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On the propagation of acoustic–gravity waves under elastic ice sheets

Published online by Cambridge University Press:  05 January 2018

Ali Abdolali Open the ORCID record for Ali Abdolali [Opens in a new window] ,
Usama Kadri ,
Wade Parsons  and
James T. Kirby
Ali Abdolali*
Affiliation:
NWS/NCEP/Environmental Modeling Center, National Oceanic and Atmospheric Administration (NOAA), College Park, MD 20740, USA University Corporation for Atmospheric Research (UCAR), Boulder, CO 80301, USA
Usama Kadri
Affiliation:
School of Mathematics, Cardiff University, CardiffCF24 4AG, UK Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Wade Parsons
Affiliation:
Faculty of Engineering and Applied Science, Memorial University of Newfoundland, 240 Prince Philip Drive, St. John’s, NL A1B 3X5, Canada
James T. Kirby
Affiliation:
Center for Applied Coastal Research, Department of Civil and Environmental Engineering, University of Delaware, Newark, DE 19716, USA
*
†Email address for correspondence: ali.abdolali@noaa.gov
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Abstract

The propagation of wave disturbances in water of varying depth bounded above by ice sheets is discussed, accounting for gravity, compressibility and elasticity effects. Considering the more realistic scenario of elastic ice sheets reveals a continuous spectrum of acoustic–gravity modes that propagate even below the cutoff frequency of the rigid surface solution where surface (gravity) waves cannot exist. The balance between gravitational forces and oscillations in the ice sheet defines a new dimensionless quantity $\mathfrak{Ka}$. When the ice sheet is relatively thin and the prescribed frequency is relatively low ($\mathfrak{Ka}\ll 1$), the free-surface bottom-pressure solution is retrieved in full. However, thicker ice sheets or propagation of relatively higher frequency modes ($\mathfrak{Ka}\gg 1$) alter the solution fundamentally, which is reflected in an amplified asymmetric signature and different characteristics of the eigenvalues, such that the bottom pressure is amplified when acoustic–gravity waves are transmitted to shallower waters. To analyse these scenarios, an analytical solution and a depth-integrated equation are derived for the cases of constant and varying depths, respectively. Together, these are capable of modelling realistic ocean geometries and an inhomogeneous distribution of ice sheets.

JFM classification

Compressible Flows: Compressible Flows Geophysical and Geological Flows: Geophysical and Geological Flows Waves/Free-surface Flows: Waves/Free-surface Flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 837 , 25 February 2018 , pp. 640 - 656
Copyright
© 2018 Cambridge University Press 

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