DOI

1

Critical behavior in the inverse to forward energy transition in two-dimensional magnetohydrodynamic flow - Seshasayanan, Kannabiran and Alexakis, Alexandros

PHYSICAL REVIEW E 93, (2016)

Abstract : We investigate the critical transition from an inverse cascade of energy to a forward energy cascade in a two-dimensional magnetohydrodynamic flow as the ratio of magnetic to mechanical forcing amplitude is varied. It is found that the critical transition is the result of two competing processes. The first process is due to hydrodynamic interactions and cascades the energy to the large scales. The second process couples small-scale magnetic fields to large-scale flows, transferring the energy back to the small scales via a nonlocal mechanism. At marginality the two cascades are both present and cancel each other. The phase space diagram of the transition is sketched.

PHYSICAL REVIEW E 93, (2016)

LPS

Abstract : We investigate the critical transition from an inverse cascade of energy to a forward energy cascade in a two-dimensional magnetohydrodynamic flow as the ratio of magnetic to mechanical forcing amplitude is varied. It is found that the critical transition is the result of two competing processes. The first process is due to hydrodynamic interactions and cascades the energy to the large scales. The second process couples small-scale magnetic fields to large-scale flows, transferring the energy back to the small scales via a nonlocal mechanism. At marginality the two cascades are both present and cancel each other. The phase space diagram of the transition is sketched.

DOI

2

Optimal Length Scale for a Turbulent Dynamo - Sadek, Mira and Alexakis, Alexandros and Fauve, Stephan

PHYSICAL REVIEW LETTERS 116, (2016)

Abstract : We demonstrate that there is an optimal forcing length scale for low Prandtl number dynamo flows that can significantly reduce the required energy injection rate. The investigation is based on simulations of the induction equation in a periodic box of size 2 pi L. The flows considered are the laminar and turbulent ABC flows forced at different forcing wave numbers k(f), where the turbulent case is simulated using a subgrid turbulence model. At the smallest allowed forcing wave number k(f) = k(min) = 1/L the laminar critical magnetic Reynolds number Rm(c)(lam) is more than an order of magnitude smaller than the turbulent critical magnetic Reynolds number Rm(c)(turb) due to the hindering effect of turbulent fluctuations. We show that this hindering effect is almost suppressed when the forcing wave number k(f) is increased above an optimum wave number kfL similar or equal to 4 for which Rm(c)(turb) is minimum. At this optimal wave number, Rm(c)(turb) is smaller by more than a factor of 10 than the case forced in k(f) = 1. This leads to a reduction of the energy injection rate by 3 orders of magnitude when compared to the case where the system is forced at the largest scales and thus provides a new strategy for the design of a fully turbulent experimental dynamo.

PHYSICAL REVIEW LETTERS 116, (2016)

LPS

Abstract : We demonstrate that there is an optimal forcing length scale for low Prandtl number dynamo flows that can significantly reduce the required energy injection rate. The investigation is based on simulations of the induction equation in a periodic box of size 2 pi L. The flows considered are the laminar and turbulent ABC flows forced at different forcing wave numbers k(f), where the turbulent case is simulated using a subgrid turbulence model. At the smallest allowed forcing wave number k(f) = k(min) = 1/L the laminar critical magnetic Reynolds number Rm(c)(lam) is more than an order of magnitude smaller than the turbulent critical magnetic Reynolds number Rm(c)(turb) due to the hindering effect of turbulent fluctuations. We show that this hindering effect is almost suppressed when the forcing wave number k(f) is increased above an optimum wave number kfL similar or equal to 4 for which Rm(c)(turb) is minimum. At this optimal wave number, Rm(c)(turb) is smaller by more than a factor of 10 than the case forced in k(f) = 1. This leads to a reduction of the energy injection rate by 3 orders of magnitude when compared to the case where the system is forced at the largest scales and thus provides a new strategy for the design of a fully turbulent experimental dynamo.

DOI

3

Fluctuations of Electrical Conductivity: A New Source for Astrophysical Magnetic Fields - Petrelis, F. and Alexakis, A. and Gissinger, C.

PHYSICAL REVIEW LETTERS 116, (2016)

Abstract : We consider the generation of a magnetic field by the flow of a fluid for which the electrical conductivity is nonuniform. A new amplification mechanism is found which leads to dynamo action for flows much simpler than those considered so far. In particular, the fluctuations of the electrical conductivity provide a way to bypass antidynamo theorems. For astrophysical objects, we show through three-dimensional global numerical simulations that the temperature-driven fluctuations of the electrical conductivity can amplify an otherwise decaying large scale equatorial dipolar field. This effect could play a role for the generation of the unusually tilted magnetic field of the iced giants Neptune and Uranus.

PHYSICAL REVIEW LETTERS 116, (2016)

LPS

Abstract : We consider the generation of a magnetic field by the flow of a fluid for which the electrical conductivity is nonuniform. A new amplification mechanism is found which leads to dynamo action for flows much simpler than those considered so far. In particular, the fluctuations of the electrical conductivity provide a way to bypass antidynamo theorems. For astrophysical objects, we show through three-dimensional global numerical simulations that the temperature-driven fluctuations of the electrical conductivity can amplify an otherwise decaying large scale equatorial dipolar field. This effect could play a role for the generation of the unusually tilted magnetic field of the iced giants Neptune and Uranus.

