Problem 1: Make Your Own Waves!

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?


1 This problem set contains 6 problems, and your final score will be based on the 4 problems on which you earned the highest scores.