Using the techniques from class, build your own 1-D shallow water model on a staggered grid.
In the center of a 1000m channel with 10m depth, there is a 110m area where the water level is 11m.
Use this as the initial condition to answer the following questions:
(1) Does the result look like a wave?
(2) Does the phase speed match the theoretical expectation? If not, why?
(3) How did you choose your spatial resolution and your time step?
(4) Define a reasonable total available potential energy of the water in the channel.
How does it evolve in time and what happens if you double the resolution and halve the time step?