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4

Turbulent 2.5-dimensional dynamos - Seshasayanan, K. and Alexakis, A.

JOURNAL OF FLUID MECHANICS 799, 246-264 (2016)

Abstract : We study the linear stage of the dynamo instability of a turbulent two-dimensional flow with three components (u(x, y, t), v(x, y, t), w(x, y, t)) that is sometimes referred to as a 2.5-dimensional (2.5-D) flow. The flow evolves based on the two-dimensional Navier-Stokes equations in the presence of a large-scale drag force that leads to the steady state of a turbulent inverse cascade. These flows provide an approximation to very fast rotating flows often observed in nature. The low dimensionality of the system allows for the realization of a large number of numerical simulations and thus the investigation of a wide range of fluid Reynolds numbers Re, magnetic Reynolds numbers Rm and forcing length scales. This allows for the examination of dynamo properties at different limits that cannot be achieved with three-dimensional simulations. We examine dynamos for both large and small magnetic Prandtl-number turbulent flows Pm = Rm/Re, close to and away from the dynamo onset, as well as dynamos in the presence of scale separation. In particular, we determine the properties of the dynamo onset as a function of Re and the asymptotic behaviour in the large Rm limit. We are thus able to give a complete description of the dynamo properties of these turbulent 2.5-D flows.

JOURNAL OF FLUID MECHANICS 799, 246-264 (2016)

LPS

Abstract : We study the linear stage of the dynamo instability of a turbulent two-dimensional flow with three components (u(x, y, t), v(x, y, t), w(x, y, t)) that is sometimes referred to as a 2.5-dimensional (2.5-D) flow. The flow evolves based on the two-dimensional Navier-Stokes equations in the presence of a large-scale drag force that leads to the steady state of a turbulent inverse cascade. These flows provide an approximation to very fast rotating flows often observed in nature. The low dimensionality of the system allows for the realization of a large number of numerical simulations and thus the investigation of a wide range of fluid Reynolds numbers Re, magnetic Reynolds numbers Rm and forcing length scales. This allows for the examination of dynamo properties at different limits that cannot be achieved with three-dimensional simulations. We examine dynamos for both large and small magnetic Prandtl-number turbulent flows Pm = Rm/Re, close to and away from the dynamo onset, as well as dynamos in the presence of scale separation. In particular, we determine the properties of the dynamo onset as a function of Re and the asymptotic behaviour in the large Rm limit. We are thus able to give a complete description of the dynamo properties of these turbulent 2.5-D flows.

DOI

5

Large-scale instabilities of helical flows - Cameron, Alexandre and Alexakis, Alexandros and Brachet, Marc-Etienne

PHYSICAL REVIEW FLUIDS 1, (2016)

Abstract : Large-scale hydrodynamic instabilities of periodic helical flows of a given wave number K are investigated using three-dimensional Floquet numerical computations. In the Floquet formalism the unstable field is expanded in modes of different spacial periodicity. This allows us (i) to clearly distinguish large from small scale instabilities and (ii) to study modes of wave number q of arbitrarily large-scale separation q << K. Different flows are examined including flows that exhibit small-scale turbulence. The growth rate sigma of the most unstable mode is measured as a function of the scale separation q/K << 1 and the Reynolds number Re. It is shown that the growth rate follows the scaling s. q if an AKA effect [Frisch et al., Physica D: Nonlinear Phenomena 28, 382 (1987)] is present or a negative eddy viscosity scaling sigma alpha q(2) in its absence. This holds both for the Re << 1 regime where previously derived asymptotic results are verified but also for Re = O(1) that is beyond their range of validity. Furthermore, for values of Re above a critical value Re-S(c) beyond which small-scale instabilities are present, the growth rate becomes independent of q and the energy of the perturbation at large scales decreases with scale separation. The nonlinear behavior of these large-scale instabilities is also examined in the nonlinear regime where the largest scales of the system are found to be the most dominant energetically. These results are interpreted by low-order models.

PHYSICAL REVIEW FLUIDS 1, (2016)

LPS

Abstract : Large-scale hydrodynamic instabilities of periodic helical flows of a given wave number K are investigated using three-dimensional Floquet numerical computations. In the Floquet formalism the unstable field is expanded in modes of different spacial periodicity. This allows us (i) to clearly distinguish large from small scale instabilities and (ii) to study modes of wave number q of arbitrarily large-scale separation q << K. Different flows are examined including flows that exhibit small-scale turbulence. The growth rate sigma of the most unstable mode is measured as a function of the scale separation q/K << 1 and the Reynolds number Re. It is shown that the growth rate follows the scaling s. q if an AKA effect [Frisch et al., Physica D: Nonlinear Phenomena 28, 382 (1987)] is present or a negative eddy viscosity scaling sigma alpha q(2) in its absence. This holds both for the Re << 1 regime where previously derived asymptotic results are verified but also for Re = O(1) that is beyond their range of validity. Furthermore, for values of Re above a critical value Re-S(c) beyond which small-scale instabilities are present, the growth rate becomes independent of q and the energy of the perturbation at large scales decreases with scale separation. The nonlinear behavior of these large-scale instabilities is also examined in the nonlinear regime where the largest scales of the system are found to be the most dominant energetically. These results are interpreted by low-order models.

