This one dimensional test problem consists of a flat ocean floor, linear continental slope, flat continental shelf, and a solid wall reflecting boundary.
It is designed to illustrate how a tsunami wave is modified as it moves from the deep ocean onto the continental shelf, and the manner in which some of the energy can be trapped on the shelf and bounce back and forth.
Populating the interactive namespace from numpy and matplotlib
Check that the CLAW environment variable is set. (It must be set in the Unix shell before starting the notebook server).
try:importclawpacklocation=clawpack.__file__.replace('clawpack/__init__.pyc','')print"Using Clawpack from ",locationexcept:print"*** Problem importing Clawpack -- check if environment variable set"
Using Clawpack from /usr/local/sage/sage-6.4/local/lib/python2.7/site-packages/clawpack/__init__.py
A few of the parameters will be redefined below for each example.
importsetrunrundata=setrun.setrun()# initialize most run-time variables for clawpack
The cells below set the following parameters:
Bocean = depth of ocean (meters below sea level)
Bshelf = depth of continental shelf
width = width of continental slope (linear section connecting floor to shelf)
start = location of start of continental slope
The initial data is a hump of water with zero velocity everywhere. Note that the intial hump splits into left-going and right-going waves. The left-going wave leaves the domain (since "non-reflecting" boundary conditions are used at the left boundary).
The right-going wave hits the continental slope, where some of the wave energy is reflected and some is transmitted onto the shelf. The transmitted wave reflects off the coastline (a vertical wall in this model). The reflected wave hits the slope again and is partly transmitted out to the ocean, and partly reflected back towards shore. Depending on the relative depths and steepness of the slope, quite a bit of energy may be trapped on the shelf and bounce back and forth for some time.
Note that the wave propagates more slowly on the shelf than in the deep ocean. In the shallow water equations the wave propagation speed is gh where g=9.81m/s2 is the gravitational acceleration and h is the water depth. The wave form also gets compressed as it moves onto the shelf because of the slower wave speed.
The width of the slope is 1 m, so essentially a step discontinuity: