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Monday 12th December 2022

Møller Institute

United Kingdom

This hybrid Open for Business event focused on applications of Dispersive Hydrodynamics related to Optics, Oceanography and Magnetism with an aim to bring together mathematicians and scientists working at the forefront of dispersive hydrodynamics and its applications, with end users from industry to further investigate potential connections.


Dispersive Hydrodynamics is a mathematical framework originally developed to describe multiscale nonlinear wave phenomena in dispersive media. This framework has further expanded and currently covers a range of phenomena including both dynamic and stochastic aspects of wave propagation. It is now a vibrant and continuously developing field, with a variety of physical applications.
Important progress has been made over the last two decades in the understanding and applications of nonlinear optical phenomena, from latest generation optical fibres and optical waveguides to atomic physics, each relying on a mathematical description where the electromagnetic field is interpreted as a fluid flow and its behaviour is determined by equations of hydrodynamic type with dispersion.
The mathematical analysis, such as the multiscale asymptotic study of solutions in some special regimes, provides guidance and inspiration for novel and challenging experiments, often pushing the boundary of experimental accuracy, where mathematical theoretical predictions meet their counterpart in the real world. Conversely, the explosion of experiments in the field of optics and photonics, often driven by the growing investment of resources in the fast communications sector, has stimulated the theoretical investigation of mathematical models aimed at identifying physical regimes where solutions with certain features may exist. Methods and techniques from dispersive hydrodynamics allow one to make effective predictions on the observability of those solutions via nonlinear Fourier transform, various perturbations analyses and modulation theory. For instance, celebrated rogue waves, which also appear in nonlinear optical fibres, are a nonlinear consequence of modulational instability of linear waves. More generally, the subject of statistical nonlinear optics deals with random waves in optical propagation where the dispersive hydrodynamic concepts of weak (wave) and strong (soliton) turbulence play an important role.
Oceanography provides a vast area for applications of methods of dispersive hydrodynamics and is a natural a source of new, important and challenging mathematical problems. The phenomena of interest include undular bores, shoaling tsunamis, rogue waves, wind-wave interactions and more. Understanding nonlinear internal waves in the ocean is paramount for several industry sectors including maritime and ocean transport and oil extraction infrastructures as working offshore requires the capacity to predict the occurrence of large waves and to assess their impact on structures and pipe lines. Submersibles routinely communicate using sound signals which are hugely distorted by internal waves. Recent studies are also providing increasing evidence that internal undular bores play an essential role in ocean mixing processes and in the energy budgets of tidal flows, thus affecting the Earth’s climate. Ocean waves are also a natural source of renewable energy.
Other prominent applications include magnetisation dynamics, Bose-Einstein condensates, cooperative and granular systems, and dynamics of porous media.
This knowledge exchange day was part of a six month research programme at the Isaac Newton Institute on Dispersive hydrodynamics: mathematics, simulation and experiments, with applications in nonlinear waves. In particular, this event followed on from Workshop 5: Physical applications, which focused on exposing the underlying mathematical similarities between phenomena which occur on vastly different scales, bringing together applied mathematicians, Physicists and Engineers that share similar mathematical models.

Aims and Objectives

The aim of this event was to bring together mathematicians and scientists working at the forefront of dispersive hydrodynamics and its applications, with end users from industry to further investigate potential connections. In particular, this event will focus on physical applications of dispersive hydrodynamics related to fluid dynamics including oceanic phenomena and nonlinear optics.
This workshop featured a series of talks that cover three main session themes:

  1. Optics
  2. Oceanography
  3. Other Applications

The Programme is available.


For those attending in person, there was the opportunity to present a poster. 

Registration and Venue

Regiatrations for this event are now closed. 

The workshop took place at the Møller Institute, Churchill College, Cambridge.