Abstract
Novel features of turbulent flows have been analyzed recently, for example: (1) the possibility of an ideal invariant, such as the energy, to be transferred both to the small scales and to the large scales, in each case with a constant flux; (2) the existence of non-Gaussian wings in Probability Distribution Functions of kinetic, magnetic, and temperature fluctuations, together with their gradients, thus displaying large-scale as well as small-scale intermittency; and (3) the linear dependence on the control parameter of the effective dissipation in turbulence when non-linear eddies and waves interact. We shall briefly review these results with examples stemming from Solar Wind data, the atmosphere and the ocean with either magnetic fields, stratification, and/or rotation. In a second part, we shall examine numerically the inverse cascades of magnetic and of generalized helicity for Hall-MHD in the presence of forcing. These helical invariants in the ideal non-dissipative case involve various cross-correlations between the velocity and vorticity, the magnetic field, and the magnetic potential. For an ion inertial length larger than the forcing scale, the effect of the waves is significant. It leads to an exponential attenuation of the inverse cascade to large scales, since, through the velocity and vorticity, small scales play an increasing dynamical role for a strong Hall current.
Similar content being viewed by others
Availability of data and material
The authors declare that the calculation material is available upon request.
References
Abramenko V, Yurchyshyn V (2010) Intermittency and multifractality spectra of the magnetic field in solar active regions. Astrophys J 722:122–130
Alexakis A (2007) Nonlocal phenomenology for anisotropic magnetohydrodynamic turbulence. Astrophys J 667:L93–L96
Alexakis A, Biferale L (2018) Cascades and transitions in turbulent flows. Phys Rep 762:1–139
Balwalda D, LaCasce J, Speer K (2016) Scale-dependent distribution of kinetic energy from surface drifters in the Gulf of Mexico. Geophys Res Lett 43:10856–10863
Bandyopadhyay R, Oughton S, Wan M, Matthaeus WH, Chhiber R, Parashar TN (2018) Incompressive energy transfer in the Earth’s magnetosheath: Magnetospheric multiscale observations. Phys. Rev. X 8(041052):106
Benzi R, Ciliberto S, Tripiccione R, Baudet C, Massaioli F, Succi S (1993) Extended self-similarity in turbulent flows. Phys Rev E 48:R29–R32
Beresniak A (2014) Spectra of strong magnetohydrodynamic turbulence from high resolution simulations. Astrophys J Lett 784(L20):500
Boffetta G, Carbone V, Giuliani P, Veltri P, Vulpiani A (1999) Power laws in solar flares: self-organized criticality or turbulence? Phys Rev Lett 83:4662–4665
Brachet ME, Bustamante M, Krstulovic G, Mininni P, Pouquet A, Rosenberg D (2013) Ideal dynamics of three-dimensional MHD flows implementing the Taylor-Green symmetries. Phys Rev E 87:013110
Brandenburg A, Oughton S (2018) Cross-helically forced and decaying hydromagnetic turbulence. Astron Nachrichten 339:641–646
Bruno R, Carbone V (2005) The solar wind as a turbulence laboratory. Liv Rev Solar Phys 2:4
Buaria D, Pumir A, Feraco F, Marino R, Pouquet A, Rosenberg D, Primavera L (2020) Single-particle Lagrangian statistics from direct numerical simulations of rotating stratified turbulence. Phys Rev Fluids 5:064801
