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Theoretical Advances

  • Vernon A. Squire
  • Roger J. Hosking
  • Arnold D. Kerr
  • Patricia J. Langhorne
Chapter
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 45)

Abstract

The theoretical response of a floating ice sheet to a moving load is discussed further in this chapter. The results described are mainly derived from our simplest acceptable mathematical model, corresponding to a thin elastic or viscoelastic plate of infinite extent resting on an incompressible inviscid fluid of finite depth. Towards the end of Chapter 3 we formulated the elastic equation (3.44) for this model, noting that the water beneath should satisfy the Laplace equation (3.33) together with a linearized kinematic (noncavitation) condition (3.37) applied at the surface z = 0 and a normal flow condition (3.39) at the bottom z = -H. The system to be solved is therefore
$$ {\nabla^2}\phi = 0,\quad \frac{{\partial \phi }}{{\partial z}}\left| {_{{z = - H}}} \right. = 0,\quad \frac{{\partial \phi }}{{\partial z}}\left| {_{{z = 0}}} \right. = \frac{{\partial \zeta }}{{\partial t}} $$
(5.1a)
$$ D{\nabla^4}\zeta + \rho 'h\frac{{{\partial^2}\zeta }}{{\partial {t^2}}} + \rho g\zeta = - \rho \frac{{\partial \phi }}{{\partial z}}\left| {_{{z = 0}}} \right. - f\left( {x,y,t} \right) $$
(5.1b)

Keywords

Gravity Wave Internal Wave Phase Speed Critical Speed Wave Crest 
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

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Vernon A. Squire
    • 1
  • Roger J. Hosking
    • 2
  • Arnold D. Kerr
    • 3
  • Patricia J. Langhorne
    • 4
  1. 1.Department of Mathematics and StatisticsUniversity of OtagoDunedinNew Zealand
  2. 2.Department of Mathematics and StatisticsJames Cook UniversityTownsvilleAustralia
  3. 3.Department of Civil EngineeringUniversity of DelawareNewarkUSA
  4. 4.Department of PhysicsUniversity of OtagoDunedinNew Zealand

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