Energy Cascade and Damping in Fast-Mode Compressible Turbulence

This letter presents hybrid and fully kinetic particle-in-cell simulations of fast-mode compressible turbulence. Turbulence damping at magnetohydrodynamic (MHD) scales closely follows linear transit-time damping theory. Despite strong phase steepening, turbulence sustains robust cross-scale energy cascading. These findings resolve the long-standing question about the validity of classical wave theories in strongly nonlinear regimes and overturn the common presumption that wave steepening disrupts compressible turbulence cascade, thereby providing a more complete picture of MHD turbulence.