Energy exchange in two-dimensional compressible Taylor-Green vortex flows

Compressible turbulence exhibits complex mechanisms of energy exchange between kinetic and internal modes, yet their dependence on Mach number remains poorly understood. This work investigates two-dimensional compressible Taylor--Green vortex flows and reveals how Mach number governs the pathway of internal-kinetic energy transfer. We identify three stages of energy evolution and derive an analytical model that predicts the initial growth of dilatational kinetic energy. The results provide new insight into compressible-flow energy exchange and inform future turbulence modeling strategies.