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6

Fate of Alpha Dynamos at Large Rm - Cameron, Alexandre and Alexakis, Alexandros

PHYSICAL REVIEW LETTERS 117, (2016)

Abstract : At the heart of today's solar magnetic field evolution models lies the alpha dynamo description. In this work, we investigate the fate of alpha dynamos as the magnetic Reynolds number Rm is increased. Using Floquet theory, we are able to precisely quantify mean-field effects like the alpha and beta effect (i) by rigorously distinguishing dynamo modes that involve large-scale components from the ones that only involve small scales, and by (ii) providing a way to investigate arbitrary large-scale separations with minimal computational cost. We apply this framework to helical and nonhelical flows as well as to random flows with short correlation time. Our results determine that the alpha description is valid for Rm smaller than a critical value Rm(c) at which small-scale dynamo instability starts. When Rm is above Rmc, the dynamo ceases to follow the mean-field description and the growth rate of the large-scale modes becomes independent of the scale separation, while the energy in the large-scale modes is inversely proportional to the square of the scale separation. The results in this second regime do not depend on the presence of helicity. Thus, alpha-type modeling for solar and stellar models needs to be reevaluated and new directions for mean-field modeling are proposed.

PHYSICAL REVIEW LETTERS 117, (2016)

LPS

Abstract : At the heart of today's solar magnetic field evolution models lies the alpha dynamo description. In this work, we investigate the fate of alpha dynamos as the magnetic Reynolds number Rm is increased. Using Floquet theory, we are able to precisely quantify mean-field effects like the alpha and beta effect (i) by rigorously distinguishing dynamo modes that involve large-scale components from the ones that only involve small scales, and by (ii) providing a way to investigate arbitrary large-scale separations with minimal computational cost. We apply this framework to helical and nonhelical flows as well as to random flows with short correlation time. Our results determine that the alpha description is valid for Rm smaller than a critical value Rm(c) at which small-scale dynamo instability starts. When Rm is above Rmc, the dynamo ceases to follow the mean-field description and the growth rate of the large-scale modes becomes independent of the scale separation, while the energy in the large-scale modes is inversely proportional to the square of the scale separation. The results in this second regime do not depend on the presence of helicity. Thus, alpha-type modeling for solar and stellar models needs to be reevaluated and new directions for mean-field modeling are proposed.

DOI

7

Rotating Taylor-Green flow - Alexakis, A.

JOURNAL OF FLUID MECHANICS 769, 46-78 (2015)

Abstract : The steady state of a forced Taylor-Green flow is investigated in a rotating frame of reference. The investigation involves the results of 184 numerical simulations for different Reynolds numbers ReF and Rossby numbers RoF. The large number of examined runs allows a systematic study that enables the mapping of the different behaviours observed to the parameter space (ReF; RoF), and the examination of different limiting procedures for approaching the large ReF small RoF limit. Four distinctly different states were identified: laminar, intermittent bursts, quasi-twodimensional condensates and weakly rotating turbulence. These four different states are separated by power-law boundaries R-OF proportional to Re-F(-gamma) in the small RoF limit. In this limit, the predictions of asymptotic expansions can be directly compared with the results of the direct numerical simulations. While the first-order expansion is in good agreement with the results of the linear stability theory, it fails to reproduce the dynamical behaviour of the quasi-two-dimensional part of the flow in the nonlinear regime, indicating that higher-order terms in the expansion need to be taken into account. The large number of simulations allows also to investigate the scaling that relates the amplitude of the fluctuations with the energy dissipation rate and the control parameters of the system for the different states of the flow. Different scaling was observed for different states of the flow, that are discussed in detail. The present results clearly demonstrate that the limits of small Rossby and large Reynolds numbers do not commute and it is important to specify the order in which they are taken.

JOURNAL OF FLUID MECHANICS 769, 46-78 (2015)

LPS

Abstract : The steady state of a forced Taylor-Green flow is investigated in a rotating frame of reference. The investigation involves the results of 184 numerical simulations for different Reynolds numbers ReF and Rossby numbers RoF. The large number of examined runs allows a systematic study that enables the mapping of the different behaviours observed to the parameter space (ReF; RoF), and the examination of different limiting procedures for approaching the large ReF small RoF limit. Four distinctly different states were identified: laminar, intermittent bursts, quasi-twodimensional condensates and weakly rotating turbulence. These four different states are separated by power-law boundaries R-OF proportional to Re-F(-gamma) in the small RoF limit. In this limit, the predictions of asymptotic expansions can be directly compared with the results of the direct numerical simulations. While the first-order expansion is in good agreement with the results of the linear stability theory, it fails to reproduce the dynamical behaviour of the quasi-two-dimensional part of the flow in the nonlinear regime, indicating that higher-order terms in the expansion need to be taken into account. The large number of simulations allows also to investigate the scaling that relates the amplitude of the fluctuations with the energy dissipation rate and the control parameters of the system for the different states of the flow. Different scaling was observed for different states of the flow, that are discussed in detail. The present results clearly demonstrate that the limits of small Rossby and large Reynolds numbers do not commute and it is important to specify the order in which they are taken.

