Geophysical Fluid Dynamics and Scalar Transport in the Tropics
 

(13 Nov - 8 Dec 2006)

~ Abstracts ~

Geophysical fluid dynamics
Djoko Wirosoetisno, University of Durham, UK

• Introduction: why Hamiltonian?
• Review of Lagrangian and Hamiltonian mechanics
   • Variational principle of mechanics
   • Symplectic structure
   • Symmetries, conservation laws and adiabatic invariance
• An example: the free rigid body
   • Kinematics: rotating frames
   • Dynamics: the free rigid body
   • Reduction: the Euler equations
• Hamiltonian models of fluid dynamics
   • Hamilton’s principle for PDEs
• More on Hamiltonian fluid dynamics
   • Continuous symmetries o Lagrangian description of fluid dynamics
   • Particle-relabelling symmetry and reduction
• Nonlinear hydrodynamic stability (*qualitative treatment)
 

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Chaotic and turbulent scalar transport
Bernard Legras, Ecole Normale Supérieure, France

• Introduction
   •Why transport and mixing is important for the distribution of chemical and biological compounds in
     geophysical flows?
   •The 2D approximation and limits to its validity
• Theories of the passive scalar transport
   •Statistical theory
       •Taylor dispersion, diffusive limit
       •Anomalous transport
       •Batchelor model, Lyapunov exponents
       •The modern theory of transport
   •Deterministic theory
       •Hamiltonian formulation
       •Periodic flows and Poincare maps
       •KAM theorem and its consequences
• Theories at work with real flows
   •Deterministic approach to the case of non periodic flows
   •Transport barriers
       •Effective diffusivity
       •Transverse Lyapunov exponent
   •Applications to geophysical flows (atmosphere, ocean, Earth mantle)

 

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