Passive scalar advection in the vicinity of two point vortices in a deformation flow (original) (raw)
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Workshop Particles in flows Prague 2014
The list of abstracts and papers presented at the Summer-school and workshop of the ERCOFTAC, Inst. of Mathematics CAS, Pittsburg Univ. USA and Czech Technical Univertity, is presented for future meetings of the Pan European Laboratory on Non Homogeneous Turbulence (ERCOFTAC). A list of contributions compiled by Tomas Bodnar et al. may be found at: http://www.prague-sum.com/site/page/view/download. Here only Workshop presentations are resumed; Dagmar Medková / Robin problem for the Oseen system Milan Pokorný / A Linearized Model for Compressible Flow past a Rotating Obstacle: Analysis via Modified Bochner–Riesz Multipliers Philippe Fraunie / Two phase flow modeling Adélia Sequeira / An Overview of Some Mathematical Models for Blood Coagulation David Wegmann / An Improved Energy Inequality for Weak Solutions of the Navier-Stokes Equations Jonas Sauer / Maximal Lp-Regularity of the Spatially Periodic Stokes Operator Petr Sváček / On the conservation of the energy for incompressible flow interacting with solid bodies/particles Hana Mizerová / Existence, uniqueness and approximation of the diffusive Peterlin viscoelastic model Peter Otčenáš / A numerical approximation of an equation of the wall in the fluid-structure interaction problem Evgeniya Stepanova / Flow Pattern Comparison of Miscible and Solid Markers in Compound Vortex Vladimír Hric / Numerical Solution of Transonic Wet Steam Flow with Non-equilibrium Condensation Viktor Šíp / Development of FVM Solver for ABL Flows Nikolay Shevtsov / Visualization of waves on the free surface of the compound vortex Tobias Seitz / Flow Reconstruction from MRV Measurements Xiaoxin Zheng / Time-dependent singularities in the Navier-Stokes system Benyahia Mohamed / On the weak solutions to the Fluid/Rigid Body interaction problem Johannes Brand / Fluid Flows & Floating Bodies Joana Silva / The Impact of the Sea-level Rise in the Hydromorphology of Alluvial Rivers Giusy Mazzone / On the inertial motions of liquid-filled rigid body with slip boundary conditions Tomoyuki Nakatsuka / On uniqueness of symmetric Navier-Stokes flows around a body in the plane Václav Mácha / Self-propelled motion in a viscous compressible fluid David Wegmann / An Improved Energy Inequality for Weak Solutions of the Navier-Stokes Equations Irina Denisova / On energy inequality for evolution problem for two fluids of different types without surface tension Eliška Cézová / Exploratory analysis of meteorological data measured in opencast coal mine Luboš Matějíček / On the experimental and numerical study of dust dispersion in complex terrain Jiří Neustupa / On steady solutions of the Bénard problem in a two dimensional quadrangular cavity Ondřej Kreml / On bounded solutions to the compressible isentropic Euler system Martin Kalousek / Homogenization of a non-Newtonian flow through a porous medium Jose Manuel Redondo / Lift off and turbidity currents in the environment Jose Manuel Redondo / PIV of convective complex flows driven by thermoelectric heat fluxes David Maltese / Error estimates for a numerical approximation to the compressible barotropic Navier-Stokes equations
Onset of chaotic advection in open flows
Physical Review E, 2008
In this paper we investigate the transition to chaos in the motion of particles advected by open flows with obstacles. By means of a topological argument, we show that the separation points on the surface of the obstacle imply the existence of a saddle point downstream from the obstacle, with an associated heteroclinic orbit. We argue that as soon as the flow becomes time periodic, these orbits give rise to heteroclinic tangles, causing passively advected particles to experience transient chaos. The transition to chaos thus coincides with the onset of time dependence in open flows with stagnant points, in contrast with flows with no stagnant points. We also show that the nonhyperbolic nature of the dynamics near the walls causes anomalous scalings in the vicinity of the transition. These results are confirmed by numerical simulations of the two-dimensional flow around a cylinder.
