Abstract
Abstract. This paper presents a novel methodology to use direct numerical simulation (DNS) to study the impact of isotropic homogeneous turbulence on the condensational growth of cloud droplets. As shown by previous DNS studies, the impact of turbulence increases with the computational domain size, that is, with the Reynolds number, because larger eddies generate higher and longer-lasting supersaturation fluctuations that affect growth of individual cloud droplets. The traditional DNS can only simulate a limited range of scales because of the excessive computational cost that comes from resolving all scales involved, that is, from large scales at which the turbulent kinetic energy (TKE) is introduced down to the Kolmogorov microscale, and from following every single droplet. The novel approach is referred to as the “scaled-up DNS”. The scaling up is done in two parts, first by increasing both the computational domain and the Kolmogorov microscale and second by using super-droplets instead of real droplets. To ensure proper dissipation of TKE and scalar variance at small scales, molecular transport coefficients are appropriately scaled up with the grid length. For the scaled-up domains, say, meters and tens of meters, one needs to follow billions of real droplets. This is not computationally feasible, and so-called super-droplets are applied in scaled-up DNS simulations. Each super-droplet represents an ensemble of identical real droplets, and the number of real droplets represented by a super-droplet is referred to as the multiplicity attribute. After simple tests showing the validity of the methodology, scaled-up DNS simulations are conducted for five domains, the largest of 643 m3 volume using a DNS of 2563 grid points and various multiplicities. All simulations are carried out with vanishing mean vertical velocity and with no mean supersaturation, similarly to past DNS studies. As expected, the supersaturation fluctuations as well as the spread in droplet size distribution increase with the domain size, with the droplet radius variance increasing in time t as t1∕2 as identified in previous DNS studies. Scaled-up simulations with different multiplicities document numerical convergence of the scaled-up solutions. Finally, we compare the scaled-up DNS results with a simple stochastic model that calculates supersaturation fluctuations based on the vertical velocity fluctuations updated using the Langevin equation. Overall, the results document similar scaling to previous small-domain DNS simulations and support the notion that the stochastic subgrid-scale model is a valuable tool for the multi-scale simulation of droplet spectral evolution applying a large-eddy simulation model.
Highlights
The impact of turbulence on the growth of cloud droplets is an important and still poorly understood aspect of cloud physics
To show that the direct numerical simulation (DNS) and scaled-up DNS feature the same turbulent kinetic energy (TKE) dissipation rate, we show the dissipation rate calculated as twice the product of the scaled-up viscosity and the mean simulated enstrophy as typically done in DNS studies
This study presents a novel modeling methodology that extends the traditional technique to simulate homogeneous isotropic turbulence, the direct numerical simulation (DNS)
Summary
The impact of turbulence on the growth of cloud droplets is an important and still poorly understood aspect of cloud physics. The increase in the small-scale dissipation is critical for traditional DNS models applying spectral techniques to simulate homogeneous isotropic turbulence as applied in this study. This is different from past turbulencerelated studies applying finite-difference models with large domains and spatially uniform diffusion coefficients (e.g., Grabowski and Clark, 1993; Mellado et al, 2018; Rotunno and Bryan, 2018) or no explicit diffusion at all as in the socalled implicit large-eddy simulation (ILES; e.g., Margolin et al, 2006; Grinstein et al, 2007).
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