Abstract
A method for extracting coherent vorticity sheets and current sheets out of three-dimensional homogeneous magnetohydrodynamic (MHD) turbulence is proposed, which is based on the orthogonal wavelet decomposition of the vorticity and current density fields. Thresholding the wavelet coefficients allows both fields to be split into coherent and incoherent parts. The fields to be analyzed are obtained by direct numerical simulation (DNS) of forced incompressible MHD turbulence without mean magnetic field, using a classical Fourier spectral method at a resolution of 5123. Coherent vorticity sheets and current sheets are extracted from the DNS data at a given time instant. It is found that the coherent vorticity and current density preserve both the vorticity sheets and the current sheets present in the total fields while retaining only a few percent of the degrees of freedom. The incoherent vorticity and current density are shown to be structureless and of mainly dissipative nature. The spectral distributions of kinetic and magnetic energies of the coherent fields only differ in the dissipative range, while the corresponding incoherent fields exhibit near-equipartition of energy. The probability distribution functions of total and coherent fields for both vorticity and current density coincide almost perfectly, while the incoherent fields have strongly reduced variances. Studying the energy flux confirms that the nonlinear dynamics is fully captured by the coherent fields only.
Highlights
Direct numerical simulationsDNSsof magnetohydrodynamicMHDturbulence, starting with the pioneering work,1 revealed the formation of organized structures, typically characterized as strong and intense vorticity and current sheets.2–5 The topology of these structures differs from those in hydrodynamicHDturbulence, where mostly tubelike structures rather than sheetlike structures have been observed.6–9 The extraction and characterization of these organized structures are a long lasting problem
We present some perspectives on the coherent vorticity sheet and current sheet simulation methodCVCSbased on the orthogonal wavelet decomposition
We introduced a method for extracting coherent vorticity sheets and current sheets out of three-dimensional homogeneous MHD turbulence
Summary
Direct numerical simulationsDNSsof magnetohydrodynamicMHDturbulence, starting with the pioneering work, revealed the formation of organized structures, typically characterized as strong and intense vorticity and current sheets. The topology of these structures differs from those in hydrodynamicHDturbulence, where mostly tubelike structures rather than sheetlike structures have been observed. The extraction and characterization of these organized structures are a long lasting problem. The coherent vortex extractionCVEmethod introduced for two- and three-dimensional hydrodynamic turbulence is one of the most useful tools for the extraction of coherent vortices from HD turbulence together with a significant reduction in the number of degrees of freedom It is based on the orthogonal wavelet decomposition of vorticity and allows the wavelet coefficients to be split into two. The CVE method was applied to DNS data of threedimensional homogeneous isotropic hydrodynamic turbulence at resolution 2563 and a Taylor microscale Reynolds number of R = 150.20 It was shown that only 3% of the wavelet coefficients of vorticity represent the coherent vortex tubes, which retain 99% of the energy and 75% of the enstrophy of the flow. Appendix A discusses the influence of divergence of the vector valued wavelet basis and Appendix B covers the dependence of the number of iterations in the CVCE method
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