Note on the triad interactions of homogeneous turbulence

Moffatt, H. K.

doi:10.1017/jfm.2013.637

Cited by 38 publications

(51 citation statements)

References 9 publications

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“…Indeed, numerical simulations have since found support to support this identification Linkmann & Dallas (2017). If further combined with the small-scale dynamo process associated with G uBB 1 )-for which small-scale magnetic field components are amplified if their helicity matches that of the flow-the dynamo processes facilitated by G BuB 2 triads may produce a helical signature compatible with the stretch-twist-fold dynamo (Vainshtein & Zel'Dovich 1972;Moffatt 1989;Childress & Gilbert 1995;Mininni 2011) as pointed out by and . Note that the small-scale dynamo process associated with G uBB 1 triads (and G uBB 3 ) identified by is not at odds with the nonexistence of G uBB i pseudo-invariants since a forward energy transfer is implied in that case.…”

Section: Associated Energy Transfer Processesmentioning

confidence: 86%

“…In fully developed turbulence, it is, however, not immediately clear to what extent the stability properties of isolated triads are applicable to the full network of triad interactions as represented by the Navier-Stokes equation (Moffatt 2014). Several numerical HD studies considering both decimated (biased) and unbiased triad networks, as well as studies on thin-layer turbulence and flows subject to strong rotation, suggest meanwhile that the stability properties are indeed useful for explaining the embedded (partial) flux contributions to the total energy flux, including forward-inverse transitions of the total energy flux [see the review by Alexakis & Biferale (2018)].…”

Section: The Spectral-helical Decompositionmentioning

confidence: 99%

“…Of the two, G BuB 2 interactions have the same helical signature as the α-effect , and have stability properties suggesting a dominant role over G BuB 3 interactions. Although care must be taken when extrapolating the behaviour of single triads to a large system of triads (Moffatt 2014), we note that the enstrophy-like conservation by G BuB 2 (and G BuB 3 ) (Figure 2a) suggests that inverse transfers from such triads might be dominated by nonlocal interactions compared to G BBu 3 and G BBu 4 triads ( Figure 2b); that is, the inverse transfer of magnetic helicity is more local than large-scale α-dynamo action.…”

Section: Scale Locality Of Interactionsmentioning

confidence: 99%

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Partial Invariants, Large-scale Dynamo Action, and the Inverse Transfer of Magnetic Helicity

Rathmann¹,

Ditlevsen²

2019

ApJ

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The existence of partially conserved enstrophy-like quantities is conjectured to cause inverse energy transfers to develop embedded in magnetohydrodynamical (MHD) turbulence, in analogy to the influence of enstrophy in two-dimensional nonconducting turbulence. By decomposing the velocity and magnetic fields in spectral space onto helical modes, we identify subsets of three-wave (triad) interactions conserving two new enstrophy-like quantities which can be mapped to triad interactions recently identified with facilitating large-scale α-type dynamo action and the inverse transfer of magnetic helicity. Due to their dependence on interaction scale locality, the invariants suggest that the inverse transfer of magnetic helicity might be facilitated by both localand nonlocal-scale interactions, and is a process more local than the α-dynamo. We test the predicted embedded (partial) energy fluxes by constructing a shell model (reduced wave-space model) of the minimal set of triad interactions (MTI) required to conserve the ideal MHD invariants. Numerically simulated MTIs demonstrate that, for a range of forcing configurations, the partial invariants are, with some exceptions, indeed useful for understanding the embedded contributions to the total spectral energy flux. Furthermore, we demonstrate that strictly inverse energy transfers may develop if enstrophy-like conserving interactions are favoured, a mechanism recently attributed to the energy cascade reversals found in nonconducting three-dimensional turbulence subject to strong rotation or confinement. The presented results have implications for the understanding of the physical mechanisms behind large-scale dynamo action and the inverse transfer of magnetic helicity, processes thought to be central to large-scale magnetic structure formation.

