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| Titel |
Nonhydrostatic correction for shallow water equations with quadratic vertical pressure distribution: A Boussinesq-type equation |
| VerfasserIn |
Anja Jeschke, Jörn Behrens |
| Konferenz |
EGU General Assembly 2015
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 17 (2015) |
| Datensatznummer |
250110226
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| Publikation (Nr.) |
 EGU/EGU2015-10204.pdf |
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| Zusammenfassung |
| In tsunami modeling, two different systems of dispersive long wave equations are common:
The nonhydrostatic pressure correction for the shallow water equations derived out of the
depth-integrated 3D Reynolds-averaged Navier-Stokes equations, and the category of
Boussinesq-type equations obtained by an expansion in the nondimensional parameters for
nonlinearity and dispersion in the Euler equations. The first system uses as an assumption a
linear vertical interpolation of the nonhydrostatic pressure, whereas the second system’s
derivation includes an quadratic vertical interpolation for the nonhydrostatic pressure.
In this case the analytical dispersion relations do not coincide. We show that the
nonhydrostatic correction with a quadratic vertical interpolation yields an equation set
equivalent to the Serre equations, which are 1D Boussinesq-type equations for the case
of a horizontal bottom. Now, both systems yield the same analytical dispersion
relation according up to the first order with the reference dispersion relation of the
linear wave theory. The adjusted model is also compared to other Boussinesq-type
equations.
The numerical model with the nonhydrostatic correction for the shallow water equations
uses Leapfrog timestepping stabilized with the Asselin filter and the P1-PNC1 finite element
space discretization. The numerical dispersion relations are computed and compared by
employing a testcase of a standing wave in a closed basin. All numerical values match their
theoretical expectations.
This work is funded by project ASTARTE - Assessment, Strategy And Risk Reduction
for Tsunamis in Europe - FP7-ENV2013 6.4-3, Grant 603839. We acknowledge the support
given by Geir K. Petersen from the University of Oslo. |
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