5.8 Exercise 12: Trajectories
109
5.7.4 Recommendation
Use either the Superbee limiter or the Super-C scheme for advection of Eulerian
tracer. Either of these schemes should also be used in replacement of the upstream
scheme in the volume-conservation equation.
5.7.5 Sample Code and Animation Script
The folder “Exercise 11” of the CD-ROM contains the computer codes for this
exercise. The “MODE” switch allows for selection of any of the above flu limiters.
5.8 Exercise 12: Trajectories
5.8.1 Aim
The aim of this exercise is to predict the pathways of individual non-buoyant
Lagrangian float subject to the lake’s steady-state circulation circulation.
5.8.2 Task Description
Using the steady-state f ow fiel predicted in Exercise 10, a large number (3000)
of Lagrangian float is introduced at random locations in the lake to predict their
pathways over a day. The horizontal displacement of a floa is calculated from:
X
n+1
m
= X
n
m + Δt U
n
m
Y
n+1
m
= Y
n
m + Δt V
n
m
where m is the floa number, X and Y specifie the location of a float and U and
V is the ambient lateral f ow interpolated to the floa location. To make this task
easier, instead of interpolating velocity to the precise location of a float we use the
velocity interpolated to the nearest “h” grid point as a proxy. Zones within a distance
of 500 m from the lake’s banks are initially kept free of float to avoid that float
become trapped in zones of little or zero f ow.
5.8.3 Results
Both the animation movie of floa locations (Fig. 5.13 shows a snapshot) and trajectories (Fig. 5.14) nicely reveal the circulation pattern established in the lake. The
southerly wind drives northward fl ws on the western and eastern sides of the lake.
In interaction with bathymetry, the resultant pattern in sea-level gradients creates a
109
5.7.4 Recommendation
Use either the Superbee limiter or the Super-C scheme for advection of Eulerian
tracer. Either of these schemes should also be used in replacement of the upstream
scheme in the volume-conservation equation.
5.7.5 Sample Code and Animation Script
The folder “Exercise 11” of the CD-ROM contains the computer codes for this
exercise. The “MODE” switch allows for selection of any of the above flu limiters.
5.8 Exercise 12: Trajectories
5.8.1 Aim
The aim of this exercise is to predict the pathways of individual non-buoyant
Lagrangian float subject to the lake’s steady-state circulation circulation.
5.8.2 Task Description
Using the steady-state f ow fiel predicted in Exercise 10, a large number (3000)
of Lagrangian float is introduced at random locations in the lake to predict their
pathways over a day. The horizontal displacement of a floa is calculated from:
X
n+1
m
= X
n
m + Δt U
n
m
Y
n+1
m
= Y
n
m + Δt V
n
m
where m is the floa number, X and Y specifie the location of a float and U and
V is the ambient lateral f ow interpolated to the floa location. To make this task
easier, instead of interpolating velocity to the precise location of a float we use the
velocity interpolated to the nearest “h” grid point as a proxy. Zones within a distance
of 500 m from the lake’s banks are initially kept free of float to avoid that float
become trapped in zones of little or zero f ow.
5.8.3 Results
Both the animation movie of floa locations (Fig. 5.13 shows a snapshot) and trajectories (Fig. 5.14) nicely reveal the circulation pattern established in the lake. The
southerly wind drives northward fl ws on the western and eastern sides of the lake.
In interaction with bathymetry, the resultant pattern in sea-level gradients creates a