# Clustering and energy spectra in two-dimensional dusty gas turbulence

## TL;DR

This study uses DNS to analyze how heavy inertial particles (dust) influence two-dimensional turbulent flows, revealing new clustering behaviors and energy spectrum scaling regimes dependent on particle properties and mass-loading.

## Contribution

It demonstrates the dependence of dust clustering and energy spectra on Stokes number and mass-loading, introducing a new scaling regime in the kinetic energy spectra.

## Key findings

- Clustering decreases with increased mass-loading.
- A new energy spectrum scaling regime emerges.
- Scaling exponent varies with Stokes number and mass-loading.

## Abstract

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 $({\phi}_{\rm m})$, 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 ${\phi}_{\rm m}$. In particular, clustering decreases as mass-loading $({\phi}_{\rm m})$, 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 $({\phi}_{\rm m} )$. 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.