DOI

8

Self-organisation and non-linear dynamics in driven magnetohydrodynamic turbulent flows - Dallas, V. and Alexakis, A.

PHYSICS OF FLUIDS 27, (2015)

Abstract : Magnetohydrodynamic (MHD) turbulent flows driven by random, large-scale, mechanical and electromagnetic external forces of zero helicities are investigated by means of direct numerical simulations. It is shown that despite the absence of helicities in the forcing, the system is attracted to helical states of large scale condensates that exhibit laminar behaviour despite the large value of the Reynolds numbers examined. We demonstrate that the correlation time of the external forces controls the time spent on these states, i.e., for short correlation times, the system remains in the turbulent state while as the correlation time is increased, the system spends more and more time in the helical states. As a result, time averaged statistics are significantly affected by the time spent on these states. These results have important implications for MHD and turbulence theory and they provide insight into various physical phenomena where condensates transpire. (C) 2015 AIP Publishing LLC.

PHYSICS OF FLUIDS 27, (2015)

LPS

Abstract : Magnetohydrodynamic (MHD) turbulent flows driven by random, large-scale, mechanical and electromagnetic external forces of zero helicities are investigated by means of direct numerical simulations. It is shown that despite the absence of helicities in the forcing, the system is attracted to helical states of large scale condensates that exhibit laminar behaviour despite the large value of the Reynolds numbers examined. We demonstrate that the correlation time of the external forces controls the time spent on these states, i.e., for short correlation times, the system remains in the turbulent state while as the correlation time is increased, the system spends more and more time in the helical states. As a result, time averaged statistics are significantly affected by the time spent on these states. These results have important implications for MHD and turbulence theory and they provide insight into various physical phenomena where condensates transpire. (C) 2015 AIP Publishing LLC.

DOI

9

Statistical Equilibria of Large Scales in Dissipative Hydrodynamic Turbulence - Dallas, V. and Fauve, S. and Alexakis, A.

PHYSICAL REVIEW LETTERS 115, (2015)

Abstract : We present a numerical study of the statistical properties of three-dimensional dissipative turbulent flows at scales larger than the forcing scale. Our results indicate that the large scale flow can be described to a large degree by the truncated Euler equations with the predictions of the zero flux solutions given by absolute equilibrium theory, both for helical and nonhelical flows. Thus, the functional shape of the large scale spectra can be predicted provided that scales sufficiently larger than the forcing length scale but also sufficiently smaller than the box size are examined. Deviations from the predictions of absolute equilibrium are discussed.

PHYSICAL REVIEW LETTERS 115, (2015)

LPS

Abstract : We present a numerical study of the statistical properties of three-dimensional dissipative turbulent flows at scales larger than the forcing scale. Our results indicate that the large scale flow can be described to a large degree by the truncated Euler equations with the predictions of the zero flux solutions given by absolute equilibrium theory, both for helical and nonhelical flows. Thus, the functional shape of the large scale spectra can be predicted provided that scales sufficiently larger than the forcing length scale but also sufficiently smaller than the box size are examined. Deviations from the predictions of absolute equilibrium are discussed.

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10

THE SIGNATURE OF INITIAL CONDITIONS ON MAGNETOHYDRODYNAMIC TURBULENCE - Dallas, V. and Alexakis, A.

ASTROPHYSICAL JOURNAL LETTERS 788, (2014)

Abstract : We demonstrate that the initial correlation between velocity and current density fluctuations can lead to the formation of enormous current sheets in freely evolving magnetohydrodynamic (MHD) turbulence. These coherent structures are observed at the peak of the energy dissipation rate and are the carriers of long-range correlations despite all of the nonlinear interactions during the formation of turbulence. The size of these structures spans our computational domain, dominating the scaling of the energy spectrum, which follows a E alpha k(-2) power law. As the Reynolds number increases, the curling of the current sheets due to Kelvin-Helmholtz-type instabilities and reconnection modifies the scaling of the energy spectrum from k(-2) toward k(-5/3). This transition occurs due to the decorrelation of the velocity and the current density which is proportional to Re-lambda(-3/2). Finite Reynolds number behavior is observed without reaching a finite asymptote for the energy dissipation rate even for a simulation of Re-lambda similar or equal to 440 with 2048(3) grid points. This behavior demonstrates that even state-of-the-art numerical simulations of the highest Reynolds numbers can be influenced by the choice of initial conditions and consequently they are inadequate to deduce unequivocally the fate of universality in MHD turbulence. Implications for astrophysical observations are discussed.

