The Azimuth Project
Nonlinear science (Rev #13, changes)

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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,

Fractals and multifractals

Complex adaptive systems

Pattern Formation

Solitons

Used in modeling Rossby solitons and they might also be important in rogue waves s like theDraupner wave. But they are not suitable to tsunami/tidal wave modeling

References

Abstract: We have numerically calculated chaotic waves of the focusing nonlinear Schr¨rodinger 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. © 2009 Elsev

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.

category: methodology