Bookcover of Adiabatic Chaos and Transport in Geophysical Fluid Flows
Booktitle:

Adiabatic Chaos and Transport in Geophysical Fluid Flows

Geometric Criterion for Lagrangian Coherent Structures

LAP LAMBERT Academic Publishing (2019-06-14 )

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ISBN-13:

978-620-0-11655-0

ISBN-10:
6200116555
EAN:
9786200116550
Book language:
English
Blurb/Shorttext:
Advances in our understanding of the dynamics of mesoscale eddies and vortex rings of the Gulf Stream have been based on modons which are nonlinear Rossby solitary wave solutions of quasigeostrophic equations. This dissertation focuses primarily on geometric singular perturbation theory and Melnikov techniques to address the problem of adiabatic chaos and transport for translating and rotating modons to the quasigeostrophic potential vorticity system. A very general and central question is what hypotheses on the equations and singular solutions guarantee that the solutions approximate some solutions for the perturbed quasigeostrophic potential vorticity system. We present a geometric approach to the problem which gives more refined a priori energy type estimates on the position of the invariant manifold and its tangent planes as the manifold passes close to a normally hyperbolic piece of a slow manifold. We apply Melnikov technique to show that the Poincare map associated with modon equations has transverse heteroclinic orbits. We appeal to the Smale-Birkhoff Theorem and KAM Theorem for onset of chaos in slowly varying perturbations of multi-degree-of-freedom Hamiltonian systems.
Publishing house:
LAP LAMBERT Academic Publishing
Website:
https://www.lap-publishing.com/
By (author) :
Maleafisha Joseph Pekwa Stephen Tladi
Number of pages:
148
Published on:
2019-06-14
Stock:
Available
Category:
Mathematics
Price:
40.90 €
Keywords:
Wave-Current Interactions, Dynamical Systems and Turbulence, Melnikov Method, Lagrangian and Eulerian Analysis, Atmospheric and Oceanic Dynamics, Rotating Stratified Fluid Flow, Geophysical Fluid Flow, Rotating Boussinesg And Quasigeostrophic Equations, Lagrangian Coherent Structures, Well-Posedness and Long-Time Dynamics, Energy-Phase Method, Geometric Singular Perturbation Theory

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