Energy occupation of waves and structures in 3D compressive MHD turbulence

Structures and propagating waves are often observed in solar wind turbulence. Their origins and features remain to be uncovered. In this work, we use 3D driven, compressible MHD turbulence simulations to investigate the global signatures of the driven fluctuations in whole spatial and temporal domain. With four-dimensional spatial-temporal (x, y, z, t) Fourier transformations implemented, we have identified two distinct main populations: waves, which satisfy the ω − k dispersion relations and are propagating; and structures, which satisfy the polarization relations but non-propagating (ω = 0). Whereas the overall turbulent energy spectrum is still consistent with k^−5/3, the contributions from waves and structures show very different behaviour in k space, with structures dominating at small k but waves becomes comparable to structures at large k. Overall, the fluctuations in the directions perpendicular to the large-scale mean field B₀ are a manifestation of structures, while along the parallel direction, the fluctuations are dominated by waves. Also, a significant portion of the incompressible structures are the Alfvénic nature, and with imbalanced increased, the waves predominantly propagate in one direction and nearly perpendicular to B₀. Differentiating the relative contributions from waves and structures could have important implications for understanding the non-linear cascade processes in the inertial range as well as particle-fluctuation interactions at small scales.