Mixing: Turbulence and Chaos — An Introduction

Hinch, E. J.

doi:10.1007/978-1-4615-4697-9_3

Cited by 12 publications

(9 citation statements)

References 1 publication

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“…where γp = N µ/t is the most probable stretching rate, and κ = N σ 2 /(2t) stands for their dispersion, both depending of the type of unsteadiness in the flow (for instance Souzy et al (2017) showed how γp and κ depend on the volume fraction of beads in a sheared suspension). The net length of the strip (t) = ρQ(ρ)dρ = s0e (γp+κ)t increases exponentially fast, a common feature of random sequential processes (Cocke 1969;Hinch 1999;Duplat & Villermaux 2000). Figure 6 shows examples of this paradigm of sequential mixing, commonplace in real-world and numerical experiments.…”

Section: Multi-step Stretchingmentioning

confidence: 94%

Mixing Versus Stirring

Villermaux

2019

Annu. Rev. Fluid Mech.

127

129

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Mixing is the operation by which a system evolves under stirring from one state of simplicity—the initial segregation of the constituents—to another state of simplicity—their complete uniformity. Between these extremes, patterns emerge, possibly interact, and die sooner or later. This review summarizes recent developments on the problem of mixing in its lamellar representation. This point of view visualizes a mixture as a set of stretched lamellae, or sheets, possibly interacting with each other. It relies on a near-exact formulation of the Fourier equation on a moving substrate and allows one to bridge the spatial structure and evolution of the concentration field with its statistical content in a direct way. Within this frame, one can precisely describe both the dynamics of the concentration levels in a mixture as a function of the intensity of the stirring motions at the scale of a single lamella and the interaction rule between adjacent lamellae, thus offering a detailed representation of the mixture content, its structure, and their evolution in time.

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Section: Multi-step Stretchingmentioning

confidence: 94%

Mixing Versus Stirring

Villermaux

2019

Annu. Rev. Fluid Mech.

127

129

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“…In 3D, the magnetic field lines, as well as the velocity field lines, may become spatially chaotic. This Eulerian chaos of velocity field lines is sometimes taken in the fluid mechanics community as the definition of turbulence [23,24]. In this case, space gradients are of the order of the local spatial exponentiation rates of these fields.…”

Section: Fig 3 Numerical Ftle σmentioning

confidence: 99%

Impact of the Eulerian chaos of magnetic field lines in magnetic reconnection

et al. 2016

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Stochasticity is an ingredient that may allow the breaking of the frozen-in law in the reconnection process. It will first be argued that non-ideal effects may be considered as an implicit way to introduce stochasticity. Yet there also exists an explicit stochasticity that does not require the invocation of non-ideal effects. This comes from the spatial (or Eulerian) chaos of magnetic field lines that can show up only in a truly three-dimensional description of magnetic reconnection since two-dimensional models impose the integrability of the magnetic field lines. Some implications of this magnetic braiding, such as the increased particle finite-time Lyapunov exponents and increased acceleration of charged particles, are discussed in the frame of tokamak sawteeth that form a laboratory prototype of spontaneous magnetic reconnection. A justification for an increased reconnection rate with chaotic vs integrable magnetic field lines is proposed. Moreover, in 3D, the Eulerian chaos of magnetic field lines may coexist with the Eulerian chaos of velocity field lines, that is more commonly named turbulence.

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“…Turbulence first stirs scalars into thin filaments (Eckart, 1948;Garrett, 1983), enhancing local scalar gradients and increasing the interfacial area of the scalar through processes of stretching and folding (Ottino, 1989;Hinch, 1999), leading to increased mixing by molecular diffusion. A blob of a weakly diffusive scalar is stirred into well-defined filaments, with alternating striations of marked and unmarked fluid; the striation thickness decreases with time, but the low molecular diffusivity initially discourages dilution at the molecular scale.…”

Section: The Role Of Instantaneous Stirringmentioning

confidence: 99%

The role of structured stirring and mixing on gamete dispersal and aggregation in broadcast spawning

Crimaldi

2012

Journal of Experimental Biology

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SummaryBroadcast-spawning benthic invertebrates synchronously release sperm and eggs from separate locations into the surrounding flow, whereupon the process depends on structured stirring by the flow field (at large scales), and sperm motility and taxis (at small scales) to bring the gametes together. The details of the relevant physical and biological aspects of the problem that result in successful and efficient fertilization are not well understood. This review paper includes relevant work from both the physical and biological communities to synthesize a more complete understanding of the processes that govern fertilization success; the focus is on the role of structured stirring on the dispersal and aggregation of gametes. The review also includes a summary of current trends and approaches for numerical and experimental simulations of broadcast spawning.

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Mixing: Turbulence and Chaos — An Introduction

Cited by 12 publications

References 1 publication

Mixing Versus Stirring

Mixing Versus Stirring

Impact of the Eulerian chaos of magnetic field lines in magnetic reconnection

The role of structured stirring and mixing on gamete dispersal and aggregation in broadcast spawning

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