ASTROPHYSICAL JOURNAL LETTERS 788, (2014)

LPS

Abstract : We demonstrate that the initial correlation between velocity and current density fluctuations can lead to the formation of enormous current sheets in freely evolving magnetohydrodynamic (MHD) turbulence. These coherent structures are observed at the peak of the energy dissipation rate and are the carriers of long-range correlations despite all of the nonlinear interactions during the formation of turbulence. The size of these structures spans our computational domain, dominating the scaling of the energy spectrum, which follows a E alpha k(-2) power law. As the Reynolds number increases, the curling of the current sheets due to Kelvin-Helmholtz-type instabilities and reconnection modifies the scaling of the energy spectrum from k(-2) toward k(-5/3). This transition occurs due to the decorrelation of the velocity and the current density which is proportional to Re-lambda(-3/2). Finite Reynolds number behavior is observed without reaching a finite asymptote for the energy dissipation rate even for a simulation of Re-lambda similar or equal to 440 with 2048(3) grid points. This behavior demonstrates that even state-of-the-art numerical simulations of the highest Reynolds numbers can be influenced by the choice of initial conditions and consequently they are inadequate to deduce unequivocally the fate of universality in MHD turbulence. Implications for astrophysical observations are discussed.

DOI

11

Role of dissipation in flexural wave turbulence: From experimental spectrum to Kolmogorov-Zakharov spectrum - Miquel, Benjamin and Alexakis, Alexandros and Mordant, Nicolas

PHYSICAL REVIEW E 89, (2014)

Abstract : The weak turbulence theory has been applied to waves in thin elastic plates obeying the Foppl-Von Karman dynamical equations. Subsequent experiments have shown a strong discrepancy between the theoretical predictions and the measurements. Both the dynamical equations and the weak turbulence theory treatment require some restrictive hypotheses. Here a direct numerical simulation of the Foppl-Von Karman equations is performed and reproduces qualitatively and quantitatively the experimental results when the experimentally measured damping rate of waves gamma(k) = a + bk(2) is used. This confirms that the Foppl-Von Karman equations are a valid theoretical framework to describe our experiments. When we progressively tune the dissipation so that to localize it at the smallest scales, we observe a gradual transition between the experimental spectrum and the Kolmogorov-Zakharov prediction. Thus, it is shown that dissipation has a major influence on the scaling properties of stationary solutions of weakly nonlinear wave turbulence.

PHYSICAL REVIEW E 89, (2014)

LPS

Abstract : The weak turbulence theory has been applied to waves in thin elastic plates obeying the Foppl-Von Karman dynamical equations. Subsequent experiments have shown a strong discrepancy between the theoretical predictions and the measurements. Both the dynamical equations and the weak turbulence theory treatment require some restrictive hypotheses. Here a direct numerical simulation of the Foppl-Von Karman equations is performed and reproduces qualitatively and quantitatively the experimental results when the experimentally measured damping rate of waves gamma(k) = a + bk(2) is used. This confirms that the Foppl-Von Karman equations are a valid theoretical framework to describe our experiments. When we progressively tune the dissipation so that to localize it at the smallest scales, we observe a gradual transition between the experimental spectrum and the Kolmogorov-Zakharov prediction. Thus, it is shown that dissipation has a major influence on the scaling properties of stationary solutions of weakly nonlinear wave turbulence.

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12

On the edge of an inverse cascade - Seshasayanan, Kannabiran and Benavides, Santiago Jose and Alexakis, Alexandros

PHYSICAL REVIEW E 90, (2014)

Abstract : We demonstrate that systems with a parameter-controlled inverse cascade can exhibit critical behavior for which at the critical value of the control parameter the inverse cascade stops. In the vicinity of such a critical point, standard phenomenological estimates for the energy balance will fail since the energy flux towards large length scales becomes zero. We demonstrate this using the computationally tractable model of two-dimensional (2D) magnetohydrodynamics in a periodic box. In the absence of any external magnetic forcing, the system reduces to hydrodynamic fluid turbulence with an inverse energy cascade. In the presence of strong magnetic forcing, the system behaves as 2D magnetohydrodynamic turbulence with forward energy cascade. As the amplitude of the magnetic forcing is varied, a critical value is met for which the energy flux towards the large scales becomes zero. Close to this point, the energy flux scales as a power law with the departure from the critical point and the normalized amplitude of the fluctuations diverges. Similar behavior is observed for the flux of the square vector potential for which no inverse flux is observed for weak magnetic forcing, while a finite inverse flux is observed for magnetic forcing above the critical point. We conjecture that this behavior is generic for systems of variable inverse cascade.