An analytical study of transport, mixing and chaos in an unsteady vortical flow
Journal of Fluid Mechanics, 1990
We examine the transport properties of a particular two-dimensional, inviscid incompressible flow using dynamical systems techniques. The velocity field is time periodic and consists of the field induced by a vortex pair plus an oscillating strainrate field. I n the absence of the strain-rate field the vortex pair moves with a constant velocity and carries with it a constant body of fluid. When the strain-rate field is added the picture changes dramatically ; fluid is entrained and detrained from the neighbourhood of the vortices and chaotic particle motion occurs. We investigate the mechanism for this phenomenon and study the transport and mixing of fluid in this flow. Our work consists of both numerical and analytical studies. The analytical studies include the interpretation of the invariant manifolds as the underlying structure which govern the transport. For small values of strain-rate amplitude we use Melnikov's technique to investigate the behaviour of the manifolds as the parameters of the problem change and to prove the existence of a horseshoe map and thus the existence of chaotic particle paths in the flow. Using the Melnikov technique once more we develop an analytical estimate of the flux rate into and out of the vortex neighbourhood. We then develop a technique for determining the residence time distribution for fluid particles near the vortices that is valid for arbitrary strainrate amplitudes. The technique involves an understanding of the geometry of the tangling of the stable and unstable manifolds and results in a dramatic reduction in computational effort required for the determination of the residence time distributions. Additionally, we investigate the total stretch of material elements while they are in the vicinity of the vortex pair, using this quantity as a measure of the effect of the horseshoes on trajectories passing through this region. The numerical work verifies the analytical predictions regarding the structure of the invariant manifolds, the mechanism for entrainment and detrainment and the flux rate.
Chaotic advection, diffusion, and reactions in open flows
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2000
We review and generalize recent results on advection of particles in open time-periodic hydrodynamical flows. First, the problem of passive advection is considered, and its fractal and chaotic nature is pointed out. Next, we study the effect of weak molecular diffusion or randomness of the flow. Finally, we investigate the influence of passive advection on chemical or biological activity superimposed on open flows. The nondiffusive approach is shown to carry some features of a weak diffusion, due to the finiteness of the reaction range or reaction velocity.
Atmospheric and Oceanographic Sciences Library, 2014
ABSTRACT This chapter deals mostly with the dynamics of discrete vortices in a two-layer fluid and has the following structure. First, two vortices (a simplest heton) are used to demonstrate the characteristic features of a system of baroclinic vortices, after which, the results of analytical and numerical studying of vortex ensembles are studied, starting from relatively complex (systems of A and A + 1 vortices) with arbitrary A to simpler ones with A = 2. A class of motions of axisymmetric vortex structures in an external deformation field. The possibility of formation of chaotic regimes is examined. The last subsection of the chapter gives formulas describing the motion of simplest stationary vortex structures in a three-layer fluid.
Chaotic advection by two interacting finite-area vortices
Physics of Fluids, 2001
This article deals with the advection of fluid particles in the velocity field of two identical vortices with various vorticity distributions. The two-dimensional velocity field is aperiodic in the range of parameters studied here, namely, the neighborhood of the critical distance for merger. Ideas and methods from the theory of transport in dynamical systems are used to describe and quantify particle advection. These methods are applied to the numerical representation of the velocity field, which is obtained by solving the Euler equations with the vortex-in-cell method. It is found that the strongest stirring of vortex fluid occurs slightly above the critical distance for merger. In this regime the fluid located between the vortices is subjected to intense stirring, and some vortex fluid may be entrained into the chaotic region depending on the smoothness of the vorticity distribution. Initial conditions below the critical distance lead to stirring of fluid mainly before merger. In this case the flow geometry is used to quantify the efficiency of merger, which is defined as the ratio of the circulation of the resultant vortex to the total circulation of the original vortices. It is found that the vortices with the smoothest vorticity profile have the lowest efficiency. Experimental visualizations in a two-dimensional rotating fluid confirm the intense stretching and folding of fluid elements that occurs before the vortices merge.