Double Cascade Turbulence and Richardson Dispersion in a Horizontal Fluid Flow Induced by Faraday Waves

Kameke, Alexandra von; Huhn, Florian; Fernández-García, Guillermo; Muñuzuri, Alberto P.; Pérez‐Muñuzuri, V.

doi:10.1103/physrevlett.107.074502

Cited by 75 publications

(93 citation statements)

References 31 publications

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“…2a for the Faraday wave driven turbulence (the forcing scale of L f E4.4 mm). At shorter times, less than the Lagrangian integral time, toT L , a clear ballistic regime is observed, hdr 2 i $ t 2 , in agreement with Equation (1), while at larger times, we find a diffusive regime /dr 2 SE2D exp t, similar to recent observations 15,19 . Here we confirm these two regimes for a broad range of forcing levels, including the 'underdeveloped' turbulence, like for example, the one shown in Fig.…”

Section: Resultssupporting

confidence: 79%

“…A similar relation has also been mentioned in von Kameke et al 15 This relation, together with the result of Fig. 3d, indicates that the Lagrangian correlation scale (or time) is not necessarily smaller than its Eulerian counterpart, L L rL E , as it has been concluded from the theoretical analysis of Middleton 10 .…”

Section: Discussionsupporting

confidence: 69%

“…In the first, turbulence is excited electromagnetically 13,14 (electromagnetically driven turbulence (EMT)). In the second set of experiments, 2D turbulence is driven by Faraday waves on the surface of a vertically vibrated fluid container (Faraday wave driven turbulence (FWT)), a method which just recently has been discovered in von Kameke et al 15 and further investigated in Francois et al 16 The tracer particles on the water surface are accelerated in the wave field and move chaotically in the horizontal plane. Though the vertical motion is also present on the rippled surface, statistics of the horizontal velocity fluctuations are fully consistent with those in 2D turbulence.…”

Section: Resultsmentioning

confidence: 99%

“…To reduce the bottom drag and to avoid the influence of the bottom boundary layer, a layer of electrolyte is placed on top of heavier (SG ¼ 1. In the second method, the horizontal motion of fluid particles is forced by the parametrically excited Faraday waves on the surface of a vertically vibrated liquid (water) 15,16 . The floaters motion on the surface resembles the motion of fluid in 2D turbulence.…”

Section: Methodsmentioning

confidence: 99%

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Lagrangian scale of particle dispersion in turbulence

et al. 2013

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Transport of mass, heat and momentum in turbulent flows by far exceeds that in stable laminar fluid motions. As turbulence is a state of a flow dominated by a hierarchy of scales, it is not clear which of these scales mostly affects particle dispersion. Also, it is not uncommon that turbulence coexists with coherent vortices. Here we report on Lagrangian statistics in laboratory two-dimensional turbulence. Our results provide direct experimental evidence that fluid particle dispersion is determined by a single measurable Lagrangian scale related to the forcing scale. These experiments offer a new way of predicting dispersion in turbulent flows in which one of the low energy scales possesses temporal coherency. The results are applicable to oceanographic and atmospheric data, such as those obtained from trajectories of freedrifting instruments in the ocean.

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Section: Resultssupporting

confidence: 79%

Section: Discussionsupporting

confidence: 69%

Section: Resultsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

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Lagrangian scale of particle dispersion in turbulence

et al. 2013

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“…4 Related problems range from fingering instabilities of reactive interfaces 5,6 or traveling chemical fronts 4 to the spatiotemporal dynamics of chemicals advected in complex flow fields. 7,8 The reaction−diffusion−convection (RDC) interplay impacts numerous applications areas as diverse as combustion, 9 polymer processing, 10 extraction techniques 5,11 and CO 2 sequestration. 12 When chemicals are passively slaved to the flow, the convective motions develop independently of the presence of reactive processes.…”

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Self-Organized Traveling Chemo-Hydrodynamic Fingers Triggered by a Chemical Oscillator