PHYSICAL REVIEW E 90, (2014)

LPS

Abstract : We demonstrate that systems with a parameter-controlled inverse cascade can exhibit critical behavior for which at the critical value of the control parameter the inverse cascade stops. In the vicinity of such a critical point, standard phenomenological estimates for the energy balance will fail since the energy flux towards large length scales becomes zero. We demonstrate this using the computationally tractable model of two-dimensional (2D) magnetohydrodynamics in a periodic box. In the absence of any external magnetic forcing, the system reduces to hydrodynamic fluid turbulence with an inverse energy cascade. In the presence of strong magnetic forcing, the system behaves as 2D magnetohydrodynamic turbulence with forward energy cascade. As the amplitude of the magnetic forcing is varied, a critical value is met for which the energy flux towards the large scales becomes zero. Close to this point, the energy flux scales as a power law with the departure from the critical point and the normalized amplitude of the fluctuations diverges. Similar behavior is observed for the flux of the square vector potential for which no inverse flux is observed for weak magnetic forcing, while a finite inverse flux is observed for magnetic forcing above the critical point. We conjecture that this behavior is generic for systems of variable inverse cascade.

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13

Large-Scale Magnetic Fields in Magnetohydrodynamic Turbulence - Alexakis, Alexandros

PHYSICAL REVIEW LETTERS 110, (2013)

Abstract : High Reynolds number magnetohydrodynamic turbulence in the presence of zero-flux large-scale magnetic fields is investigated as a function of the magnetic field strength. For a variety of flow configurations, the energy dissipation rate epsilon follows the scaling epsilon proportional to U-rms(3)/l even when the large-scale magnetic field energy is twenty times larger than the kinetic energy. A further increase of the magnetic energy showed a transition to the epsilon proportional to (UrmsBrms)-B-2/l scaling implying that magnetic shear becomes more efficient at this point at cascading the energy than the velocity fluctuations. Strongly helical configurations form nonturbulent helicity condensates that deviate from these scalings. Weak turbulence scaling was absent from the investigation. Finally, the magnetic energy spectra support the Kolmogorov spectrum k(-5/3) while kinetic energy spectra are closer to the Iroshnikov-Kraichnan spectrum k(-3/2) as observed in the solar wind. DOI: 10.1103/PhysRevLett.110.084502

PHYSICAL REVIEW LETTERS 110, (2013)

LPS

Abstract : High Reynolds number magnetohydrodynamic turbulence in the presence of zero-flux large-scale magnetic fields is investigated as a function of the magnetic field strength. For a variety of flow configurations, the energy dissipation rate epsilon follows the scaling epsilon proportional to U-rms(3)/l even when the large-scale magnetic field energy is twenty times larger than the kinetic energy. A further increase of the magnetic energy showed a transition to the epsilon proportional to (UrmsBrms)-B-2/l scaling implying that magnetic shear becomes more efficient at this point at cascading the energy than the velocity fluctuations. Strongly helical configurations form nonturbulent helicity condensates that deviate from these scalings. Weak turbulence scaling was absent from the investigation. Finally, the magnetic energy spectra support the Kolmogorov spectrum k(-5/3) while kinetic energy spectra are closer to the Iroshnikov-Kraichnan spectrum k(-3/2) as observed in the solar wind. DOI: 10.1103/PhysRevLett.110.084502

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14

Transition from Wave Turbulence to Dynamical Crumpling in Vibrated Elastic Plates - Miquel, Benjamin and Alexakis, Alexandros and Josserand, Christophe and Mordant, Nicolas

PHYSICAL REVIEW LETTERS 111, (2013)

Abstract : We study the dynamical regime of wave turbulence of a vibrated thin elastic plate based on experimental and numerical observations. We focus our study on the strongly nonlinear regime described in a previous Letter by Yokoyama and Takaoka. At small forcing, a weakly nonlinear regime is compatible with the weak turbulence theory when the dissipation is localized at high wave number. When the forcing intensity is increased, a strongly nonlinear regime emerges: singular structures dominate the dynamics at large scales whereas at small scales the weak turbulence is still present. A turbulence of singular structures with folds and D cones develops that alters significantly the energy spectra and causes the emergence of intermittency.

PHYSICAL REVIEW LETTERS 111, (2013)

LPS

Abstract : We study the dynamical regime of wave turbulence of a vibrated thin elastic plate based on experimental and numerical observations. We focus our study on the strongly nonlinear regime described in a previous Letter by Yokoyama and Takaoka. At small forcing, a weakly nonlinear regime is compatible with the weak turbulence theory when the dissipation is localized at high wave number. When the forcing intensity is increased, a strongly nonlinear regime emerges: singular structures dominate the dynamics at large scales whereas at small scales the weak turbulence is still present. A turbulence of singular structures with folds and D cones develops that alters significantly the energy spectra and causes the emergence of intermittency.

DOI

15

Structures and dynamics of small scales in decaying magnetohydrodynamic turbulence - Dallas, V. and Alexakis, A.

