Conference on water waves at the Newton Institute
Thursday 15 December 2011
The Newton Institute has awarded funding for a four-week programme on the theory of water waves to be held in July 2014. The organisers are Tom Bridges (Surrey), Mark Groves (Saarbrucken), Paul Milewski (Bath) and David Nicholls (Chicago).
Water waves are a dramatic, potentially dangerous, yet beautiful phenomena that are omnipresent and impact every aspect of life on the planet. At the 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 well understood, and there has been a wide range of research into the equations. However, the equations are highly nonlinear, and the level of difficulty is so great that theory has yet to only 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. The open problems are 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 focussed conference on water waves.
This conference will bring together 30-40 of the world's leading researchers in the theory of water waves. Some of the research themes to be studied at the conference are existence theories, stability of waves, pattern formation on the ocean surface, numerical methods for waves, theories for wave breaking, rogue waves and other extreme events, Hamiltonian, Lagrangian and other variational principles, differential geometry of the sea surface, the exchange of information between the sea surface and atmosphere, and the role of unsteadiness and three-dimensionality.