Buchlin E, Aletti V, Galtier S, Velli M, Einaudi G, Vial JC (2003) A simplified numerical model of coronal energy dissipation based on reduced MHD. Astron Astrophys 406:1061–1070
Chasapis A, Matthaeus WH, Parashar TN, Wan M, Haggerty CC, Pollock CJ, Giles BL, Paterson WR, Dorelli J, Gershman DJ, Torbert RB, Russell CT, Lindqvist PA, Khotyaintsev Y, Moore TE, Ergun RE, Burch JL (2018) In Situ observation of intermittent dissipation at kinetic scales in the Earth’s magnetosheath. Astrophys J Lett 856:L19
Chhiber R, Goldstein M, Maruca BA, Chasapis A, Matthaeus WH, Ruffolo M, Bandyopadhyay R, Parashar TN, Qudsi R, de Wit TD, Bale S, Bonnell J, Goetz K, Harvey P, MacDowall R, Malaspina D, Pulupa M, Kasper J, Korreck K, Case A, Stevens M, Whittlesey P, Larson D, Livi R, Velli M, Raouafi N (2020) Clustering of intermittent magnetic and flow structures near parker solar probes first perihelion—a partial-variance-of-increments analysis. Astrophys J Supp 246(31):1
Chong MS, Perry AE, Cantwell BJ (1990) A general classification of three-dimensional flow fields. Phys Fluids A 2(5):765–777. https://doi.org/10.1063/1.857730
Cichowlas C, Bonaïti P, Debbasch F, Brachet M (2005) Effective dissipation and turbulence in spectrally truncated Euler flows. Phys Rev Lett 95:264502
de Giorgio A, Servidio S, Veltri PL (2017) Coherent structure formation through nonlinear interactions in 2d magnetohydrodynamic turbulence. Sci Rep 7:13849
Dewan E (1997) Saturated-cascade similitude theory of gravity wave spectra. J Geophys Res 102:29799–29817
Djenidi L, Lefeuvre N, Kamruzzaman M, Antonia R (2017) On the normalized dissipation \(c_\epsilon \) in decaying turbulence. J Fluid Mech 817:61–79
Dobrowolny M, Mangeney A, Veltri P (1980) Fully developed anisotropic hydromagnetic turbulence in interplanetary space. Phys Rev Lett 45:144–148
Drake JF, Swisdak M, Che H, Shay MA (2006) Electron acceleration from contracting magnetic islands during reconnection. Nature 443:553
Ergun RE, Goodrich KA, Wilder FD, Ahmadi N, Holmes JC, Eriksson S, Stawarz JE, Nakamura R, Genestreti KJ, Hesse M, Burch JL, Torbert RB, Phan TD, Schwartz SJ, Eastwood JP, Strangeway RJ, Le Contel O, Russell CT, Argall M, Lindqvist PA, Chen LJ, Cassak PA, Giles BL, Dorelli JC, Gershman D, Leonard TW, Lavraud B, Retino A, Matthaeus W, Vaivads A (2018) Magnetic reconnection, turbulence, and particle acceleration: Observations in the Earth’s magnetotail. Geophys Res Lett 45:3338–3347
Feraco F, Marino R, Pumir A, Primavera L, Mininni P, Pouquet A, Rosenberg D (2018) Vertical drafts and mixing in stratified turbulence: sharp transition with Froude number. Eur Phys Lett 123:44002
Fontana M, Bruno OP, Mininni PD, Dmitruk P (2020) Fourier continuation method for incompressible fluids with boundaries. Comput Phys Commun 256:107482
Frisch U, Pouquet, Sulem P, Meneguzzi M (1983) The dynamics of two-dimensional ideal mhd. J Méc Théor Appl 2(Special Issue):191–216
Fujisawa A, Shimizu A, Nakano H, Ohshima S, Itoh K, Nagashima Y, Itoh SI, Iguchi H, Yoshimura Y, Minami T, Nagaoka K, Takahashi C, Kojima M, Nishimura S, Isobe M, Suzuki C, Akiyama T, Ido T, Matsuoka K, Okamura S, Diamond PH (2007) Intermittent characteristics in coupling between turbulence and zonal flows. Plasma Phys Controll Fusion 49(3):211. http://stacks.iop.org/0741-3335/49/i=3/a=002
Galtier S (2018) Turbulence in space plasmas and beyond. J Phys A Math Theor 51:293001
Galtier S (2016) Introduction to Modern Magnetohydrodynamics. Cambridge University Press, Cambridge
