Statistics of Energy in Isothermal Supersonic Turbulence

Turbulence is a key process in many astrophysical systems. In this work we explore the statistics of thermal and kinetic energy of isothermal, supersonic, turbulent gas. We develop analytic formulas for the PDF of thermal and kinetic energies and their joint PDF. We compare these analytical models with a suite of simulations with a fixed resolution of ${1024}^3$ cells across 4 different Mach numbers (1, 2, 4, 8) and three different driving patterns (compressive, mixed, solenoidal). We discover an interesting jump discontinuity in the thermal energy PDF, which carries onto the joint PDF.