A Class of Chrystal-Type Equations

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


This chapter is concerned with the derivation of an approximate system of equations for slender fluid bodies using free-surface hydrodynamics on the rotating Earth. Early methods of computing free oscillations or wind-forced responses of oblong lakes or ocean basins assume exclusively uniaxial motion of the water in the long direction of the lake. Consistent derivation of the governing equations from the balances of mass and momentum requires that the rotation of the Earth is ignored. These traditional methods of calculating free oscillations are the channel approximations, of which the classical example is the set of Chrystal equations [4,  5] for barotropic motions. In the linear approximation the corresponding two-layer channel equations can also be derived. They yield the V1Hm modes By ‘V1Hm’ a baroclinic seiche mode is characterized which is of vertical mode 1 and horizontal mode m. For elongated basins Hm is sometimes replaced by Lm. of a 2-layered fluid with free surface, subject to the neglect of the effects of the rotation of the Earth.


Channel Approximation Channel Model Surface Elevation Free Oscillation Straight Channel 
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© 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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