WorkshopsShallow water approximations for water waves over a moving bottom
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In numerical simulation of tsunamis due to submarine earthquakes, one usually uses the shallow water equations by assuming that the initial displacement of the water surface is equal to the permanent shift of the seabed and that the initial velocity field is equal to zero. In this talk, starting from the full water wave problem (a free boundary problem for an irrotational flow of an incompressible ideal fluid under the gravitational field) we derive mathematically rigorously the shallow water model mentioned above, that is, we will show that the solution of the full water wave problem can be approximated by the solution of the shallow water model in some limits of parameters. We also mention a higher order approximation by the so-called Green--Nagdhi equations in the case where the seabed deforms over a long period of time.
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Tatsuo Iguchi
2011-08-29
11:30:00 - 12:20:00
101 , Mathematics Research Center Building (ori. New Math. Bldg.)
In numerical simulation of tsunamis due to submarine earthquakes, one usually uses the shallow water equations by assuming that the initial displacement of the water surface is equal to the permanent shift of the seabed and that the initial velocity field is equal to zero. In this talk, starting from the full water wave problem (a free boundary problem for an irrotational flow of an incompressible ideal fluid under the gravitational field) we derive mathematically rigorously the shallow water model mentioned above, that is, we will show that the solution of the full water wave problem can be approximated by the solution of the shallow water model in some limits of parameters. We also mention a higher order approximation by the so-called Green--Nagdhi equations in the case where the seabed deforms over a long period of time.
For material related to this talk, click here.