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The shallow water equation and the vorticity equation for a change in height of the topography

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  • ChaoJiu Da
  • BingLu Shen
  • PengCheng Yan
  • DeShan Ma
  • Jian Song

Abstract

We consider the shallow water equation and the vorticity equations for a variable height of topography. On the assumptions that the atmosphere is incompressible and a constant density, we simplify the coupled dynamic equations. The change in topographic height is handled as the sum of the inherent and changing topography using the perturbation method, together with appropriate boundary conditions of the atmosphere, to obtain the relationship between the relative height of the flow, the inherent topography and the changing topography. We generalize the conservation of the function of relative position, and quantify the relationship between the height of the topography and the relative position of a fluid element. If the height of the topography increases (decreases), the relative position of a fluid element descends (ascends). On this basis, we also study the relationship between the vorticity and the topography to find the vorticity decreasing (increasing) for an increasing (decreasing) height of the topography.

Suggested Citation

  • ChaoJiu Da & BingLu Shen & PengCheng Yan & DeShan Ma & Jian Song, 2017. "The shallow water equation and the vorticity equation for a change in height of the topography," PLOS ONE, Public Library of Science, vol. 12(6), pages 1-11, June.
    • Handle: RePEc:plo:pone00:0178184
    DOI: 10.1371/journal.pone.0178184
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    1. Li, Li, 2015. "Patch invasion in a spatial epidemic model," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 342-349.
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