DOI

1

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

2

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.

DOI

3

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.