Reynolds-number dependence of turbulence enhancement on collision growth

Abstract. This study investigates the Reynolds-number dependence of turbulence enhancement on the collision growth of cloud droplets. The Onishi turbulent coagulation kernel proposed in Onishi et al. (2015) is updated by using the direct numerical simulation (DNS) results for the Taylor-microscale-based Reynolds number (Re_λ) up to 1140. The DNS results for particles with a small Stokes number (St) show a consistent Reynolds-number dependence of the so-called clustering effect with the locality theory proposed by Onishi et al. (2015). It is confirmed that the present Onishi kernel is more robust for a wider St range and has better agreement with the Reynolds-number dependence shown by the DNS results. The present Onishi kernel is then compared with the Ayala–Wang kernel (Ayala et al., 2008a; Wang et al., 2008). At low and moderate Reynolds numbers, both kernels show similar values except for r₂ ∼ r₁, for which the Ayala–Wang kernel shows much larger values due to its large turbulence enhancement on collision efficiency. A large difference is observed for the Reynolds-number dependences between the two kernels. The Ayala–Wang kernel increases for the autoconversion region (r₁, r₂ < 40 µm) and for the accretion region (r₁ < 40 and r₂ > 40 µm; r₁ > 40 and r₂ < 40 µm) as Re_λ increases. In contrast, the Onishi kernel decreases for the autoconversion region and increases for the rain–rain self-collection region (r₁, r₂ > 40 µm). Stochastic collision–coalescence equation (SCE) simulations are also conducted to investigate the turbulence enhancement on particle size evolutions. The SCE with the Ayala–Wang kernel (SCE-Ayala) and that with the present Onishi kernel (SCE-Onishi) are compared with results from the Lagrangian Cloud Simulator (LCS; Onishi et al., 2015), which tracks individual particle motions and size evolutions in homogeneous isotropic turbulence. The SCE-Ayala and SCE-Onishi kernels show consistent results with the LCS results for small Re_λ. The two SCE simulations, however, show different Reynolds-number dependences, indicating possible large differences in atmospheric turbulent clouds with large Re_λ.