Spatiotemporal Properties of Compressible Magnetohydrodynamic Turbulence from Space Plasma

Previous studies have established that a weak-to-strong transition occurs in Alfvenic magnetohydrodynamic (MHD) turbulence as energy cascades from large to small scales. However, the spatiotemporal (frequency-wavenumber) properties of compressible MHD turbulence involving all eigenmodes, which encode the strength of nonlinear interactions, remain difficult to characterize observationally. Consequently, whether a similar weak-to-strong transition occurs in compressible turbulence remains elusive. Using a novel multi-spacecraft, polarization-based mode-decomposition technique with measurements from the Cluster spacecraft in Earth's magnetosheath, we obtain spatiotemporal power spectra of all MHD eigenmodes and present the first quantitative assessment of nonlinear frequency broadening. Our results show that slow modes exhibit a weak-to-strong transition, evolving from wave-like peaks to frequency-broadened spectra as nonlinearity increases, whereas fast modes remain weakly turbulent with narrow peaks near their eigenfrequencies. Both Alfvenic and compressible fluctuations contribute significantly to low-frequency, large-scale quasi-two-dimensional structures. These findings provide a comprehensive observational characterization of compressible turbulence across mode composition, spatiotemporal scales, and weak-strong turbulence regimes, with implications for energetic particle transport, turbulent dynamos, plasma heating, and solar wind-magnetosphere coupling.