Skip to main content
×
×
Home

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

  • Ali Abdolali (a1) (a2), Usama Kadri (a3) (a4), Wade Parsons (a5) and James T. Kirby (a6)
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.

  • View HTML
    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      On the propagation of acoustic–gravity waves under elastic ice sheets
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      On the propagation of acoustic–gravity waves under elastic ice sheets
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      On the propagation of acoustic–gravity waves under elastic ice sheets
      Available formats
      ×
Copyright
Corresponding author
Email address for correspondence: ali.abdolali@noaa.gov
References
Hide All
Abdolali, A. & Kirby, J. T. 2017 Role of compressibility on tsunami propagation. J. Geophys. Res. Oceans 122, doi:10.1002/2017JC013054.
Abdolali, A., Kirby, J. T. & Bellotti, G. 2015 Depth-integrated equation for hydro-acoustic waves with bottom damping. J. Fluid Mech. 766, R1.
Caplan-Auerbach, J., Dziak, R. P., Bohnenstiehl, D. R., Chadwick, W. W. & Lau, T.-K. 2014 Hydroacoustic investigation of submarine landslides at West Mata volcano, Lau Basin. Geophys. Res. Lett. 41 (16), 59275934; 2014GL060964.
Cecioni, C., Bellotti, G., Romano, A., Abdolali, A. & Sammarco, P. 2014 Tsunami early warning system based on real-time measurements of hydro-acoustic waves. Procedia Engng 70 (C), 311320.
Chierici, F., Pignagnoli, L. & Embriaco, D. 2010 Modeling of the hydroacoustic signal and tsunami wave generated by seafloor motion including a porous seabed. J. Geophys. Res. 115, C03015.
Eyov, E., Klar, A., Kadri, U. & Stiassnie, M. 2013 Progressive waves in a compressible-ocean with an elastic bottom. Wave Motion 50 (5), 929939.
Hansen, J. 2007 Climate catastrophe. New Sci. 195 (2614), 3034.
Hendin, G. & Stiassnie, M. 2013 Tsunami and acoustic–gravity waves in water of constant depth. Phys. Fluids 25 (8), 086103.
Hosking, R. J., Sneyd, A. D. & Waugh, D. W. 1988 Viscoelastic response of a floating ice plate to a steadily moving load. J. Fluid Mech. 196, 409430.
Kadri, U. 2014 Deep ocean water transport by acoustic-gravity waves. J. Geophys. Res. 119 (11), 79257930.
Kadri, U. 2015 Wave motion in a heavy compressible fluid: revisited. Eur. J. Mech. (B/Fluids) 49, Part A, 50–57.
Kadri, U. 2016a Generation of hydroacoustic waves by an oscillating ice block in arctic zones. Adv. Acoust. Vib. 2016, 17.
Kadri, U. 2016b Triad resonance between a surface-gravity wave and two high frequency hydro-acoustic waves. Eur. J. Mech. (B/Fluids) 55, Part 1, 157–161.
Kadri, U. 2017 Tsunami mitigation by resonant triad interaction with acoustic–gravity waves. Heliyon 3 (1), e00234.
Kadri, U. & Akylas, T. R. 2016 On resonant triad interactions of acoustic-gravity waves. J. Fluid Mech. 788, R1.
Kadri, U. & Stiassnie, M. 2012 Acoustic-gravity waves interacting with the shelf break. J. Geophys. Res. 117 (C3), c03035.
Kadri, U. & Stiassnie, M. 2013 Generation of an acoustic-gravity wave by two gravity waves, and their subsequent mutual interaction. J. Fluid Mech. 735, R6.
Kirby, J. T. 1992 Water waves in variable depth under continuous sea ice. In Proceedings of the Second International Conference on Offshore and Polar Engineering Conference, pp. 7076. International Society of Offshore and Polar Engineers.
Oliveira, T. C. A. & Kadri, U. 2016 Pressure field induced in the water column by acoustic-gravity waves generated from sea bottom motion. J. Geophys. Res. 121 (10), 77957803.
Renzi, E. & Dias, F. 2014 Hydro-acoustic precursors of gravity waves generated by surface pressure disturbances localised in space and time. J. Fluid Mech. 754, 250262.
Sammarco, P., Cecioni, C., Bellotti, G. & Abdolali, A. 2013 Depth-integrated equation for large-scale modelling of low-frequency hydroacoustic waves. J. Fluid Mech. 722, R6.
Schulkes, R. M. S. M., Hosking, R. J. & Sneyd, A. D. 1987 Waves due to a steadily moving source on a floating ice plate. Part 2. J. Fluid Mech. 180, 297318.
Stiassnie, M. 2010 Tsunamis and acoustic-gravity waves from underwater earthquakes. J. Engng Maths 67 (1–2), 2332.
Yamamoto, T. 1982 Gravity waves and acoustic waves generated by submarine earthquakes. Intl J. Soil Dyn. Earthq. Engng 1 (2), 7582.
Zakharov, D. D. 2008 Orthogonality of 3D guided waves in viscoelastic laminates and far field evaluation to a local acoustic source. Intl J. Solids Struct. 45 (6), 17881803.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords:

Metrics

Altmetric attention score

Full text views

Total number of HTML views: 12
Total number of PDF views: 118 *
Loading metrics...

Abstract views

Total abstract views: 373 *
Loading metrics...

* Views captured on Cambridge Core between 5th January 2018 - 27th April 2018. This data will be updated every 24 hours.