Tsunami-Waves: Mathematical Modelling and Forecasting
On this page we gathered material accompanying a workshop "catastrophe mathematics" at the Tag der Talente 2017. The material documents the day's sequence. The workshop took place in Café Moskau in Berlin.
A short kick-off presentation introduces the tsunami phenomenon. Find the presentation slides below.
In a 1.5 m long wave tank we generated waves and measured their run time. Those run times were recorded in a spreadsheet (corresponding Excel and Open Office documents are attached below). At different water depths we recorded different run times. The measured wave dispersion times were compared to theoretical values and it could be demonstrated - considering some uncertainty due to measurement errors - that the theoretical values and the measured ones correspond well.
With such observations a model of the wave dispersion can be formulated. It turns out that the so called shallow water equations (also Saint Venant Equations), consisting of a coupled non-linear system of two partial differential equations. The two equations describe the conservation of mass and momentum. They can be solved numerically by replacing the differential operators by finite differences. Such a solution method is implemented using the programming environment Python (scripts are provided below).
- How fast is a Tsunami? (PDF File, 4.50 MB)
- Wave measurements (ZIP-File with Excel and Open Office Spreadsheet, 67 KB)
- Shallow water modell (PDF print-out of iPython Notebook, 131 KB)
- Shallow water modell (ZIP-File with Python script and iPython Notebook, 11 KB)