontal extent, being resolved by equidistant horizontal grid spacings of Δx = Δy = 100 m, and variable bathymetry.
Figure 5.7 shows the lake’s bathymetry used by the author. Consider a uniform
southerly wind stress of τ
wind
y
= 0.2 Pa in strength being linearly adjusted from zero
to its fina value over 2 days to avoid unwanted inertial and gravity waves. Simulate the steady-state circulation resulting from the wind-stress forcing applied. Five
days of simulation should be sufficien for this. Set the bottom-friction coefficien
to r = 0.001. I used a time step of Δt = 3 s, which satisfie the CFL stability
criterion.