Effect of pressure-dilatation on energy spectrum evolution in compressible turbulence

The effect of internal-kinetic energy exchange on transient spectral energy transfer in compressible turbulence is investigated. We derive the spectral evolution equations for kinetic energy and pressure fields to highlight the key mechanisms that affect the turbulence spectral evolution. Direct numerical simulations of decaying isotropic turbulence are performed from solenoidal, dilatational, and mixed velocity initial conditions. It is shown that internal-kinetic energy exchange arising due to pressure-dilatation renders the dilatational kinetic energy amplitudes at large scales of motion to be oscillatory. The oscillatory behavior of amplitude diminishes with increasing wavenumber. The dilatational energy spectrum also exhibits a wider range of scales due to its inherent tendency to form shocks. The findings are expected to lead to an improved understanding of energy dynamics in high-speed compressible flows.