Theoretical Advances

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


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
$$ {\nabla^2}\phi = 0,\quad \frac{{\partial \phi }}{{\partial z}}\left| {_{{z = - H}}} \right. = 0,\quad \frac{{\partial \phi }}{{\partial z}}\left| {_{{z = 0}}} \right. = \frac{{\partial \zeta }}{{\partial t}} $$
$$ D{\nabla^4}\zeta + \rho 'h\frac{{{\partial^2}\zeta }}{{\partial {t^2}}} + \rho g\zeta = - \rho \frac{{\partial \phi }}{{\partial z}}\left| {_{{z = 0}}} \right. - f\left( {x,y,t} \right) $$


Gravity Wave Internal Wave Phase Speed Critical Speed Wave Crest 
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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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