DOI

1

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

2

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.

DOI

3

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

4

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.

DOI

5

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

DOI

6

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

7

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.