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Section: Associated Energy Transfer Processesmentioning

confidence: 86%

Section: The Spectral-helical Decompositionmentioning

confidence: 99%

Section: Scale Locality Of Interactionsmentioning

confidence: 99%

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Partial Invariants, Large-scale Dynamo Action, and the Inverse Transfer of Magnetic Helicity

Rathmann¹,

Ditlevsen²

2019

ApJ

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“…Homochiral interactions tend to transfer on average energy to the large scales while heterochiral interactions tend to transfer energy on average to the small scales. This was first conjectured by Waleffe (1992) based on the stability properties of isolated triads, and discussed in may works (Waleffe 1993;Chen et al 2003;Rathmann & Ditlevsen 2017;Moffatt 2014). The homochiral interactions, when isolated so that the flow is driven only by them, they to lead to an inverse cascade (Biferale et al 2012(Biferale et al , 2013Sahoo et al 2017;Sahoo & Biferale 2018).…”

Section: Helical Decompositionmentioning

confidence: 97%

On the thermal equilibrium state of large-scale flows

Alexakis

Brachet

2019

J. Fluid Mech.

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In a forced three-dimensional turbulent flow the scales larger than the forcing scale have been conjectured to reach a thermal equilibrium state forming a k 2 energy spectrum. In this work we examine the properties of these large scales in turbulent flows with the use of numerical simulations. We show that the choice of forcing can strongly affect the behavior of the large scales. A spectrally-dense forcing (a forcing that acts on all modes inside a finite-width spherical shell) with long correlation times may lead to strong deviations from the k 2 energy spectrum, while a spectrally-sparse forcing (a forcing that acts only on a few modes) with short correlated time-scale can reproduce the thermal spectrum. The origin of these deviations is analysed and the involved mechanisms is unraveled by examining: (i) the number of triadic interactions taking place, (ii) the spectrum of the non-linear term, (iii) the amplitude of interactions and the fluxes due to different scales, and (iv) the transfer function between different shells of wavenumbers. It is shown that the spectrally-dense forcing allows for numerous triadic interactions that couple one large scale mode with two forced modes and this leads to an excess of energy input in the large scales. This excess of energy is then moved back to the small-scales by selfinteractions of the large-scale modes and by interactions with the turbulent small-scales. The overall picture that arises from the present analysis is that the large scales in a turbulent flow resemble a reservoir that is in (non-local) contact with a second out-of equilibrium reservoir consisting of the smaller (forced, turbulent and dissipative) scales. If the injection of energy at the large scales from the forced modes is relative weak (as is the case for the spectrally sparse forcing) then the large-scale spectrum remains close to a thermal equilibrium and the role of long-range interactions is to set the global energy (temperature) of the equilibrium state. If, on the other hand, the long-range interactions are dominant (as is the case for the spectrally dense forcing), the large-scale self-interactions cannot respond fast enough to bring the system into equilibrium. Then the large scales deviate from the equilibrium state with energy spectrum that may display exponents different from the k 2 spectrum. † Email address for correspondence: alexakis@lps.ens.fr arXiv:1812.06294v1 [physics.flu-dyn]

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“…The growth of r(0, k f ,t) is only possible through the internal energy transfers operated by the nonlinear term u · ∇u. It is known that the nonlinear term redistributes the energy (injected by the external forcing) among the Fourier modes a(k,t) in such a way that the total transfer of energy among modes is zero [152,153]. Note that both the nonlinear term and the pressure gradient conserve energy since…”

Section: Application To a Turbulent Fluid Flowmentioning

confidence: 99%

Extreme Events: Mechanisms and Prediction

Farazmand

Sapsis

2019

Applied Mechanics Reviews

112

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Extreme events, such as rogue waves, earthquakes and stock market crashes, occur spontaneously in many dynamical systems. Because of their usually adverse consequences, quantification, prediction and mitigation of extreme events are highly desirable. Here, we review several aspects of extreme events in phenomena described by high-dimensional, chaotic dynamical systems. We specially focus on two pressing aspects of the problem: (i) Mechanisms underlying the formation of extreme events and (ii) Real-time prediction of extreme events. For each aspect, we explore methods relying on models, data or both. We discuss the strengths and limitations of each approach as well as possible future research directions.

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Note on the triad interactions of homogeneous turbulence

Cited by 38 publications

References 9 publications

Partial Invariants, Large-scale Dynamo Action, and the Inverse Transfer of Magnetic Helicity

Partial Invariants, Large-scale Dynamo Action, and the Inverse Transfer of Magnetic Helicity

On the thermal equilibrium state of large-scale flows

Extreme Events: Mechanisms and Prediction

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