Particle sedimentation in the vicinity of a fixed horizontal vortex with time-dependent intensity can be chaotic, provided gravity is sufficient to displace the particle cloud while the vortex is off or weak. This "stretch, sediment and fold" mechanism is close to the so-called blinking vortex effect, which is responsible for chaotic transport of perfect tracers, except that in the present case the vortex motion is replaced by gravitational settling. In the present work this phenomenon is analyzed for heavy Stokes particles moving under the sole effect of gravity and of a linear drag. The vortex is taken to be a fixed isolated point vortex the intensity of which varies under the effect of either boundary conditions or volume force. When the unsteadiness of the vortex is weak and the free-fall velocity is of the order of the fluid velocity, and the particle response time is small, the particle motion equation can be written asymptotically as a perturbed hamiltonian system the phase portrait of which displays a homoclinic trajectory. A homoclinic bifurcation is therefore likely to occur, and the contribution of particle inertia to the occurrence of this bifurcation is analyzed asymptotically by using Melnikov's method.
The sedimentation of a pair of rigid circular particles in a two-dimensional vertical channel containing a Newtonian fluid is investigated numerically, for terminal particle Reynolds numbers ranging from 1 to 10, and for a confinement ratio equal to 4. While it is widely admitted that sufficiently inertial pairs should sediment by performing a regular DKT oscillation (Drafting-Kissing-Tumbling), the present analysis shows in contrast that a chaotic regime can also exist for such particles, leading to a much slower sedimentation velocity. It consists of a nearly horizontal pair, corresponding t…
Convection in rotating spherical geometries is an important physical process in planetary and stellar systems. Using continuation methods at low Prandtl number, we find both strong equatorially asymmetric and symmetric polar nonlinear rotating waves in a model of thermal convection in thin rotating spherical shells with stress-free boundary conditions. For the symmetric waves convection is confined to high latitude in both hemispheres but is only restricted to one hemisphere close to the pole in the case of asymmetric waves. This is in contrast to what is previously known from studies in the f…
The long therm behavior of chaotic flows is investigated by means of time dependent frequency analysis. The system under test consists of an electrically conducting fluid, confined between two differentially rotating spheres. The spherical setup is exposed to an axial magnetic field. The classical Fourier Transform method provides a first estimation of the time dependence of the frequencies associated to the flow, as well as its volume-averaged properties. It is however unable to detect strange attractors close to regular solutions in the Feigenbaum as well as Newhouse-Ruelle-Takens bifurcatio…
Chaotic cold accretion (CCA) profoundly differs from classic black hole accretion models. Using 3D high-resolution simulations, we probe the impact of rotation on the hot and cold accretion flow in a typical massive galaxy. In the hot mode, with or without turbulence, the pressure-dominated flow forms a geometrically thick rotational barrier, suppressing the accretion rate to ~1/3 of the Bondi rate. When radiative cooling is dominant, the gas loses pressure support and quickly circularizes in a cold thin disk. In the more common state of a turbulent and heated atmosphere, CCA drives the dynami…
In the Stokesian limit, the streamline topology around a single neutrally buoyant sphere is identical to the topology of pair-sphere pathlines, both in an ambient simple shear flow. In both cases there are fore-aft symmetric open and closed trajectories spatially demarcated by an axisymmetric separatrix surface. This topology has crucial implications for both scalar transport from a single sphere, and for the rheology of a dilute suspension of spheres. We show that the topology of the fluid pathlines around a neutrally buoyant freely rotating spheroid, in simple shear flow, is profoundly diffe…
The research is devoted to the stability of convective flow in a nonuniformly rotating layer of an electrically conducting fluid in a spiral magnetic field. The stationary and oscillatory modes of magnetic convection are considered depending on the profile of the angular rotation velocity (Rossby number $\textrm{Ro}$) and on the profile of the external azimuthal magnetic field (magnetic Rossby number $\textrm{Rb}$). The nonlinear dynamic system of Lorentz type equations is obtained by using the Galerkin method. Numerical analysis of these equations has shown the presence of chaotic behavior of…
We investigate the local self-sustained process underlying spiral turbulence in counter-rotating Taylor-Couette flow using a periodic annular domain, shaped as a parallelogram, two of whose sides are aligned with the cylindrical helix described by the spiral pattern. The primary focus of the study is placed on the emergence of drifting-rotating waves ({\sc drw}) that capture, in a relatively small domain, the main features of coherent structures typically observed in developed turbulence. The transitional dynamics of the subcritical region, far below the first instability of the laminar circul…
We study a new type of large-scale instability, which arises in obliquely rotating stratified electroconductive fluid with an external uniform magnetic field and a small-scale external force having zero helicity. This force gives rise to small-scale oscillations of the velocity with a small Reynolds number. Using the method of multi-scale asymptotic expansions there are obtained nonlinear equations for vortex and magnetic perturbations in the third order in Reynolds number. Studied is the linear stage of magneto-vortex dynamo caused by instabilities of $α$-effect type. Stationary solutions for…
We propose a novel strategy for designing chaotic micromixers using curved channels confined between two flat planes. The location of the separatrix between the Dean vortices, induced by centrifugal force, is dependent on the location of the maxima of axial velocity. An asymmetry in the axial velocity profile can change the location of the separatrix. This is achieved physically by introducing slip alternatingly at the top and bottom walls. This leads to streamline crossing and Lagrangian chaos. An approximate analytical solution of the velocity field is obtained using perturbation theory. Thi…
Segregation patterns of size-bidisperse particle mixtures in a fully-three-dimensional flow produced by alternately rotating a spherical tumbler about two perpendicular axes are studied over a range of particle sizes and volume ratios using both experiments and a continuum model. Pattern formation results from the interaction of size segregation with chaotic regions and non-mixing islands of the flow. Specifically, large particles in the flowing surface layer are preferentially deposited in non-mixing islands despite the effects of collisional diffusion and chaotic transport. The protocol-depe…
We present an extensive study of Boussinesq thermal convection including a temperature-dependent internal heating source, based on numerical three-dimensional simulations. The temperature dependence mimics triple-$α$ nuclear reactions and the fluid geometry is a rotating spherical shell. These are key ingredients for the study of convective accreting neutron star oceans. A dimensionless parameter ${\rm Ra}_n$, measuring the relevance of nuclear heating, is defined. We explore how flow characteristics change with increasing ${\rm Ra}_n$ and give an astrophysical motivation. The onset of convect…
