Nonlinear hydroelastic waves with applications to ice sheets
Lead Research Organisation:
University of Bath
Department Name: Mathematical Sciences
Abstract
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People |
ORCID iD |
| Paul Milewski (Principal Investigator) |
Publications
Kim B
(2012)
On weakly nonlinear gravity-capillary solitary waves
in Wave Motion
Milewski P
(2013)
Three Dimensional Flexural-Gravity Waves
in Studies in Applied Mathematics
Milewski P
(2016)
Self-focusing dynamics of patches of ripples
in Physica D: Nonlinear Phenomena
Milewski P
(2013)
Steady dark solitary flexural gravity waves
in Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Milewski PA
(2014)
Transversally periodic solitary gravity-capillary waves.
in Proceedings. Mathematical, physical, and engineering sciences
Trichtchenko O
(2018)
Stability of periodic traveling flexural-gravity waves in two dimensions
in Studies in Applied Mathematics
Trichtchenko O
(2018)
Solitary flexural-gravity waves in three dimensions.
in Philosophical transactions. Series A, Mathematical, physical, and engineering sciences
Wang Z
(2014)
Asymmetric gravity-capillary solitary waves on deep water
in Journal of Fluid Mechanics
Wang Z
(2014)
Numerical study of interfacial solitary waves propagating under an elastic sheet.
in Proceedings. Mathematical, physical, and engineering sciences
Wang Z
(2014)
Computation of Three-dimensional Flexural-gravity Solitary Waves in Arbitrary Depth
in Procedia IUTAM
| Description | Some of our main discoveries are (1) The depth of the fluid has a large impact on the nonlinear behaviour of the waves. Localised travelling waves can be found in shallow water at any amplitude but in deep water only large waves exist. (2) The waves can be violently unstable, and nonlinearly self-focus in some situations. In the ice-sheet application, this would lead to a violent breakup of the ice. (3) The waves can be coupled with internal waves due to density differences in the fluid below. This has applications to detecting internal waves in polar regions. |
| Exploitation Route | The findings can be taken forward by oceanographers and incorporated into models for ice sheets in the ocean. |
| Sectors | Environment |
| Description | Our findings have greatly expanded fundamental knowledge on nonlinear hydroelastic waves, including interaction of surface and internal waves. These waves model, for example, ocean waves travelling under a floating ice layer and our work therefore has implications into the dynamics and breakup of floating ice sheets. This, in turn is important in studies of climate change as it is conjectured that with more violent storms generating larger waves, the breakup of ice-sheets in the Arctic and Antarctic will occur earlier in the season and be more extensive. In particular we discovered a mechanism where waves under ice sheets may "self focus" enhancing the breakup further. The work has been used to help understand: the natural hazard associated to tsunamis under ice-cover, as has occurred following landslides in ice covered lakes; the hazard of vehicles driving over ice; and the deflection of surface ice cover on the ocean when internal waves propagate deep below the ice cover. |
| First Year Of Impact | 2014 |
| Sector | Environment |
| Description | Wolfson Research Merit Award |
| Amount | £125,000 (GBP) |
| Organisation | The Royal Society |
| Sector | Charity/Non Profit |
| Country | United Kingdom |
| Start | 08/2011 |
| End | 08/2016 |
| Description | UCL - Prof. J-M Vanden-Broeck |
| Organisation | University College London |
| Department | Mathematics |
| Country | United Kingdom |
| Sector | Academic/University |
| PI Contribution | This partnership involves the complementary analysis/numerical skills between Milewski's group at Bath and Vanden-Broeck's group at UCL. Milewski brings experience in time dependent problems, spectral methods and internal waves. |
| Collaborator Contribution | This partnership involves the complementary analysis/numerical skills between Milewski's group at Bath and Vanden-Broeck's group at UCL. Vandal-Broeck brings experience in nonlinear free-boundary steady problems and numerical methods. |
| Impact | See joint publications. |
| Start Year | 2011 |
| Description | UEA - Dr. E. Parau |
| Organisation | University of East Anglia |
| Country | United Kingdom |
| Sector | Academic/University |
| PI Contribution | This partnership involves the complementary analysis/numerical skills between Milewski's group at Bath and Parau's group at UEA. Milewski brings experience in time dependent problems, spectral methods and internal waves. |
| Collaborator Contribution | This partnership involves the complementary analysis/numerical skills between Milewski's group at Bath and Parau's group at UEA. Parau brings experience in three dimensional boundary integral methods and free boundary problems. |
| Impact | see publications |
| Start Year | 2011 |