Comparative numerical-experimental analysis of the universal impact of arbitrary perturbations on transport in three-dimensional unsteady flows

Wu, Fan; Speetjens, Mfm Michel; Vainchtein, Dmitri; Trieling, RR Ruben; Clercx, Hjh Herman

doi:10.1103/physreve.90.063002

Cited by 5 publications

(17 citation statements)

References 30 publications

(76 reference statements)

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“…Its occurrence for a wide range of forcing protocols (Pouransari et al, 2010;Speetjens et al, 2006c,d) and different systems (Moharana et al, 2013) suggests that resonance-induced merger is a universal phenomenon and is part of an essentially 3D route to chaos. The study in Wu et al (2014) supports this assertion by demonstrating that resonance-induced merger can in fact be triggered by weak perturbations of arbitrary nature and provides the first experimental evidence of its physical existence.…”

Section: Response Of Invariant Spheroidssupporting

confidence: 59%

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Frontiers of chaotic advection

et al. 2017

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This work reviews the present position of and surveys future perspectives in the physics of chaotic advection: the field that emerged three decades ago at the intersection of fluid mechanics and nonlinear dynamics, which encompasses a range of applications with length scales ranging from micrometers to hundreds of kilometers, including systems as diverse as mixing and thermal processing of viscous fluids, microfluidics, biological flows, and oceanographic and atmospheric flows.

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Section: Response Of Invariant Spheroidssupporting

confidence: 59%

“…We should emphasize that inertia is not the only mechanism to induce chaos. It is also possible to obtain chaos from a breaking of time reversibility by the time derivative in the time-dependent Stokes equation, see Eckhardt and Hascoët (2005), or simply by minor imperfections in an experimental set-up, see Wu et al (2014).…”

Section: B Effect Of Fluid Inertiamentioning

confidence: 99%

Frontiers of chaotic advection

et al. 2017

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“…The above findings are to date only indirectly supported by experimental evidence [20]. Moreover, full explanation of the underlying mechanisms exists only for some instances of RIM; other manifestations of this phenomenon are beyond current theories.…”

Section: Introductionmentioning

confidence: 90%

“…The system considered by [20] is adopted as representative case for investigation of the dynamics of flows with spheroidal invariant surfaces and corresponds with the configuration of the above-mentioned computational studies that first exposed RIM [12][13][14]. It consists of a solenoidal time-periodic flow u(ξ, t ) = u(ξ, t + T ) in a cylinder (radius R and height H = 2R), with T the period time and ξ = (x 1 , x 2 , x 3 ) the Cartesian reference frame, driven by repetition of the sequence of piecewise steady translations of the bottom wall at velocity U and angles θ k = 2kπ/3 (k ∈ {0, 1, 2}) with the x axis and of duration T /3 (Fig.…”

Section: A Configuration and Unperturbed Dynamicsmentioning

confidence: 99%

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Physical topology of three-dimensional unsteady flows with spheroidal invariant surfaces

2020

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Topological analysis of a mixing flow generated by natural convection

2016

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We use topological tools to describe the natural convective motion and the Lagrangian trajectories of a flow generated by stepwise, alternating heating and cooling protocol of opposite vertical walls of a cubic container. The working fluid considered is Newtonian and the system is in presence of the acceleration of gravity but the nonlinear terms are neglected, i.e., we study the piece-wise steady and linear problem. For this convective mixing flow, we identify invariant surfaces formed by the Lagrangian orbits of massless tracers that are topologically equivalent to spherical shells and period-1 lines with elliptic and hyperbolic segments that are located on symmetry planes. We describe the previous features as functions of the Rayleigh number in the range 3 × 104 ≤ Ra ≤ 5 × 105. We show that this system shares properties with other systems with non-toroidal invariant surfaces.

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Comparative numerical-experimental analysis of the universal impact of arbitrary perturbations on transport in three-dimensional unsteady flows

Cited by 5 publications

References 30 publications

Frontiers of chaotic advection

Frontiers of chaotic advection

Physical topology of three-dimensional unsteady flows with spheroidal invariant surfaces

Topological analysis of a mixing flow generated by natural convection

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