Cascade and damping of compressible turbulence: theory vs. observations

Compressible turbulence plays a central role in mediating energy transfer across scales in space and astrophysical plasmas. In this work, we present recent advances in both theoretical and observational studies of compressible turbulence. Using large-scale kinetic simulations, we investigate turbulence–particle interactions and demonstrate that damping at magnetohydrodynamic (MHD) scales quantitatively agrees with transit-time damping theory, even within fully developed nonlinear states. Remarkably, the turbulent cascade persists despite strong phase steepening, revealing robustness of cross-scale energy transfer. Furthermore, by applying an improved compressible MHD mode decomposition algorithm to Cluster spacecraft observations, we show that magnetic anisotropy in solar wind turbulence is strongly mode-dependent. Specifically, Alfvénic fluctuations exhibit a broad distribution of propagation angles, whereas compressible modes are predominantly concentrated near the quasi-parallel (slab-like) direction—consistent with our theoretical predictions. Together, these results bridge kinetic simulations and in situ measurements, advancing our understanding of of compressible turbulence.