Escala

Budroni

Landeira

et al. 2014

J. Phys. Chem. Lett.

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Pulsatile chemo-hydrodynamic patterns due to a coupling between an oscillating chemical reaction and buoyancy-driven hydrodynamic flows can develop when two solutions of separate reactants of the Belousov−Zhabotinsky reaction are put in contact in the gravity field and conditions for chemical oscillations are met in the contact zone. In regular oscillatory conditions, localized periodic changes in the concentration of intermediate species induce pulsatile density gradients, which, in turn, generate traveling convective fingers breaking the transverse symmetry. These patterns are the self-organized result of a genuine coupling between chemical and hydrodynamic modes. SECTION: Liquids; Chemical and Dynamical Processes in SolutionO ut-of-equilibrium, breaking of symmetries and related spatiotemporal patterns have been much studied in hydrodynamic and reaction−diffusion (RD) systems. 1−3 At the intersection between these two fields, chemo-hydrodynamics focuses on analyzing patterns and instabilities that result from a nonlinear coupling of hydrodynamic and RD processes. 4 Related problems range from fingering instabilities of reactive interfaces 5,6 or traveling chemical fronts 4 to the spatiotemporal dynamics of chemicals advected in complex flow fields. 7,8 The reaction−diffusion−convection (RDC) interplay impacts numerous applications areas as diverse as combustion, 9 polymer processing, 10 extraction techniques 5,11 and CO 2 sequestration. 12 When chemicals are passively slaved to the flow, the convective motions develop independently of the presence of reactive processes. On the other hand, in presence of active chemistry, the reactions modify a physical property of the fluid like its density, viscosity, or surface tension for instance. Concentration gradients in RD processes can then trigger unfavorable mobility gradients, which in turn can yield convection. As an example, even when starting from an initially stable density stratification of a less dense reactive solution on top of a denser one in the gravity field, chemical processes can trigger buoyancy-driven convection. This occurs when the reaction produces either a denser product locally or when differential diffusion phenomena implying the various chemicals 6,13−16 or heat and mass 17 come into play. The hydrodynamic patterns are then typically convective fingers growing vertically. Simple A+B→ C reactions have been shown to be able to break the up−down symmetry of such convective fingers. 13 More complex reactions prone to produce spatiotemporal RD structures can induce other synergetic combinations of chemical and hydrodynamic modes. Typical examples of such intrinsic chemo-hydrodynamic scenarios include reaction-driven convection around a traveling chemical front stably stratified from both solutal and thermal perspectives 4,17,18 and buoyancy or Marangoni-induced convective cells following chemical waves in excitable and oscillatory systems. 19−23 In such cases, the chemical kinetics drives the source of the convective flows, and the velo...

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Turbulence

Shats

Xia

2017

Encyclopedia of Maritime and Offshore Engineering

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Turbulence is a ubiquitous state for many flows in nature and engineering. As the flow velocity is increased, the nonlinear energy transfer generates fluid motion in a broad range of scales forming continuous wave number spectra of the kinetic energy. In isotropic homogeneous incompressible turbulence, energy flux is related to the third‐order velocity structure function via the Kolmogorov 4/5 law. In three‐dimensional turbulence, the energy is transferred from large to smaller scales in the process of the energy cascade. In two‐dimensional turbulence, energy is transferred from smaller to larger scales, the inverse energy cascade. Turbulence greatly increases the rate of mixing in fluids and dispersion. Transport of matter in turbulent flows requires Lagrangian description, in which the observer follows the fluid particles wherever they move. Here, we review the approaches to turbulence description in two and three dimensions.

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Double Cascade Turbulence and Richardson Dispersion in a Horizontal Fluid Flow Induced by Faraday Waves

Cited by 75 publications

References 31 publications

Lagrangian scale of particle dispersion in turbulence

Lagrangian scale of particle dispersion in turbulence

Self-Organized Traveling Chemo-Hydrodynamic Fingers Triggered by a Chemical Oscillator

Turbulence

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