Grappin R, Frisch U, Léorat J, Pouquet A (1982) Alfvénic fluctuations as asymptotic states of MHD turbulence. Astron Astrophys 102:6–14
Grauer R, Homann H, cois Pinton JF (2012) Longitudinal and transverse structure functions in high-Reynolds-number turbulence. New J Phys 14:063016
Hide R (1976) A note on helicity. Geophys Astrophys Fluid Dyn 7:157–161
Hide R (2002) Helicity, superhelicity and weighted relative potential vorticity: Useful diagnostic pseudoscalars? Q J R Met Soc 128:1759–1762
Homann H, Ponty Y, Krstulovic G, Grauer R (2014) Structures and Lagrangian statistics of the Taylor-Green dynamo. New J Phys 16:075014
Howes G, TenBarge J, Dorland W (2011) A weakened cascade model for turbulence in astrophysical plasmas. Phys Plasmas 18:102305
Iroshnikov PS (1963) Turbulence of a conducting fluid in a strong magnetic field. Sov Astron 7:566–571
Ivey G, Winters K, Koseff J (2008) Density stratification, turbulence but how much mixing? Ann Rev Fluid Mech 40:169–184
Kafiabad H, Bartello P (2016) Balance dynamics in rotating stratified turbulence. J Fluid Mech 795:914–949
Karimabadi H, Roytershteyn V, Wan M, Matthaeus WH, Daughton W, Wu P, Shay M, Loring B, Borovsky J, Leonardis E, Chapman SC, Nakamura TKM (2013) Coherent structures, intermittent turbulence, and dissipation in high-temperature plasmas. Phys Plasmas 20:012303
Klimas AJ, Uritsky VM (2017) Criticality and turbulence in a resistive magnetohydrodynamic current sheet. Phys Rev E 95:023209
Kolmogorov AN (1941) The local structure of turbulence in incompressible viscous fluid for very large Reynolds number. Dokl Akad Nauk SSSR 30:9–13
Kraichnan RH (1965) Inertial-range spectrum of hydromagnetic turbulence. Phys Fluids 8:1385–1387
Krstulovic G, Brachet M, Pouquet A (2011) Alfvén waves and ideal two-dimensional Galerkin truncated magnetohydrodynamics. Phys Rev E 84:016410
Le Contel O, Retinó A, Breuillard H, Mirioni L, Robert P, Chasapis A, Lavraud B, Chust T, Rezeau L, Wilder FD, Graham DB, Argall MR, Gershman DJ, Lindqvist PA, Khotyaintsev YV, Marklund G, Ergun RE, Burch JLKAG, Torber RB, Needell J, Chutter M, Rau D, Dors I, Russell CT, Magnes W, Strangeway RJ, Bromund KR, Leinweber HK, Plaschke F, Fischer D, Anderson BJ, Le G, Moore TE, Pollock CJ, Giles BL, Dorelli JC, Avanov L, Saito Y (2016) Whistler mode waves and Hall fields detected by MMS during a dayside magnetopause crossing. Geophys Res Lett 43:5943–5952
Loureiro NF, Schekochihin AA, Uzdensky DA (2013) Plasmoid and Kelvin-Helmholtz instabilities in Sweet-Parker current sheets. Phys Rev E 87:013102
Lu ET, Hamilton RJ (1991) Avalanches and the distribution of solar flares. Astrophys J 380:L89–L92
Mahajan S, Yoshida Z (1998) Double curl Beltrami flow: Diamagnetic structures. Phys Rev Lett 99:4863–4866
Marino R, Sorriso-Valvo L, Carbone V, Veltri P, Noullez A, Bruno R (2011) The magnetohydrodynamic turbulent cascade in the ecliptic solar wind: Study of Ulysses data. Planet Sp Sci 59:592–597
Marino R, Sorriso-Valvo L, D’Amicis R, Carbone V, Bruno R, Veltri P (2012) On the occurence of the third-order scaling in high latitude Solar Wind. Astrophys J 750:41
Marino R, Mininni P, Rosenberg D, Pouquet A (2013) Emergence of helicity in rotating stratified turbulence. Phys Rev E 87:033016
Marino R, Mininni P, Rosenberg D, Pouquet A (2013) Inverse cascades in rotating stratified turbulence: Fast growth of large scales. Europhys Lett 102:44006
