IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence

This work brings together previously unpublished notes contributed by participants of the IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence (Moscow, 25-30 August 2006). The study of vortex motion is of great interest to fluid and gas dynamics: since all real flows are vortical in nature, applications of the vortex theory are extremely diverse, many of them (e.g. aircraft dynamics, atmospheric and ocean phenomena) being especially important. The last few decades have shown that serious possibilities for progress in the research of real turbulent vortex motions are essentially related to the combined use of mathematical methods, computer simulation and laboratory experiments. These approaches have led to a series of interesting results which allow us to study these processes from new perspectives. Based on this principle, the papers collected in this proceedings volume present new results on theoretical and applied aspects of the processes of formation and evolution of various flows, wave and coherent structures in gas and fluid. Much attention is given to the studies of nonlinear regular and chaotic regimes of vortex interactions, advective and convective motions. The contributors are leading scientists engaged in fundamental and applied aspects of the above mentioned fields.

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Contenu
Vortex Dynamics: The Legacy of Helmholtz and Kelvin.- Vortex Dynamics of Wakes.- Vorticity Equation of 2D-Hydrodynamics, Vlasov Steady-State Kinetic Equation and Developed Turbulence.- A New Integrable Problem of Motion of Point Vortices on The Sphere.- Nonintegrability and Fractional Kinetics Along Filamented Surfaces.- Two-Dimensional Turbulence on A Bounded Domain.- Analogy of A Vortex-Jet Filament With The Kirchhoff Elastic Rod and Its Dynamical Extension.- Adiabatic Invariance in Volume-Preserving Systems.- Unstable-Periodic-Flow Analysis of Couette Turbulence.- Motion of an Elliptic Vortex Ring and Particle Transport.- Hetonic Quartet: Exploring the Transitions in Baroclinic Modons.- Dynamics of a Solid Affected by a Pulsating Point Source of Fluid.- Phase Transitions to Superrotation in a Coupled FluidRotating Sphere System.- Vortex Kelvin Modes with Nonlinear Critical Layers.- Non-Divergent 2D Vorticity Dynamics and the Shallow Water Equations on the Rotating Earth.- High-Dimensional Hamiltonian Dynamical Systems: Theory and Computational Realization for Theoretical Chemistry.- On Statistical Mechanics of Vortex Lines.- Numerical Verification of Weakly Turbulent Law of Wind Wave Growth.- The Size Distribution Function For Mixed-Layer Thermals in The Convective Atmosphere.- Families Of Translating Neutral Vortex Street Configurations.- Lagrangian Flow Geometry of Tripolar Vortex.- Clustering and Mixing of Floating Particles by Surface Waves.- Resolution of Near-Wall Pressure in Turbulence on the Basis of Functional Approach.- Triplet of Helical Vortices.- Long-Wave Transition To Instability of Flows in Horizontally Extended Domains of Porous Media.- Non-Dissipative and Low-Dissipative Shocks with Regular and Stochastic Structures in Non-Linear Media WithDispersion.- Hyperchaos in Piezoceramic Systems with Limited Power Supply.- About Analytic Solvability of Nonstationary Flow of Ideal Fluid with a Free Surface.- Nonintegrable Perturbations of Two Vortex Dynamics.- Rossby Solitary Waves in the Presence of a Critical Layer.- Adjustment of Lens-Like Stratified Axisymmetric Vortices to Pulsons.- Evolution of an Intense Vortex in a Periodic Sheared Flow.- Vortex Interaction in an Unsteady Large-Scale Shear/Strain Flow.- Modified Shallow Water Equations. Simple Waves and Riemann Problem.- Estimation of Optimal for Chaotic Transport Frequency of Non-Stationary Flow Oscillation.- A Unified Linear Wave Theory of the Shallow Water Equations on a Rotating Plane.- Chaotic Advection and Nonlinear Resonances in a Periodic Flow above Submerged Obstacle.- Trapped Vortex Cores in Internal Solitary Waves Propagating in a Thin Stratified Layer Embedded in a Deep Homogeneous Fluid.- On the Stability of Stratified Quasi-Geostrophic Currents with Vertical Shear above Isolated Topographic Features.- Dynamics of Two Rings of Vortices on a Sphere.- On the Motion of Two Mass Vortices in Perfect Fluid.- Rubber Rolling: Geometry and Dynamics of 2-3-5 Distributions.- On the Motion of A + 1 Vortices in a Two-Layer Rotating Fluid.- Cascades of Period Multiplying in the Planar Hill's Problem.