The evolution of the energy dissipation rate per unit mass, , in runs 1 and 2 performed up to and , respectively. Here, is the initial large eddy turnover time defined by , and is the initial integral length scale given by .
Isosurfaces of vorticity (left) and current density (right) of the total (top), coherent (middle), and incoherent contributions (bottom) in . The values of the isosurfaces are taken as for the total and coherent vorticity and for the current density. For the incoherent vorticity and current density fields, the isosurfaces are set to and , respectively. Here, and are the mean values of and for the total vorticity and current density fields, respectively, and and are standard deviation values of and , respectively. Cubes of size are visualized.
PDFs of the components of (a) the velocity and (b) the magnetic fields for the total, coherent, and incoherent fields in . Dotted lines: The Gaussian distributions with zero mean and the same standard deviation as each corresponding incoherent component.
PDFs of the components of (a) the vorticity and (b) the current density fields for the total, coherent, and incoherent fields in .
(a) Kinetic and (b) magnetic energy spectra of the total, coherent, and incoherent fields in .
Energy fluxes in .
Scale-dependent flatness of (a) velocity and (b) magnetic fields vs in .
Scale-dependent compression rates and vs in for and .
Scale-dependent overlap rate vs in .
(a) Kinetic and (b) magnetic enstrophy spectra of divergence-free parts in .
Compression rates and vs number of iterations in for and .
Scale-dependent overlap rate vs in . The rates for and are denoted by the solid curve with and the dashed curve with ●, respectively.
DNS parameters of runs 1 and 2. Here, is the maximum wavenumber of the retained modes and is the time increment. Note that .
Characteristics of the two DNS runs at .
Overall compression rates and , the percentages of the number of the wavelet coefficients retained by the coherent vorticity and current density fields over all scales, respectively, and percentages of kinetic energy, magnetic energy, kinematic enstrophy, and magnetic enstrophy kept by the coherent and incoherent fields. The CVCE method is applied to .
Statistical properties of the total, coherent, and incoherent fields obtained by CVCE applied to .
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