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A Scaling Law for the Flexural Motion of Floating Ice

  • Colin Fox
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 94)

Abstract

This paper presents a mathematical study of flexural motion of floating ice, including hydrodynamic effects, to derive a scaling law by reducing the deep-water dispersion equation to scale-independent form. The scaling shows that the well-known characteristic length, \( {l_c} = \sqrt[4]{{D/\rho g}} \) and less well known characteristic time, \( {t_c} = \sqrt {{l_c}/g} \) , are unique in reducing solutions to canonical, scale-independent, form. The canonical solutions show that flexural motion is quasi-static for periods much greater than 2πtc , and is dynamic for shorter periods, with significant propagating waves. These conclusions are largely independent of the geometry of the ice sheet under consideration, the surrounding ice/water conditions, or distribution of applied forcing.

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Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Colin Fox
    • 1
  1. 1.Department of MathematicsThe University of AucklandAucklandNew Zealand

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