Diffusional growth of cloud droplets in homogeneous isotropic turbulence: DNS, scaled-up DNS, and stochastic model
<p>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, t...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Copernicus Publications
2020-07-01
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| Series: | Atmospheric Chemistry and Physics |
| Online Access: | https://www.atmos-chem-phys.net/20/9087/2020/acp-20-9087-2020.pdf |
| _version_ | 1818036894205739008 |
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| author | L. Thomas L. Thomas W. W. Grabowski B. Kumar |
| author_facet | L. Thomas L. Thomas W. W. Grabowski B. Kumar |
| author_sort | L. Thomas |
| collection | DOAJ |
| description | <p>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 <span class="inline-formula">64<sup>3</sup></span> m<span class="inline-formula"><sup>3</sup></span> volume using a DNS of <span class="inline-formula">256<sup>3</sup></span> 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 <span class="inline-formula"><i>t</i></span> as <span class="inline-formula"><i>t</i><sup>1∕2</sup></span> 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.</p> |
| first_indexed | 2024-12-10T07:18:12Z |
| format | Article |
| id | doaj.art-7efc4608f57b4b6cb281d0590b1c9e94 |
| institution | Directory Open Access Journal |
| issn | 1680-7316 1680-7324 |
| language | English |
| last_indexed | 2024-12-10T07:18:12Z |
| publishDate | 2020-07-01 |
| publisher | Copernicus Publications |
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| series | Atmospheric Chemistry and Physics |
| spelling | doaj.art-7efc4608f57b4b6cb281d0590b1c9e942022-12-22T01:57:53ZengCopernicus PublicationsAtmospheric Chemistry and Physics1680-73161680-73242020-07-01209087910010.5194/acp-20-9087-2020Diffusional growth of cloud droplets in homogeneous isotropic turbulence: DNS, scaled-up DNS, and stochastic modelL. Thomas0L. Thomas1W. W. Grabowski2B. Kumar3HPCS, Indian Institute of Tropical Meteorology, Ministry of Earth Sciences, Pune 411008, IndiaDepartment of Atmospheric and Space Sciences, Savitribai Phule Pune University, Pune 411007, IndiaNational Center for Atmospheric Research, Boulder, Colorado, USAHPCS, Indian Institute of Tropical Meteorology, Ministry of Earth Sciences, Pune 411008, India<p>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 <span class="inline-formula">64<sup>3</sup></span> m<span class="inline-formula"><sup>3</sup></span> volume using a DNS of <span class="inline-formula">256<sup>3</sup></span> 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 <span class="inline-formula"><i>t</i></span> as <span class="inline-formula"><i>t</i><sup>1∕2</sup></span> 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.</p>https://www.atmos-chem-phys.net/20/9087/2020/acp-20-9087-2020.pdf |
| spellingShingle | L. Thomas L. Thomas W. W. Grabowski B. Kumar Diffusional growth of cloud droplets in homogeneous isotropic turbulence: DNS, scaled-up DNS, and stochastic model Atmospheric Chemistry and Physics |
| title | Diffusional growth of cloud droplets in homogeneous isotropic turbulence: DNS, scaled-up DNS, and stochastic model |
| title_full | Diffusional growth of cloud droplets in homogeneous isotropic turbulence: DNS, scaled-up DNS, and stochastic model |
| title_fullStr | Diffusional growth of cloud droplets in homogeneous isotropic turbulence: DNS, scaled-up DNS, and stochastic model |
| title_full_unstemmed | Diffusional growth of cloud droplets in homogeneous isotropic turbulence: DNS, scaled-up DNS, and stochastic model |
| title_short | Diffusional growth of cloud droplets in homogeneous isotropic turbulence: DNS, scaled-up DNS, and stochastic model |
| title_sort | diffusional growth of cloud droplets in homogeneous isotropic turbulence dns scaled up dns and stochastic model |
| url | https://www.atmos-chem-phys.net/20/9087/2020/acp-20-9087-2020.pdf |
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