# The Azimuth Project Nonlinear science (Rev #16, changes)

Showing changes from revision #15 to #16: Added | Removed | Changed

# Contents

## Idea

To have an Azimuth springboard to this increasingly growing field, which currently encompasses:

just to mention the major research subfields.

## Details and environmental scientific usage

### Capsule History

Many of these areas have arised from questions in dynamics of earth and its atmosphere like three-body collisions which is what got Poincare’ to spin-off topology, and later physics researcher n-body simulations. Lorenz who found strange attractors in the weather models he used.

towards instability with laminar flow:

Kelvin and Helmholtz with their instability theory as an precursor and predictor of turbulence. Mandelbrot who finds fractals in many places in both natural and anthropogenic phenomena.You know you are dealing with a nonlinear system if the output is not proportional to the input data.

### Chaos

Applied or originated in some research fields like climate modeling,

### Solitons

They are almost ubiquitous and exists in size from $10^{-7} - 10^10$. Used in modeling Rossby solitons and they might also be important in rogue waves like the Draupner wave. But they are not suitable to tsunami/tidal wave modeling

## References

Abstract: We have numerically calculated chaotic waves of the focusing nonlinear Schrodinger equation (NLSE), starting with a plane wave modulated by relatively weak random waves. We show that the peaks with highest amplitude of the resulting wave composition (rogue waves) can be described in terms of exact solutions of the NLSE in the form of the collision of Akhmediev breathers.

Abstract: Large-amplitude internal solitary waves (or ‘‘solitons’’) occurring in packets near the shelf break in the Bay of Biscay are well-documented and understood. The presence of similar features has now also been reported in the central Bay, E150 km from the nearest shelf break topography. The present paper analyses available remote-sensing synthetic aperture radar (SAR) data from the ERS satellites in this region. By doing so, we are able to provide convincing support for the hypothesis that these waves, instead of having travelled along the thermocline from the shelf break, are instead generated locally in the central Bay by the surfacing of a beam of internal tidal energy originating from the shelf break. This reinforces the results of a previous independent study, while at the same time providing a much more extensive investigation than was then possible. We have also exploited the large swath width (100 km) and high spatial resolution (100m100m) of the SAR to examine for the ﬁrst time the full surface structure of the internal waves in the central Bay, which are found to have a mean wavelength of 1.35 km, and a mean along-crest ‘‘coherence’’ length of 21.55 km.

• N. Akhmediev,M. Soto-Crespo, A. Ankiewicz [How to excite a rogue wave+(http://physics.aps.org/pdf/10.1103/PhysRevA.80.043818.pdf)]

We propose initial conditions that could facilitate the excitation of rogue waves. Understanding the initial conditions that foster rogue waves could be useful both in attempts to avoid them by seafarers and in generating highly energetic pulses in optical ﬁbers

category: methodology, climate