Cancellation exponent and multifractal structure in two-dimensional magnetohydrodynamics: direct numerical simulations and Lagrangian averaged modeling

Abstract

We present direct numerical simulations and Lagrangian averaged (also known as alpha-model) simulations of forced and free decaying magnetohydrodynamic turbulence in two dimensions. The statistics of sign cancellations of the current at small scales is studied using both the cancellation exponent and the fractal dimension of the structures. The alpha-model is found to have the same scaling behavior between positive and negative contributions as the direct numerical simulations. The alpha-model is also able to reproduce the time evolution of these quantities in free decaying turbulence. At large Reynolds numbers, an independence of the cancellation exponent with the Reynolds numbers is observed.

Finite size box effects have been taken into account in the definition of the partition function. This has resulted in a more clear scaling in all figures. Several points are clarified in the text

References in corpus (8)

• The Camassa-Holm equations as a closure model for turbulent channel flow
• A connection between the Camassa-Holm equations and turbulent flows in channels and pipes
• Direct Numerical Simulations of the Navier-Stokes Alpha Model
• Numerical study of dynamo action at low magnetic Prandtl numbers
• Averaged Lagrangians and the mean dynamical effects of fluctuations in continuum mechanics
• Analysis of cancellation in two-dimensional magnetohydrodynamic turbulence
• Numerical solutions of the three-dimensional magnetohydrodynamic alpha-model
• A numerical study of the alpha model for two-dimensional magnetohydrodynamic turbulent flows

Cited by in corpus (10)

• On the lack of universality in decaying magnetohydrodynamic turbulence
• Highly turbulent solutions of LANS-alpha and their LES potential
• The dynamics of unforced turbulence at high Reynolds number for Taylor-Green vortices generalized to MHD
• Turbulent magnetic dynamo excitation at low magnetic Prandtl number
• The Lagrangian-averaged model for magnetohydrodynamics turbulence and the absence of bottleneck
• Sign singularity of the local energy transfer in space plasma turbulence
• Adaptive mesh refinement with spectral accuracy for magnetohydrodynamics in two space dimensions
• High Reynolds number magnetohydrodynamic turbulence using a Lagrangian model
• Cancellation exponents in isotropic turbulence and magnetohydrodynamic turbulence
• Instrumental and Observational Artifacts in Quiet Sun Magnetic Flux Cance llation Functions