相关论文: Mathematically established chaos and forecast of s…
Taylor-Couette flow is often used as a simplified model for complex rotating flows in the interior of stars and accretion disks. The flow dynamics in these objects is influenced by magnetic fields. For example, quasi-Keplerian flows in…
Unstable periodic orbits (UPOs) are the non-chaotic, dynamical building blocks of spatio-temporal chaos, motivating a first-principles based theory for turbulence ever since the discovery of deterministic chaos. Despite their key role in…
A chaotic system is called ultra-chaos when its statistics have sensitivity dependence on initial condition and/or other small disturbances. In this paper, using two-dimensional turbulent Kolmogorov flow as an example, we illustrate that…
Spatio-temporally chaotic dynamics of transitional plane Couette flow may give rise to regular turbulent-laminar stripe patterns with a large-scale pattern wavelength and an oblique orientation relative to the laminar flow direction. A…
Chaotic dynamics of low-dimensional systems, such as Lorenz or R\"ossler flows, is guided by the infinity of periodic orbits embedded in their strange attractors. Whether this also be the case for the infinite-dimensional dynamics of…
We consider two stable heteroclinic cycles rotating in opposite directions, coupled via diffusive terms. A complete synchronization in this system is impossible, and numerical exploration shows that chaos is abundant at low levels of…
We track the secondary bifurcations of coherent states in plane Couette flow and show that they undergo an incomplete periodic doubling cascade that ends with a crisis bifurcation. We introduce a symbolic dynamics for the orbits and show…
We study the Couette Taylor instabilities for an incompressible viscous fluid between two coaxial cylinders of nearly equal radii, allowing counter-rotation with the ratio of rotation rate $\mu \in [-1,1]$. Working in a rotating frame and…
Motivated by recent success in the dynamical systems approach to transitional flow, we study the efficiency and effectiveness of extracting simple invariant sets (recurrent flows) directly from chaotic/turbulent flows and the potential of…
We study a shell model for the energy cascade in three dimensional turbulence at varying the coefficients of the non-linear terms in such a way that the fundamental symmetries of Navier-Stokes are conserved. When a control parameter…
We study a shell model for the energy cascade in three dimensional turbulence at varying the coefficients of the non-linear terms in such a way that the fundamental symmetries of Navier-Stokes are conserved. When a control parameter…
For a simple model of chaotic dynamical systems with a large number of degrees of freedom, we find that there is an ensemble of unstable periodic orbits (UPOs) with the special property that the expectation values of macroscopic quantities…
The existence and dynamical role of particular unstable Navier-Stokes solutions (exact coherent structures) is revealed in laboratory studies of weak turbulence in a thin, electromagnetically-driven fluid layer. We find that the dynamics…
ONE of the main goals in the development of theory of chaotic dynamical system has been to make progress in understanding of turbulence. The attempts to related turbulence to chaotic motion got strong impetus from the celebrated paper by…
The decay of turbulent and laminar oblique bands in the lower transitional range of plane Couette flow is studied by means of direct numerical simulations of the Navier--Stokes equations. We consider systems that are extended enough for…
The quasi-periodic doubling cascade is shown to occur in the transition from regular to weakly turbulent behaviour in simulations of incompressible Navier-Stokes flow on a three-periodic domain. Special symmetries are imposed on the flow…
Laboratory experiments point out the existence of patterns made of alternately laminar and turbulent oblique bands in plane Couette flow in its way to/from turbulence as the Reynolds number R is varied. Many previous theoretical and…
Time-independent Hamiltonian flows are viewed as geodesic flows in a curved manifold, so that the onset of chaos hinges on properties of the curvature two-form entering into the Jacobi equation. Attention focuses on ensembles of orbit…
Periodicity plays a significant role in the chaos theory from the beginning since the skeleton of chaos can consist of infinitely many unstable periodic motions. This is true for chaos in the sense of Devaney [1], Li-Yorke [2] and the one…
Contrasting with free shear flows presenting velocity profiles with inflection points which cascade to turbulence in a relatively mild way, wall bounded flows are deprived of (inertial) instability modes at low Reynolds numbers and become…