Kinetic energy dissipation rate field in the bulk of fully compressible convection*

We investigate the local statistics of the kinetic energy dissipation rate and its solenoidal, dilatational, and inhomogeneous components in the bulk of fully compressible convection (FCC). We employ direct numerical simulations in a fluid layer of aspect ratio Γ = 4 for fixed Prandtl number Pr = 0.7, superadiabaticity ε = 0.45 and dissipation number D = 0.5. The Rayleigh number Ra varies from 10⁵ to 10⁷. We observe that probability distribution functions (pdfs) are close to those in homogeneous isotropic turbulence: the left tails of the total and solenoidal dissipation rate fields follow 3/2 and 1/2 power laws, respectively, while the right tails follow a stretched exponential. The pdfs also show that FCC is markedly more intermittent than Boussinesq convection, a finding that is further reinforced by our multifractal analysis. Moreover, using the statistical and multifractal properties of the three parts of the dissipation rate field and their relative magnitude, we study their contribution to turbulent mixing in the bulk of the turbulent convection layer.