PHYSICS OF FLUIDS 25, (2013)

Abstract : The topological and dynamical features of small scales are studied in the context of decaying magnetohydrodynamic turbulent flows using direct numerical simulations. Joint probability density functions (PDFs) of the invariants of gradient quantities related to the velocity and the magnetic fields demonstrate that structures and dynamics at the time of maximum dissipation depend on the large scale initial conditions at the examined Reynolds numbers. This is evident in particular from the fact that each flow has a different shape for the joint PDF of the invariants of the velocity gradient in contrast to the universal teardrop shape of hydrodynamic turbulence. The general picture that emerges from the analysis of the invariants is that regions of high vorticity are correlatedwith regions of high strain rate S also in contrast to hydrodynamic turbulent flows. Magnetic strain dominated regions are also well correlated with region of high current density j. Viscous dissipation (proportional to S-2) as well as Ohmic dissipation (proportional to j(2)) resides in regions where strain and rotation are locally almost in balance. The structures related to the velocity gradient possess different characteristics than those associated with the magnetic field gradient with the latter being locally more quasi-two dimensional. (C) 2013 AIP Publishing LLC.

PHYSICS OF FLUIDS 25, (2013)

LPS

Abstract : The topological and dynamical features of small scales are studied in the context of decaying magnetohydrodynamic turbulent flows using direct numerical simulations. Joint probability density functions (PDFs) of the invariants of gradient quantities related to the velocity and the magnetic fields demonstrate that structures and dynamics at the time of maximum dissipation depend on the large scale initial conditions at the examined Reynolds numbers. This is evident in particular from the fact that each flow has a different shape for the joint PDF of the invariants of the velocity gradient in contrast to the universal teardrop shape of hydrodynamic turbulence. The general picture that emerges from the analysis of the invariants is that regions of high vorticity are correlatedwith regions of high strain rate S also in contrast to hydrodynamic turbulent flows. Magnetic strain dominated regions are also well correlated with region of high current density j. Viscous dissipation (proportional to S-2) as well as Ohmic dissipation (proportional to j(2)) resides in regions where strain and rotation are locally almost in balance. The structures related to the velocity gradient possess different characteristics than those associated with the magnetic field gradient with the latter being locally more quasi-two dimensional. (C) 2013 AIP Publishing LLC.

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16

Origins of the k(-2) spectrum in decaying Taylor-Green magnetohydrodynamic turbulent flows - Dallas, V. and Alexakis, A.

PHYSICAL REVIEW E 88, (2013)

Abstract : We investigate the origins of k(-2) spectrum in a decaying Taylor-Green magnetohydrodynamic flow with zero large scale magnetic flux that was reported by Lee et al. [Phys. Rev. E 81, 016318 ( 2010)]. So far, a possible candidate for this scaling exponent has been the weak turbulence phenomenology. From our numerical simulations, we observe that current sheets in the magnetic Taylor-Green flow are formed in regions of magnetic discontinuities. Based on this observation and by studying the influence of the current sheets on the energy spectrum, using a filtering technique, we argue that the discontinuities are responsible for the -2 power law scaling of the energy spectra of this flow.

PHYSICAL REVIEW E 88, (2013)

LPS

Abstract : We investigate the origins of k(-2) spectrum in a decaying Taylor-Green magnetohydrodynamic flow with zero large scale magnetic flux that was reported by Lee et al. [Phys. Rev. E 81, 016318 ( 2010)]. So far, a possible candidate for this scaling exponent has been the weak turbulence phenomenology. From our numerical simulations, we observe that current sheets in the magnetic Taylor-Green flow are formed in regions of magnetic discontinuities. Based on this observation and by studying the influence of the current sheets on the energy spectrum, using a filtering technique, we argue that the discontinuities are responsible for the -2 power law scaling of the energy spectra of this flow.

DOI

17

Symmetry breaking of decaying magnetohydrodynamic Taylor-Green flows and consequences for universality - Dallas, V. and Alexakis, A.

PHYSICAL REVIEW E 88, (2013)

Abstract : We investigate the evolution and stability of a decaying magnetohydrodynamic Taylor-Green flow, using pseudospectral simulations with resolutions up to 2048(3). The chosen flow has been shown to result in a steep total energy spectrum with power law behavior k(-2). We study the symmetry breaking of this flow by exciting perturbations of different amplitudes. It is shown that for any finite amplitude perturbation there is a high enough Reynolds number for which the perturbation will grow enough at the peak of dissipation rate resulting in a nonlinear feedback into the flow and subsequently break the Taylor-Green symmetries. In particular, we show that symmetry breaking at large scales occurs if the amplitude of the perturbation is sigma(crit) similar to Re-1 and at small scales occurs if sigma(crit) similar to Re-3/2. This symmetry breaking modifies the scaling laws of the energy spectra at the peak of dissipation rate away from the k(-2) scaling and towards the classical k(-5/3) and k(-3/2) power laws.

PHYSICAL REVIEW E 88, (2013)

LPS

Abstract : We investigate the evolution and stability of a decaying magnetohydrodynamic Taylor-Green flow, using pseudospectral simulations with resolutions up to 2048(3). The chosen flow has been shown to result in a steep total energy spectrum with power law behavior k(-2). We study the symmetry breaking of this flow by exciting perturbations of different amplitudes. It is shown that for any finite amplitude perturbation there is a high enough Reynolds number for which the perturbation will grow enough at the peak of dissipation rate resulting in a nonlinear feedback into the flow and subsequently break the Taylor-Green symmetries. In particular, we show that symmetry breaking at large scales occurs if the amplitude of the perturbation is sigma(crit) similar to Re-1 and at small scales occurs if sigma(crit) similar to Re-3/2. This symmetry breaking modifies the scaling laws of the energy spectra at the peak of dissipation rate away from the k(-2) scaling and towards the classical k(-5/3) and k(-3/2) power laws.

