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Programme theme
Water waves are a dramatic, potentially dangerous, yet beautiful phenomena that is omnipresent and impacts every aspect of life on the planet. At smaller length scales the ripples driven by surface tension affect remote sensing. At intermediate length scales waves in the mid-ocean affect shipping and near the shoreline they control the coastal morphology and the ability to navigate along shore. At larger length scales waves such as tsunamis and hurricane-generated waves can cause devastation on a global scale. Across all length scales an exchange of momentum and thermal energy between ocean and atmosphere occurs affecting the global weather system and the climate.
From a mathematical viewpoint water waves pose rich challenges.The governing equations for water waves are a widely accepted model and they have been the subject of a wide range of research. However, the equations are highly nonlinear and the level of difficulty is so great that theory has yet to scratch the surface of the subject. The solutions to the equations that describe fluid motion are elusive and whether they even exist in the most general case is one of the most difficult unanswered questions in mathematics.
On the other hand, there is good reason to be buoyant about the headway that mathematics can make in tackling the great open problems posed by water waves. In light of recent developments the questions are now clearer, new methodologies are emerging, computational approaches are becoming much more sophisticated and the number of researchers at the highest international level involved is growing. All these indicators point to an opportune time to have a focused conference on water waves. Particular themes will include:
The initial-value problem (IVP)
- Well-posedness, theory in two versus three dimensions,Lagrangian versus Eulerian formulations
- Vortex sheet formulations, singularities
- Numerical methods for the IVP, simulations
- Theoretical aspects of wave breaking
Existence and classification of waves
- Traveling waves in two and three dimensions
- Periodic, multi-periodic, and localized patterns
- Surface waves versus interfacial waves
- Numerical methods for steady waves and their bifurcations
- Nonlinear time-periodic waves: Standing waves and beyond
Linear and nonlinear stability of waves
- Stability and instability of the waves mentioned above (e.g., periodic and multi-periodic traveling waves, localized traveling waves, standing waves)
- Beyond (symmetric) short-crested waves: Stability of genuinely three-dimensional traveling waves.
- Wave interactions
- Rogue waves and other extreme events
- Energetic stability
Dynamical systems and geometric techniques
- Hamiltonian and Lagrangian formulations, variational principles
- Center-manifold reduction, spatial dynamics, and generalizations
- Differential geometry of the sea surface
- The effect of bottom topography
Beyond irrotational flow
- Waves with vorticity
- Weakly viscous potential flow
- Waves with forcing and dissipation
Click here to download the programme's final scientific report
Preprints
| Title | Year | Programme |
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Well-posedness of two-dimensional hydroelastic wavesAuthors: David Ambrose, M Siegel |
2014 | TWW |
Seminars
| Monday 14th July 2014 | |||
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| 10:00 to 11:00 | Room 2 | 
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| 11:00 to 12:00 | Room 2 |
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| 13:00 to 14:00 | Room 2 |
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| 14:00 to 15:00 | Room 2 |
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| 15:30 to 16:30 | Room 2 |
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| 16:30 to 17:30 | Room 2 |
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| Tuesday 15th July 2014 | |||
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| 09:30 to 10:30 | Room 2 |
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| 11:00 to 12:00 |
Short Course: The Unified Transform and Boundary Value Problems: I |
Room 2 |
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| 13:00 to 14:00 | Room 2 |
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| 14:00 to 15:00 | Room 2 |
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| 15:30 to 16:30 |
New nonsymmetric gravity-capillary solitary waves and related problems |
Room 2 |
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| Wednesday 16th July 2014 | |||
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| 09:30 to 10:30 |
Short Course: High Order Perturbation of Surfaces (HOPS) Methods for Water Waves: II |
Room 2 |
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| 11:00 to 12:00 |
Short Course: The Unified Transform and Boundary Value Problems: II |
Room 2 |
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| 13:00 to 14:00 | Room 2 |
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| 14:00 to 15:00 |
Stability of periodic travelling waves of the water wave problem in one dimension |
Room 2 |
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| 15:30 to 16:30 | Room 2 |
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| 16:30 to 17:30 | Room 2 |
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| Thursday 17th July 2014 | |||
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| 09:30 to 10:30 |
Short Course: High Order Perturbation of Surfaces (HOPS) Methods for Water Waves: III |
Room 2 |
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| 11:00 to 12:00 |
Short Course: The Unified Transform and Boundary Value Problem: III |