Marino R, Mininni P, Rosenberg D, Pouquet A (2014) Large-scale anisotropy in stably stratified rotating flows. Phys Rev E 90:023018
Marino R, Pouquet A, Rosenberg D (2015) Resolving the paradox of oceanic large-scale balance and small-scale mixing. Phys Rev Lett 114:114504
Matthaeus W, Lamkin S (1986) Turbulent magnetic reconnection. Phys Fluids 29:2513–2534
Matthaeus W, Velli M (2011) Who needs turbulence? a review of turbulence effects in the heliosphere and on the fundamental process of reconnection. Sp Sci Rev 160:145–168
Matthaeus WH, Wan M, Servidio S, Greco A, Osman KT, Oughton S, Dmitruk P (2015) Intermittency, nonlinear dynamics and dissipation in the solar wind and astrophysical plasmas. Philos Trans R Soc A 373:20140154
McManus MD, Bowen TA, Mallet A, Chen CH, Chandran BD, Bale SD, Livi R, Larson DE, de Wit TD, Kasper J, Stevens M, Whittlesey P, Korreck KE, Goetz K, Harvey PR, Pulupa M, MacDowal RJ, Malaspina DM, Case AW, Bonnell J (2020) Cross helicity reversals in magnetic switchbacks. Astrophys J Suppl Ser 246:67
Meyrand R, Kiyani KH, Galtier S (2015) Weak magnetohydrodynamic turbulence and intermittency. J Fluid Mech 770(R1):1–11
Miloshevich G, Passot T, Sulem P (2020) Modeling imbalanced collisionless Alfvén wave turbulence with nonlinear diffusion equations. Astrophys J Lett 888:L7
Miloshevich G, Laveder D, Passot T, Sulem P (2020) Inverse cascade and magnetic vortices in kinetic Alfvén-wave turbulence. Preprint, see arXiv:2007.06976v1
Mininni PD, Pouquet A (2007) Energy spectra stemming from interactions of Alfvén waves and turbulent eddies. Phys Rev Lett 99:254502
Mininni P, Pouquet A (2009) Finite dissipation and intermittency in MHD. Phys Rev E 80:025401
Mininni P, Pouquet A (2009) Helicity cascades in rotating turbulence. Phys Rev E 79:026304
Mininni P, Gómez DO, Mahajan SM (2002) Dynamo action in Hall magnetohydrodynamics. Astrophys J 567:L81–L83
Mininni P, Alexakis A, Pouquet A (2006) Large-scale flow effects, energy transfer, and self-similarity on turbulence. Phys Rev E 74:016303
Mininni PD, Alexakis A, Pouquet A (2007) Energy transfer in Hall-MHD turbulence, cascades, backscatter and dynamo action. J Plasma Phys 73:377–401
Mininni P, Rosenberg D, Pouquet A (2012) Isotropization at small scale of rotating helically driven turbulence. J Fluid Mech 699:263–279
Morize C, Moisy F, Rabaud M (2005) Decaying grid-generated turbulence in a rotating tank. Phys Fluids 17:095105
Müller W, Malapaka S (2013) Role of helicities for the dynamics of turbulent magnetic fields. Geophys Astrophys Fluid Dyn 107:93–100
Müller W, Malapaka S, Busse A (2012) Inverse cascade of magnetic helicity in magnetohydrodynamic turbulence. Phys Rev E 85:015302
Narita Y, Glassmeier KH, Treumann R (2006) Wave-number spectra and intermittency in the terrestrial foreshock region. Phys Rev Lett 97:191101
Nore C, Brachet M, Politano H, Pouquet A (1997) Dynamo action in a Taylor-Green vortex near threshold. Phys Plasmas Lett 4:1–3
Øieroset M, Lin R, Phan T, Larson DE, Bale S (2002) Evidence for electron acceleration up to \(\approx \) 300 keV in the magnetic reconnection diffusion region of Earth’s magnetotail. Phys Rev Lett 89:195001
Osman KT, Matthaeus WH, Gosling JT, Greco A, Servidio S, Hnat B, Chapman SC, Phan TD (2014) Magnetic reconnection and intermittent turbulence in the solar wind. Phys Rev Lett 112:215002