DOI

18

Anomalous Exponents at the Onset of an Instability - Petrelis, F. and Alexakis, A.

PHYSICAL REVIEW LETTERS 108, (2012)

Abstract : Critical exponents are calculated exactly at the onset of an instability, by using asymptotic expansion techniques. When the unstable mode is subject to multiplicative noise whose spectrum at zero frequency vanishes, we show that the critical behavior can be anomalous; i.e., the mode amplitude X scales with departure from onset mu as < X > proportional to mu(beta) with an exponent beta different from its deterministic value. This behavior is observed in a direct numerical simulation of the dynamo instability, and our results provide a possible explanation for recent experimental observations.

PHYSICAL REVIEW LETTERS 108, (2012)

LPS

Abstract : Critical exponents are calculated exactly at the onset of an instability, by using asymptotic expansion techniques. When the unstable mode is subject to multiplicative noise whose spectrum at zero frequency vanishes, we show that the critical behavior can be anomalous; i.e., the mode amplitude X scales with departure from onset mu as < X > proportional to mu(beta) with an exponent beta different from its deterministic value. This behavior is observed in a direct numerical simulation of the dynamo instability, and our results provide a possible explanation for recent experimental observations.

DOI

19

Critical Exponents in Zero Dimensions - Alexakis, A. and Petrelis, F.

JOURNAL OF STATISTICAL PHYSICS 149, 738-753 (2012)

Abstract : In the vicinity of the onset of an instability, we investigate the effect of colored multiplicative noise on the scaling of the moments of the unstable mode amplitude. We introduce a family of zero dimensional models for which we can calculate the exact value of the critical exponents beta (m) for all the moments. The results are obtained through asymptotic expansions that use the distance to onset as a small parameter. The examined family displays a variety of behaviors of the critical exponents that includes anomalous exponents: exponents that differ from the deterministic (mean-field) prediction, and multiscaling: non-linear dependence of the exponents on the order of the moment.

JOURNAL OF STATISTICAL PHYSICS 149, 738-753 (2012)

LPS

Abstract : In the vicinity of the onset of an instability, we investigate the effect of colored multiplicative noise on the scaling of the moments of the unstable mode amplitude. We introduce a family of zero dimensional models for which we can calculate the exact value of the critical exponents beta (m) for all the moments. The results are obtained through asymptotic expansions that use the distance to onset as a small parameter. The examined family displays a variety of behaviors of the critical exponents that includes anomalous exponents: exponents that differ from the deterministic (mean-field) prediction, and multiscaling: non-linear dependence of the exponents on the order of the moment.

DOI

20

Nonlinear dynamos at infinite magnetic Prandtl number - Alexakis, Alexandros

PHYSICAL REVIEW E 83, (2011)

Abstract : The dynamo instability is investigated in the limit of infinite magnetic Prandtl number. In this limit the fluid is assumed to be very viscous so that the inertial terms can be neglected and the flow is enslaved to the forcing. The forcing consist of an external forcing function that drives the dynamo flow and the resulting Lorentz force caused by the back reaction of the magnetic field. The flows under investigation are the Archontis flow and the ABC flow forced at two different scales. The investigation covers roughly 3 orders of magnitude of the magnetic Reynolds number above onset. All flows show a weak increase of the averaged magnetic energy as the magnetic Reynolds number is increased. Most of the magnetic energy is concentrated in flat elongated structures that produce a Lorentz force with small solenoidal projection so that the resulting magnetic field configuration is almost force free. Although the examined system has zero kinetic Reynolds number at sufficiently large magnetic Reynolds number the structures are unstable to small scale fluctuations that result in a chaotic temporal behavior.

PHYSICAL REVIEW E 83, (2011)

LPS

Abstract : The dynamo instability is investigated in the limit of infinite magnetic Prandtl number. In this limit the fluid is assumed to be very viscous so that the inertial terms can be neglected and the flow is enslaved to the forcing. The forcing consist of an external forcing function that drives the dynamo flow and the resulting Lorentz force caused by the back reaction of the magnetic field. The flows under investigation are the Archontis flow and the ABC flow forced at two different scales. The investigation covers roughly 3 orders of magnitude of the magnetic Reynolds number above onset. All flows show a weak increase of the averaged magnetic energy as the magnetic Reynolds number is increased. Most of the magnetic energy is concentrated in flat elongated structures that produce a Lorentz force with small solenoidal projection so that the resulting magnetic field configuration is almost force free. Although the examined system has zero kinetic Reynolds number at sufficiently large magnetic Reynolds number the structures are unstable to small scale fluctuations that result in a chaotic temporal behavior.