Related papers: Passive Scalars and Three-Dimensional Liouvillian …
Laminar-turbulent intermittency is intrinsic to the transitional regime of a wide range of fluid flows including pipe, channel, boundary layer and Couette flow. In the latter turbulent spots can grow and form continuous stripes, yet in the…
A model of the passive vector field advected by the uncorrelated in time Gaussian velocity with power-like covariance is studied by means of the renormalization group and the operator product expansion. The structure functions of the…
We study Hamiltonian flows in a real separable Hilbert space endowed with a symplectic structure. Measures on the Hilbert space that are invariant with respect to the flows of completely integrable Hamiltonian systems are investigated.…
Lie scale invariance is used to reduce the incompressible Navier-Stokes equations to non-linear ordinary equations. This yields a formulation in terms of logarithmic spirals as independent variables. We give the equations when the spirals…
Interactions between an internal flow and wall deformation occur in many biological systems. Such interactions can involve a complex and rich dynamical behavior and a number of peculiarities which depend on the flow parameter range. The aim…
Area preserving maps provide the simplest and most accurate means to visualize and quantify the behavior of nonlinear systems. Convenience of the mapping equations of motion for investigation of transition to chaotic behavior in dynamics of…
We study statistical properties of turbulent inverse cascades in a class of nonlinear models describing a scalar field transported by a two-dimensional incompressible flow. The class is characterized by a linear relation between the…
In the Eulerian approach, the motion of an incompressible fluid is usually described by the velocity field which is given by the Navier--Stokes system. The velocity field generates a flow in the space of volume-preserving diffeomorphisms.…
In this paper we construct a new class of surfaces whose geodesic flow is integrable (in the sense of Liouville). We do so by generalizing the notion of tubes about curves to 3-dimensional manifolds, and using Jacobi fields we derive…
Advective transport of scalar quantities through surfaces is of fundamental importance in many scientific applications. From the Eulerian perspective of the surface it can be quantified by the well-known integral of the flux density. The…
We discuss the time evolution of a two-dimensional active scalar flow, which extends some properties valid for a two-dimensional incompressible nonviscous fluid. In particular we study some characteristics of the dynamics when the field is…
A general link between geometry and intermittency in passive scalar turbulence is established. Intermittency is qualitatively traced back to events where tracer particles stay for anomalousy long times in degenerate geometries characterized…
For a continuous map on the unit interval or circle, we define the bifurcation set to be the collection of those interval holes whose surviving set is sensitive to arbitrarily small changes of their position. By assuming a global…
Previous works have been devoted to the study of two-dimensional noninvertible maps, obtained using a coupling between one-dimensional logistic maps. This paper is devoted to the study of a specific one, in order to complete previous…
We consider evolution of a passive scalar (concentration of pollutants or temperature) in a chaotic (turbulent) flow. A universal asymptotic behavior of the passive scalar decay (homogenization) related to peripheral regions (near walls) is…
Invariant manifolds are fundamental tools for describing and understanding nonlinear dynamics. In this paper, we present a theory of stable and unstable manifolds for infinite dimensional random dynamical systems generated by a class of…
We study the Rayleigh-Taylor instability for two miscible, incompressible, inviscid fluids. Scale-invariant estimates for the size of the mixing zone and coarsening of internal structures in the fully nonlinear regime are established…
We develop a general theory of transport barriers for three-dimensional unsteady flows with arbitrary time-dependence. The barriers are obtained as two-dimensional Lagrangian Coherent Structures (LCSs) that create locally maximal…
Invariant tori are prominent features of symplectic and volume preserving maps. From the point of view of chaotic transport the most relevant tori are those that are barriers, and thus have codimension one. For an $n$-dimensional…
The advection-diffusion equation is studied via a global Lagrangian coordinate transformation. The metric tensor of the Lagrangian coordinates couples the dynamical system theory rigorously into the solution of this class of partial…