June 24, 2024


April 29-June 28, 2013
Thematic Program on the
Mathematics of Oceans
Fields Institute, 222 College St., Toronto (Map)
W. Craig (McMaster University), D. Dutykh (University College-Dublin, and CNRS)
D. Henderson (Pennsylvania State University), K. Lamb (University of Waterloo)
M. Onorato (Università di Torino), E. Pelinovsky (Russian Academy of Sciences)
C. Sulem (University of Toronto)

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Fields Institute program on the Mathematics of Oceans is to take place in the year 2013 as a part of the initiative for the Mathematics of Planet Earth.

Overview of the Program

Humankind has always had a fascination with the sea, and advances in civilisation are closely connected with man's enterprises on the oceans. The topic of nonlinear waves has its origin in the study of surface water waves, which have relevant applications to both coastal engineering and naval architecture. The study of global currents in the Earth's oceans is a topic of importance to the question of climate stability. Finally, statistical descriptions of nonlinear processes, such as the wave motion of the sea, are similar to models widely used in quantum field theory and Navier-Stokes turbulence. Furthermore they are currently in use in sea state weather prediction, for example in the North Atlantic, and are therefore relevant to the enterprise of shipping and global supply chains. All of the above topics are associated with major advances in mathematics, and as well with major open problems of current interest and mathematical activity.

The purpose of this Fields Institute program is to bring mathematical analysts and applied mathematicians together, along with practicing ocean scientists, to discuss the recent points of progress of these two domains. Furthermore, our goals are to bring these two communities into contact with ocean scientists, in a venue in which they can articulate the results of their recent progress, and ideally to understand its importance and/or relevance to genune oceanographic applications. There are three principal themes for this program:
(1) nonlinear ocean wave dynamics, including extreme wave dynamics such as rogue waves and tsunamis,
(2) oceanic circulation and ocean-atmosphere interaction, including global scale phenomena such as the meridional overturning circulation and currents such as the Gulf Stream, mesoscale processes described by quasi-geostrophic flows, as well as highly nonlinear submesoscale processes, including their role in the stability of the earth's climate, and the impact of their variations; and
(3) wave interactions and turbulence, including statistical descriptions of ocean wave spectra and its role in predictions of sea state and weather.

The Program will involve cooperation with AARMS, the Bedford Institute of Oceanography (Dartmouth, NS), and the Institute of Ocean Sciences (Sydney, BC).

Program Activities

Coxeter Lecture Series

May 7,9,10, 2013 at 3:30 p.m.
Vladimir Zakharov,
University of Arizona
Wind-driven sea as a subject for theoretical physics

Location: Stewart Library, Fields Institute



May 13 - 16

Short Course on Modeling of Nonlinear ocean waves
Wooyoung Choi (NJIT), Roberto Camassa (North Carolina at Chapel Hill), Denys Dutykh (University College Dublin), Claudio Viotti (University College Dublin)

June 17 - 20

Short Course on Stochastic Fluid Dynamics
Armen Shirikyan (Universite de Cergy - Pontoise), Vladimir Zeitlin (Laboratoire de Meteorology Dynamique, ENS - Paris)

June 23 - 27
Short Course on Hamiltonian PDEs and water waves
Walter Craig (McMaster), David Lannes (Ecole Normale Supereure), Catherine Sulem (Toronto)


May 6-11, 2013
Workshop on Ocean Wave Dynamics
Organizing Committee: Walter Craig (McMaster), Diane Henderson (Penn State), Miguel Onorato (Universita di Torino), Efim Pelinovsky (Russian Academy of Sciences), C. Sulem (Toronto)
On Thursday May 9 there will be a Special Session on Air-Ocean Interactions organized by Diane Henderson (Penn State University).

May 20-24, 2013
Workshop on Wave Interactions and Turbulence
Organizing Committee: Walter Craig (McMaster), Sergei Kuksin (Ecole Polytechnique, Palaiseau), Sergey Nazarenko (Warwick), Efim Pelinovsky (Russian Academy of Sciences), Catherine Sulem (Toronto)

June 11-14, 2013
Workshop on Sub-mesoscale Ocean Processes
Organizing Committee: Kevin Lamb (Waterloo), Francis Poulin (Waterloo)

Location: Fields Institute

Time Speaker and Abstract

June 26, Wednesday
2:00 p.m. - 3:00 p.m.
Room 230

Leo Maas (NIOZ Royal Netherlands Institute for Sea Research & IMAU, Utrecht University)
Waves and wave attractors in geophysical flows (lecture notes)
May 30, Thursday
2:00 p.m. - 3:00 p.m.
Stewart Library
Jean-Marc Delort (Ecole Normale Superieure, Paris)
Global solutions of water waves equations in 1 dimension

We prove global existence and modified scattering in physical space for solutions of the one dimensional water wave equation, with smooth, small and rapidly decaying Cauchy data. The proof relies on the one hand on the use of the "good unknown" of Alinhac and normal forms to establish ${L^2}$ estimates. On the other hand, ${L^{\infty}}$ bounds are obtained combining Klainerman vector fields and semi-classical analysis to deduce from the PDE an ODE allowing one to get the asymptotics of the solution. (Joint work with Thomas Alazard).

May 15, Wednesday
2:00 p.m. - 3:00 p.m.
Stewart Library
Christophe Lacave (l'université Paris-Diderot)
Some Elliptic Tools for Inviscid Fluids

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