Paoletti MS, Fisher ME, Sreenivasan KR, Lathrop DP (2008) Velocity statistics distinguish quantum turbulence from classical turbulence. Phys Rev Lett 101:154501
Parashar TN, Goldstein M, Maruca BA, Matthaeus WH, Ruffolo M, Bandyopadhyay R, Chhiber R, Chasapis A, Qudsi R, Vech D, Roberts DA, Bale SD, Bonnell JW, MacDowall RJ, Malaspina D, Pulupa M, Kasper JC, Whittlesey P, Larson D, Livi R, Velli M, Raouafi N (2020) Measures of scale-dependent Alfvénicity in the first PSP solar encounter. Astrophys J Supp 246:58
Passot T, Sulem P (2015) A model for the non-universal power law of the Solar Wind sub-ion scale magnetic spectrum. Astrophys J Lett 812:37
Passot T, Sulem PL (2019) Imbalanced kinetic Alfvén wave turbulence: from weak turbulence theory to nonlinear diffusion models for the strong regime. J Plasma Phys 85:905850301
Petoukhov V, Eliseev A, Klein R, Oesterle H (2008) On statistics of the free-troposphere synoptic component: an evaluation of skewnesses and mixed third-order moments contribution to the synoptic-scale dynamics and fluxes of heat and humidity. Tellus 60A:11–31
Phan TD, Eastwood JP, Shay MA, Drake JF, Sonnerup BUÖ, Fujimoto M, Cassak PA, Øieroset M, Burch JL, Torbert RB, Rager AC, Dorelli JC, Gershman DJ, Pollock C, Pyakurel PS, Haggerty CC, Khotyaintsev Y, Lavraud B, Saito Y, Oka M, Ergun RE, Retino A, Le Contel O, Argall MR, Giles BL, Moore TE, Wilder FD, Strangeway RJ, Russell CT, Lindqvist PA, Magnes W (2018) Electron magnetic reconnection without ion coupling in Earth’s turbulent magnetosheath. Nature 557:202–206
Politano H, Pouquet A (1998) Dynamical length scales for turbulent magnetized flows. Geophys Res Lett 25:273–276
Politano H, Pouquet A (1998) von Kármán-Howarth equation for magnetohydrodynamics and its consequences on third-order longitudinal structure and correlation functions. Phys Rev E 57:R21
Politano H, Pouquet A, Sulem P (1989) Inertial ranges and resistive instabilities in two-dimensional MHD turbulence. Phys Fluids B 1:2330–2339
Politano H, Pouquet A, Sulem P (1995) Current and vorticity dynamics in three-dimensional turbulence. Phys Plasmas 2:2931–2939
Politano H, Gomez T, Pouquet A (2003) von Kàrmàn-Howarth relationship for helical magnetohydrodynamic flows. Phys Rev E 68:026315
Pouquet A, Sulem PL, Meneguzzi M (1988) Influence of velocity-magnetic field correlations on decaying magnetohydrodynamic turbulence with neutral X-points. Phys Fluids 31:2635–2643
Pouquet A, Rosenberg D, Marino R, Herbert C (2018) Scaling laws for mixing and dissipation in unforced rotating stratified turbulence. J Fluid Mech 844:519–545
Pouquet A, Rosenberg D, Marino R (2019) Linking dissipation, anisotropy and intermittency in rotating stratified turbulence. Phys Fluids 31:105116
Pouquet A, Stawarz J, Rosenberg D (2020) Coupling large eddies and waves in turbulence: Case study of magnetic helicity at the ion inertial scale. Atmosphere 11:00203
Pumir A (1996) Turbulence in homogeneous shear flows. Phys Fluids 8:3112–3127
Rorai C, Mininni P, Pouquet A (2014) Turbulence comes in bursts in stably stratified flows. Phys Rev E 89:043002
Rosenberg D, Pouquet A, Marino R, Mininni P (2015) Evidence for Bolgiano-Obukhov scaling in rotating stratified turbulence using high-resolution direct numerical simulations. Phys Fluids 27:055105
Rosenberg D, Marino R, Herbert C, Pouquet A (2016) Variations of characteristic time-scales in rotating stratified turbulence using a large parametric numerical study. Eur Phys J E 39:8
