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Nonlinear higher-order spectral solution for a two-dimensional moving load on ice

Published online by Cambridge University Press:  12 February 2009

FÉLICIEN BONNEFOY ,
MICHAEL H. MEYLAN  and
PIERRE FERRANT
FÉLICIEN BONNEFOY*
Affiliation:
Laboratoire de Mécanique des Fluides, Centrale Nantes, France
MICHAEL H. MEYLAN
Affiliation:
Department of Mathematics, The University of Auckland, New Zealand
PIERRE FERRANT
Affiliation:
Laboratoire de Mécanique des Fluides, Centrale Nantes, France
*
†Email address for correspondence: felicien.bonnefoy@ec-nantes.fr
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Abstract

We calculate the nonlinear response of an infinite ice sheet to a moving load in the time domain in two dimensions, using a higher-order spectral method. The nonlinearity is due to the moving boundary, as well as the nonlinear term in Bernoulli's equation and the elastic plate equation. We compare the nonlinear solution with the linear solution and with the nonlinear solution found by Parau & Dias (J. Fluid Mech., vol. 460, 2002, pp. 281–305). We find good agreement with both solutions (with the correction of an error in the Parau & Dias 2002 results) in the appropriate regimes. We also derive a solitary wavelike expression for the linear solution – close to but below the critical speed at which the phase speed has a minimum. Our model is carefully validated and used to investigate nonlinear effects. We focus in detail on the solution at a critical speed at which the linear response is infinite, and we show that the nonlinear solution remains bounded. We also establish that the inclusion of nonlinearities leads to significant new behaviour, which is not observed in the linear solution.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 621 , 25 February 2009 , pp. 215 - 242
Copyright
Copyright © Cambridge University Press 2009

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References

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