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Topographic Waves in Basins with Complex Shapes and Complex Bathymetries

  • Kolumban HutterEmail author
  • Yongqi Wang
  • Irina P. Chubarenko
Chapter
Part of the Advances in Geophysical and Environmental Mechanics and Mathematics book series (AGEM, volume 2)

Abstract

In the last two chapters, construction of analytical solutions to the topographic wave (TW)-equation in enclosed basins subject to the no-flux boundary condition was possible only for basins of simple geometries and simple bathymetries. The situations were generally such that the linear boundary value problems could be constructed and solved by the method of separation of variables leading to two-point-eigenvalue problems of ordinary differential equations with homogeneous boundary conditions, which could be expressed in terms of simple functions. However, unless the bathymetry was approximately expressible by very simple exponential or power law functions, the differential equations soon took forms, which were no longer expressible by common functions of mathematical physics, or the mathematical expressions for the solution would be so tedious to handle, that they are very likely better solved numerically. As an example, we presented the solutions of the few lowest order TW-modes in a circular basin with parabolic radial profile in terms of hypergeometric polynomials (see Chap. 20, formulae (20.23)). It is also known that the interior of a circle can be transformed by a conformal mapping onto the interior of a rectangle.

Keywords

Dispersion Relation Stream Function Mode Unit Stokes Drift Incident Mode 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Kolumban Hutter
    • 1
    Email author
  • Yongqi Wang
    • 2
  • Irina P. Chubarenko
    • 3
  1. 1.c/o Versuchsanstalt für Wasserbau Hydrologie und Glaziologie ETH-ZentrumETH ZürichZürichSwitzerland
  2. 2.Department of Mechanical EngineeringDarmstadt University of TechnologyDarmstadtGermany
  3. 3.P.P. Shirshov Institute of OceanologyRussian Academy of SciencesKaliningradRussia

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