Experiments confirm 35 year old theory of periodic rogue waves
Experiments in optics have confirmed a 35 year old theory predicting that intense nonlinear waves can
evolve periodically. This result may point to a previously unsuspected class of rogue wave behavior on
the ocean.
Rogue waves are giant oceanic walls of water that appear seemingly from nowhere and which have been
associated with numerous maritime catastrophes. The science of these unusual and destructive events is a
hot topic of research in physics, and one explanation being intensely studied is that of nonlinear
amplification described by a model known as the nonlinear Schrödinger equation (NLSE). In this model,
noise on the ocean’s surface of a particular kind can be amplified to form a large amplitude wave that
grows rapidly, sucking energy from the background to grow to high intensity before decaying just as
rapidly back to its initial state.
Interestingly, it is also possible to study nonlinear rogue wave evolution by measuring the propagation of
light in an optical fiber, and researchers have this month reported highly significant results in the journal
Scientific Reports that may point to a previously unsuspected class of periodic rogue wave behavior.
Using advanced optical fiber technology, the researchers were able to confirm a theory of periodic
evolution in the NLSE which was first derived in 1977 by Professor Evgeny Kuznetsov using the
advanced mathematical technique known as “inverse scattering.” His periodic solution is now known as
the Kuznetsov-Ma or “KM Soliton” but although the calculations are complex, the result is simple to
write down. This is important as it was then easy for the researchers to compare the measured growth and
decay of the KM soliton and confirm Kuznetsov’s theory.
These results are novel because they suggest that the giant rogue waves on the ocean may not always be
singular isolated events, but could sometimes appear in regular wave trains. Perhaps this is a previouslyunsuspected class of rogue wave event? Of course this will need further testing, especially in the natural
hydrodynamic environment, and effects of loss will need to be carefully considered. These results will
also be presented in a symposium at UCD next week organized by the International Union of Theoretical
and Applied Mechanics (IUTAM). Of particular interest will be the fact that Professor Kuznetsov, as
well as mathematics pioneer Professor Vladimir Zakharov who invented the inverse scattering technique
itself, will both be attending the symposium in person.
The research was carried out as part of an international effort to understand these dynamics funded by the
French National Research Agency and the European Research Council MULTIWAVE project involving
Professor Frederic Dias from UCD Dublin, Ireland and Professor John Dudley from Besançon in France.
The journal Scientific Reports is an open access primary research publication from the publishers of
Nature, covering all areas of the natural sciences.
References:
B. Kibler et al. Observation of Kuznetsov-Ma soliton dynamics in optical fibre
Scientific Reports 2: 463. DOI:10.1038/srep00463
http://www.nature.com/srep/2012/120618/srep00463/full/srep00463.html
E. Kuznetsov, Solitons in a parametrically unstable plasma
Sov. Phys. Dokl. 22, 507–508 (1977)
[email protected]
[email protected]
[+35317162559]
[+33670361732]
Contacts:
Professor Frédéric Dias
Professor John Dudley
Event:
IUTAM Symposium 2012: Understanding Common Aspects of Extreme Events in Fluids
University College Dublin, Ireland Monday, July 2nd - Friday, July 6th 2012
Kuznetsov’s 1977 theory may suggest that rogue waves propagate periodically.