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Fully dispersive models for moving loads on ice sheets

Published online by Cambridge University Press:  31 July 2019

E. Dinvay Open the ORCID record for E. Dinvay [Opens in a new window] ,
H. Kalisch Open the ORCID record for H. Kalisch [Opens in a new window]  and
E. I. Părău Open the ORCID record for E. I. Părău [Opens in a new window]
E. Dinvay
Affiliation:
Department of Mathematics, University of Bergen, Postbox 7800, 5020 Bergen, Norway
H. Kalisch*
Affiliation:
Department of Mathematics, University of Bergen, Postbox 7800, 5020 Bergen, Norway
E. I. Părău
Affiliation:
School of Mathematics, University of East Anglia, Norwich Research Park, NorwichNR4 7TJ, UK
*
†Email address for correspondence: [email protected]
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Abstract

The response of a floating elastic plate to the motion of a moving load is studied using a fully dispersive weakly nonlinear system of equations. The system allows for an accurate description of waves across the whole spectrum of wavelengths and also incorporates nonlinearity, forcing and damping. The flexural–gravity waves described by the system are time-dependent responses to a forcing with a described weight distribution, moving at a time-dependent velocity. The model is versatile enough to allow the study of a wide range of situations including the motion of a combination of point loads and loads of arbitrary shape. Numerical solutions of the system are compared to data from a number of field campaigns on ice-covered lakes, and good agreement between the deflectometer records and the numerical simulations is observed in most cases. Consideration is also given to waves generated by a decelerating load, and it is shown that a decelerating load may trigger a wave response with a far greater amplitude than a load moving at constant celerity.

JFM classification

Geophysical and Geological Flows: Ice sheets Waves/Free-surface Flows: Elastic waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 876 , 10 October 2019 , pp. 122 - 149
Copyright
© 2019 Cambridge University Press 

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