DOI

1

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

2

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

3

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.

DOI

4

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

5

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.