Room 2 |
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| 15:00 to 16:00 |
Dynamics of critical layer in turbulent shear flows above unsteady water waves |
Room 1 |
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| 16:00 to 17:00 |
New results on wind driven waves and negative tsunami waves at coastlines |
Room 1 |
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| 17:00 to 18:00 | No Room Required | ||
| Friday 18th July 2014 | |||
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| 09:30 to 10:30 |
Short Course: High Order Perturbation of Surfaces (HOPS) Methods for Water Waves: IV |
Room 2 |
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| 13:00 to 14:00 | Room 2 | ||
| 14:00 to 15:00 | Room 2 |
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| 15:30 to 16:30 |
Finite element method for nonlinear free surfaces water waves |
Room 2 |
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| Tuesday 22nd July 2014 | |||
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| 09:30 to 14:00 | Discussion Room | ||
| 14:00 to 15:00 | Room 2 |
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| 15:00 to 16:00 | Room 2 |
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| 16:30 to 17:30 | Room 2 |
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| Wednesday 23rd July 2014 | |||
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| 10:30 to 11:10 | No Room Required | ||
| 11:10 to 11:15 | No Room Required | ||
| 11:15 to 12:00 | Room 1 | ||
| 12:00 to 14:00 | No Room Required | ||
| 14:00 to 14:45 | Room 1 |
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| 14:45 to 15:30 | Room 1 |
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| 15:30 to 16:15 | No Room Required | ||
| 16:15 to 17:00 | Room 1 |
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| 17:00 to 18:00 | No Room Required | ||
| Thursday 24th July 2014 | |||
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| 11:00 to 12:00 | Room 1 |
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| 12:00 to 12:30 | Room 1 |
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| 14:00 to 15:00 | Room 2 |
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| 15:00 to 16:00 | Room 2 |
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| Monday 28th July 2014 | |||
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| 14:00 to 15:00 | Room 1 |
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| Tuesday 29th July 2014 | |||
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| 14:00 to 15:00 |
Resonance curves of finite-amplitude gravity waves in shallow-water limit |
Room 2 |
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| 15:00 to 16:00 |
Maximum finite depth waves: breaking, kinematics and particle drift |
Room 2 | |
| 16:30 to 17:30 |
Impacts from highly nonlinear waves on walls and substructures of wind turbines |
Room 2 |
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| Wednesday 30th July 2014 | |||
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| 14:10 to 14:40 |
Ocean Wave Measurements: The Challenges and Consequences for the Wave Energy Industry |
Room 1 |
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| 15:00 to 15:30 | No Room Required | ||
| 16:00 to 16:30 |
100-year and 10,000-year Extreme Significant Wave Heights - How Sure Can We Be of These Figures? |
Room 1 |
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| Thursday 31st July 2014 | |||
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| 14:00 to 15:00 | Room 2 |
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| 15:00 to 16:00 |
Global bifurcation for steady gravity water waves with constant vorticity and critical layers |
Room 2 |
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| 16:30 to 17:30 |
Hydrodynamic Surface Wave Analogues for Quantum Mechanics and Nonlinear Optics |
Room 1 |
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| Tuesday 5th August 2014 | |||
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| 14:00 to 15:00 |
Changing forms and sudden smooth transitions of tsunami waves |
Room 2 |
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| 15:00 to 16:00 |
Why bouncing droplets are a pretty good model of quantum mechanics |
Room 2 |
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| 16:30 to 17:30 | Room 2 |
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| Wednesday 6th August 2014 | |||
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| 09:15 to 09:45 | No Room Required | ||
| 09:45 to 10:00 | No Room Required | ||
| 10:00 to 12:30 |
Initial Value Problem and Vortex Sheets: Analysis and Computation |
No Room Required | |
| 14:00 to 15:00 | No Room Required | ||
| 15:00 to 15:30 | No Room Required | ||
| 15:30 to 16:30 | No Room Required | ||
| 16:45 to 17:45 | No Room Required | ||
| Thursday 7th August 2014 | |||
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| 10:00 to 12:30 | No Room Required | ||
| 12:30 to 13:30 | No Room Required | ||
| 14:00 to 15:00 | No Room Required | ||
| 15:00 to 15:30 | No Room Required | ||
| 15:30 to 16:30 | No Room Required | ||
| 19:30 to 22:00 | No Room Required | ||
| Friday 8th August 2014 | |||
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| 10:00 to 12:30 |
Variational Water Waves: on Continuum and Discrete Modelling, and Experimental Validation |
No Room Required | |
| 14:00 to 15:00 | No Room Required | ||
| 15:00 to 15:30 | No Room Required | ||
| 15:30 to 16:30 | No Room Required | ||
Organisers
- Tom Bridges University of Surrey
- Mark Groves Loughborough University
- Paul Milewski Aalborg Universitet
- David Nicholls University of Notre Dame
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