Related papers: Chaotic advection in three-dimensional unsteady in…
We introduce and study the first model of an experimentally realizable three-dimensional time-dependent nonturbulent fluid flow to display the phenomenon of global diffusion of passive-scalar particles at arbitrarily small values of the…
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…
Elastic turbulence is a chaotic flow state observed in dilute polymer solutions in the absence of inertia. It was discovered experimentally in circular geometries and has long been thought to require a finite amplitude perturbation in…
We study the Lagrangian flow associated to velocity fields arising from various models of fluid mechanics subject to white-in-time, $H^s$-in-space stochastic forcing in a periodic box. We prove that in many circumstances, these flows are…
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…
Global aspects of the motion of passive scalars in time-dependent incompressible fluid flows are well described by volume-preserving (Liouvillian) three-dimensional maps. In this paper the possible invariant structures in Liouvillian maps…
Lagrangian chaos is experimentally investigated in a convective flow by means of Particle Tracking Velocimetry. The Finite Size Lyapunov Exponent analysis is applied to quantify dispersion properties at different scales. In the range of…
The decay of a passive scalar in a three-dimensional chaotic flow is studied using high-resolution numerical simulations. The (volume-preserving) flow considered is a three-dimensional extension of the randomised alternating sine flow…
Incompressible Navier-Stokes equations in the spherical coordinates are solved using a pseudo-spectral method to simulate the problem of spherical Couette flow. The flow is investigated for a narrow gap ratio with only the inner sphere…
Statistical properties of $d$-dimensional incompressible flows with and without cylindrical reduction are studied, leading to several explanations and conjectures about turbulent flows and passive scalars, such as the de-correlation between…
Lagrangian tracer particle trajectories for invariant solutions of the Navier-Stokes equations confined to the three-dimensional geometry of plane Couette flow are studied. Treating the Eulerian velocity field of an invariant solution as a…
We investigate the 3D stationary flow of a weakly conducting fluid in a cubic cavity, driven by the Lorentz force created by two permanent magnets and a weak constant current. Our goal is to determine the conditions leading to efficient…
A simple analytical solution for turbulent plane Couette flow is obtained from a subset of the Navier-Stokes equations. This approach analyses the effect of the unsteady state Lagrangian diffusion of viscous momentum on the smoothed phase…
We study the stability of Couette flow in the 3d Navier-Stokes equations with rotation, as given by the Coriolis force. Hereby, the nature of linearized dynamics near Couette flow depends crucially on the force balance between background…
We provide a integration of Navier-Stokes equations concerning the unsteady-state laminar flow of an incompressible, isothermal (newtonian) fluid in a cylindrical vessel spinning about its symmetry axis, say $z$, and inside which the liquid…
We demonstrate that at long times the rate of passive scalar decay in a turbulent, or simply chaotic, flow is dominated by regions (in real space or in inverse space) where mixing is less efficient. We examine two situations. The first is…
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…
We consider a test problem for Navier-Stokes solvers based on the flow around a cylinder that exhibits chaotic behavior, to examine the behavior of various numerical methods. We choose a range of Reynolds numbers for which the flow is…
Lagrangian chaos is experimentally investigated in a convective flow by means of Particle Tracking Velocimetry. The Fnite Size Lyapunov Exponent analysis is applied to quantify dispersion properties at different scales. In the range of…
Dynamical and statistical properties of tracer advection are studied in a family of flows produced by three point-vortices of different signs. A collapse of all three vortices to a single point is then possible. Tracer dynamics is analyzed…