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In this Letter, we report compressible mode effects on relativisticmagnetohydrodynamic (RMHD) turbulence in Poynting-dominated plasmas using3-dimensional numerical simulations. We decomposed fluctuations in theturbulence into 3 MHD modes (fast, slow, and Alfv\'en) following the proceduremode decomposition in (Cho & Lazarian 2002), and analyzed their energy spectraand structure functions separately. We also analyzed the ratio of compressiblemode to Alfv\'en mode energy with respect to its Mach number. We found theratio of compressible mode increases not only with the Alfv\'en Mach number butwith the background magnetization, which indicates a strong coupling betweenthe fast and Alfv\'en modes and appearance of a new regime of RMHD turbulencein Poynting-dominated plasmas where the fast and Alfv\'en modes stronglycouples and cannot be separated, different from the non-relativistic MHD case.This finding will affect particle acceleration efficiency obtained by assumingAlfv\'enic critical balance turbulence, and will change the resulting photonspectra by non-thermal electrons.

Compressible Relativistic Magnetohydrodynamic Turbulence in Magnetically-Dominated Plasmas And Implications for A Strong-Coupling Regime