Clustering and energy spectra in two-dimensional dusty gas turbulence

We present Direct Numerical Simulation (DNS) of heavy inertial particles (dust) immersed in two-dimensional turbulent flow (gas). The dust are modeled as mono-dispersed heavy particles capable of modifying the flow through two-way coupling. By varying the Stokes number (St) and the mass-loading parameter $({\varphi }_{\mathrm{m}})$, we study the clustering phenomenon and the gas phase kinetic energy spectra. We find that the dust-dust correlation dimension $(d_2)$ also depends on ${\varphi }_{\mathrm{m}}$. In particular, clustering decreases as mass-loading $({\varphi }_{\mathrm{m}})$, is increased. In the kinetic energy spectra of gas we show: (i) emergence of a new scaling regime, (ii) the scaling exponent in this regime is not unique but rather a function of both St and $({\varphi }_{\mathrm{m}})$. Using a scale-by-scale enstrophy budget analysis we show in the new scaling regime, viscous dissipation due to the gas balances back-reaction from the dust.