Rosenberg D, Mininni PD, Reddy R, Pouquet A (2020) GPU parallelization of a hybrid pseudo-spectral fluid turbulence framework using CUDA. Atmosphere 11:178
Schreiner A, Saur J (2017) A model for dissipation of solar wind magnetic turbulence by kinetic Alfvén waves at electron scales: comparison with observations. Astrophys J 835:133
Scott R, Wang F (2005) Direct evidence of an oceanic inverse kinetic energy cascade from satellite altimetry. J Phys Oceano 35:1650–1666
Seshasanayan K, Alexakis A (2016) Critical behavior in the inverse to forward energy transition in two-dimensional magnetohydrodynamic flow. Phys Rev E 93:013104
Seshasanayan K, Benavides S, Alexakis A (2014) On the edge of an inverse cascade. Phys Rev E 90:051003(R)
Smith CW, Stawarz J, Vasquez BJ, Forman MA, MacBride BT (2009) Turbulent cascade at 1 AU in high cross-helicity flows. Phys Rev Lett 103:201101
Sorriso-Valvo L, Carbone V, Giuliani P, Veltri P, Bruno R, Antoni V, Martines E (2001) Intermittency in plasma turbulence. Planet Sp Sci 49:1193–1200
Sorriso-Valvo L, Carbone V, Abramenko V, Yurchysshyn V, Noullez A, Politano H, Pouquet A, Veltri P (2004) Topological changes of the photospheric magnetic field inside active regions: a prelude to flares? Planet Sp Sci 52:937–943
Sorriso-Valvo L, Marino R, Carbone V, Noullez A, Lepreti F, Veltri P, Bruno R, Bavassano B, Pietropaolo E (2007) Observation of inertial energy cascade in interplanetary space plasma. Phys Rev Lett 99:115001
Sorriso-Valvo L, Marino R, Lijoi L, Perri S, Carbone V (2015) Self-consistent Castaing distribution of Solar Wind turbulent fluctuations. Astrophys J 807:86
Sorriso-Valvo L, Catapano F, Retinò A, Olivier L, Perrone D, Roberts OW, Coburn JT, Panebianco V, Valentini F, Perri S, Greco A, Malara F, Carbone V, Veltri P, Pezzi O, Fraternale F, Di Mare F, Marino R, Giles B, Moore TE, Russell CT, Torbert RB, Burch JL, Khotyaintsev YV (2019) Turbulence-driven ion beams in the magnetospheric kelvin-helmholtz instability. Phys Rev Lett 122:035102
Stawarz J, Smith C, Vasquez B, Forman M, MacBride BT (2010) The turbulent cascade for high cross-helicity states at 1 AU. Astrophys J 713:920–934
Stawarz JE, Gershman DJ, Eastwood JP, Phan TD, Gingell IL, Shay MA, Burch JL, Ergun RE, Giles BL, Le Contel O, Lindqvist PA, Russell CT, Strangeway RJ, Torbert RB, Argall MR, Fischer D, Magnes W, Franci L (2019) Properties of the turbulence associated with electron-only magnetic reconnection in Earth’s magnetosheath. Astrophys J Lett 877:L37 (7 pp)
Sujovolsky N, Mininni P (2019) Invariant manifolds in stratified turbulence. Phys Rev Fluids 4:052402
Sujovolsky N, Mininni P (2020) From waves to convection and back again: the phase space of stably stratified turbulence. arXiv:1912.03160v1
Sun J, Nappo CJ, Mahrt L, Belusic D, Finnigan JJ, Yagüe C, Grisogono B, Pouquet A, Stauer DR, Smith RB, Svenson G, Pulido M, Staquet C, Mayor SD, Jiang Q, Galperin B, Grachev AA, Neff WD (2015) Review of wave turbulence interactions in the stable atmospheric boundary layer. Rev Geophys 53:1–38. https://doi.org/10.1002/2015RG000487
Uritsky V, Paczuski M, Davila JM, Jones SI (2007) Coexistence of self-organized criticality and intermittent turbulence in the solar corona. Phys Rev Lett 99:025001
van Kan A, Nemoto T, Alexakis A (2019) Rare transitions to thin-layer turbulent condensates. J Fluid Mech 878:356–369
