M V Budyansky | PubMed Health

PubMed2006

Clustering in randomly driven Hamiltonian systems.

The motion of oscillatorylike nonlinear Hamiltonian systems, driven by a weak noise, is considered. A general method to find regions of stability in the phase space of a randomly driven system, based on a specific Poincaré map, is proposed and justified. Physical manifestations of these regions of stability are coherent clusters. We illustrate the method and demonstrate the appearance of coherent clusters with two models motivated by the problems of waveguide sound propagation and Lagrangian mixing of passive scalars in the ocean. We find bunches of sound rays propagating coherently in an underwater waveguide through a randomly fluctuating ocean at long distances. We find clusters of passive particles to be advected coherently for a comparatively long time by a random two-dimensional flow modeling mixing around a fixed vortex.

Journal Article↗

PubMed2006

Chaotic mixing and transport in a meandering jet flow.

Mixing and transport of passive particles are studied in a simple kinematic model of a meandering jet flow motivated by the problem of lateral mixing and transport in the Gulf Stream. We briefly discuss a model stream function, Hamiltonian advection equations, stationary points, and bifurcations. The phase portrait of the chosen model flow in the moving reference frame consists of a central eastward jet, chains of northern and southern circulations, and peripheral westward currents. Under a periodic perturbation of the meander's amplitude, the topology of the phase space is complicated by the presence of chaotic layers and chains of oscillatory and ballistic islands with sticky boundaries immersed into a stochastic sea. Typical chaotic trajectories of advected particles are shown to demonstrate a complicated behavior with long flights in both the directions of motion intermittent with trapping in the circulation cells being stuck to the boundaries of vortex cores and resonant islands. Transport is asymmetric in the sense that mixing between the circulations and the peripheral currents is, in general, different from mixing between the circulations and the jet. The transport properties are characterized by probability distribution functions (PDFs) of durations and lengths of flights. Both the PDFs exhibit at their tails power-law decay with different values of exponents.

Models, Statistical↗