Veltri P (1999) MHD turbulence in the solar wind: self-similarity, intermittency and coherent structures. Plasma Phys Control Fusion 41:A787–A795
Veltri P, Nigro G, Malara F, Carbone V, Mangeney A (2005) Intermittency in MHD turbulence and coronal nanoflares modelling. Nonlinear Proc Geophys 12:245–255
Veltri P, Carbone V, Lepreti F, Nigro G (2009) Self-organization in magnetohydrodynamic turbulence. In: Meyers RA (ed) Encyclopedia of Complexity and System Science. Springer, Berlin
Vieillefosse P (1984) Internal motion of a small element of fluid in an inviscid flow. Phys A 125:150–162
Woltjer L (1960) On the theory of hydromagnetic equilibrium. Rev Mod Phys 32:914–915
Yoffe SR, McComb WD (2018) Onset criteria for freely decaying isotropic turbulence. Phys Rev F 3:104605
Yokoi N (2013) Cross helicity and related dynamo. Geophys Astrophys Fluid Dyn 107:114–184
Young RMB, Read PL (2017) Forward and inverse kinetic energy cascades in Jupiter’s turbulent weather layer. Nature Phys 13:1135–1142
Zhdankin V, Boldyrev S, Uzdensky DA (2016) Scalings of intermittent structures in magnetohydrodynamic turbulence. Phys Plasmas 23(5):055705
Zhou Y, Matthaeus W, Dmitruk P (2004) MHD turbulence and time scales in astrophysical and space plasmas. Rev Mod Phys 76:1015–1035
Acknowledgements
This text emanates from the talk given by one of us (AP) at the meeting held in honor of PierLuigi Veltri in October 2019 at the University of Calabria in Cosenza (Italy). It is a pleasure to acknowledge the many facets of his work, a little part of which is evoked here in the context of specific Solar Wind theoretical models and observations, and to reminisce about our discussions on many issues of MHD turbulence and on the complexity of the behavior of such systems. The runs analyzed in this paper have used an open allocation on the Janus super-computer at LASP/CU, which is gratefully acknowledged. NCAR is supported by the National Science Foundation. Support for AP, from LASP and in particular from Bob Ergun, is gratefully acknowledged as well.
Funding
The work of Julia E. Stawarz was supported in part by the project UKR/STFC Grant ST/S000364/1.
Author information
Authors and Affiliations
Contributions
All three authors have equally contributed to the research work presented in this article. Finally, the authors declare that this manuscript is in compliance with the Journal Ethical Standards.
Corresponding author
Ethics declarations
Conflicts of interest
The authors declare that there are no conflicts of interest.
Availability of code
The authors declare that the code is available upon request.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
This paper is a peer-reviewed version of a contribution at the International Conference ‘Plasma Physics and Astrophysics up to 2020 and beyond’ organized by the Department of Physics of Università della Calabria in honor of Pierluigi Veltri’s 70th birthday and held October 7–8, 2019 at Università della Calabria, Rende (Italy).
Rights and permissions
About this article
Cite this article
Pouquet, A., Rosenberg, D. & Stawarz, J.E. Interplay between turbulence and waves: large-scale helical transfer, and small-scale dissipation and mixing in fluid and Hall-MHD turbulence. Rend. Fis. Acc. Lincei 31, 949–961 (2020). https://doi.org/10.1007/s12210-020-00951-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12210-020-00951-5