scholarly journals Comments on “Diffusional growth of cloud droplets in homogeneous isotropic turbulence: DNS, scaled-up DNS, and stochastic model” by Thomas et al.

2020 ◽  
Author(s):  
Anonymous
Keyword(s):  
Stochastic Model ◽  
Isotropic Turbulence ◽  
Homogeneous Isotropic Turbulence ◽  
Diffusional Growth ◽  
Cloud Droplets

scholarly journals Cloud droplet diffusional growth in homogeneous isotropic turbulence: bin microphysics versus Lagrangian superdroplet simulations

2020 ◽  
Author(s):  
Wojciech W. Grabowski ◽  
Lois Thomas
Keyword(s):  
Fluid Flow ◽  
Time Scale ◽  
Isotropic Turbulence ◽  
Spectral Width ◽  
Small Scale ◽  
Computational Domain ◽  
Homogeneous Isotropic Turbulence ◽  
Diffusional Growth ◽  
Droplet Concentration ◽  
Bin Microphysics

Abstract. Increase of the spectral width of initially monodisperse population of cloud droplets in homogeneous isotropic turbulence is investigated applying a finite-difference fluid flow model combined with either Eulerian bin microphysics or Lagrangian particle-based scheme. The turbulence is forced applying a variant of the so-called linear forcing method that maintains the mean turbulent kinetic energy (TKE) and the TKE partitioning between velocity components. The latter is important for maintaining the quasi-steady forcing of the supersaturation fluctuations that drive the increase of the spectral width. We apply a large computational domain, 643 m3, one of the domains considered in Thomas et al. (2020). The simulations apply 1 m grid length and are in the spirit of the implicit large eddy simulation (ILES), that is, with explicit small-scale dissipation provided by the model numerics. This is in contrast to the scaled-up direct numerical simulation (DNS) applied in Thomas et al. (2020). Two TKE intensities and three different droplet concentrations are considered. Analytic solutions derived in Sardina et al. (2015), valid for the case when the turbulence time scale is much larger than the droplet phase relaxation time scale, are used to guide the comparison between the two microphysics simulation techniques. The Lagrangian approach reproduces the scalings relatively well. Representing the spectral width increase in time is more challenging for the bin microphysics because appropriately high resolution in the bin space is needed. The bin width of 0.5 μm is only sufficient for the lowest droplet concentration, 26 cm−3. For the highest droplet concentration, 650 cm−3, even an order of magnitude smaller bin size is not sufficient. The scalings are not expected to be valid for the lowest droplet concentration and the high TKE case, and the two microphysics schemes represent similar departures. Finally, because the fluid flow is the same for all simulations featuring either low or high TKE, one can compare point-by-point simulation results. Such a comparison shows very close temperature and water vapor point-by-point values across the computational domain, and larger differences between simulated mean droplet radii and spectral width. The latter are explained by fundamental differences in the two simulation methodologies, numerical diffusion in the Eulerian bin approach and relatively small number of Lagrangian particles that are used in the particle-based microphysics.

Non-Gaussianity in turbulent relative dispersion

2019 ◽  
Vol 867 ◽  
pp. 877-905
Author(s):  
B. J. Devenish ◽  
D. J. Thomson
Keyword(s):  
Stochastic Model ◽  
Velocity Distribution ◽  
Relative Velocity ◽  
Isotropic Turbulence ◽  
Dispersion Model ◽  
Original Model ◽  
Direct Numerical Simulations ◽  
Relative Dispersion ◽  
Lagrangian Stochastic Model ◽  
Homogeneous Isotropic Turbulence

We present an extension of Thomson’s (J. Fluid Mech., vol. 210, 1990, pp. 113–153) two-particle Lagrangian stochastic model that is constructed to be consistent with the $4/5$ law of turbulence. The rate of separation in the new model is reduced relative to the original model with zero skewness in the Eulerian longitudinal relative velocity distribution and is close to recent measurements from direct numerical simulations of homogeneous isotropic turbulence. The rate of separation in the equivalent backwards dispersion model is approximately a factor of 2.9 larger than the forwards dispersion model, a result that is consistent with previous work.

scholarly journals Reynolds-number dependence of turbulence enhancement on collision growth

2016 ◽  
Vol 16 (19) ◽  
pp. 12441-12455 ◽  
Author(s):  
Ryo Onishi ◽  
Axel Seifert
Keyword(s):  
Reynolds Number ◽  
Isotropic Turbulence ◽  
Reynolds Numbers ◽  
Stokes Number ◽  
Homogeneous Isotropic Turbulence ◽  
Collision Efficiency ◽  
Cloud Droplets ◽  
Clustering Effect ◽  
Reynolds Number Dependence ◽  
Coagulation Kernel

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 (Reλ) 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 Reλ 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 Reλ. The two SCE simulations, however, show different Reynolds-number dependences, indicating possible large differences in atmospheric turbulent clouds with large Reλ.

scholarly journals Turbulent Condensation of Droplets: Direct Simulation and a Stochastic Model

2009 ◽  
Vol 66 (3) ◽  
pp. 723-740 ◽  
Author(s):  
Roberto Paoli ◽  
Karim Shariff
Keyword(s):  
Turbulent Mixing ◽  
Isotropic Turbulence ◽  
Droplet Size Distribution ◽  
Temperature Fluctuations ◽  
Stochastic Equations ◽  
Direct Simulation ◽  
Homogeneous Isotropic Turbulence ◽  
Cloud Droplets ◽  
Droplet Condensation

Abstract The effect of turbulent mixing on droplet condensation is studied via direct numerical simulations of a population of droplets in a periodic box of homogeneous isotropic turbulence. Each droplet is tracked as a fluid particle whose radius grows by condensation of water vapor. Forcing of the small wavenumbers is used to sustain velocity, vapor, and temperature fluctuations. Temperature and vapor fluctuations lead to supersaturation fluctuations, which are responsible for broadening the droplet size distribution in qualitative agreement with in situ measurements. A model for the condensation of a population of cloud droplets in a homogeneous turbulent flow is presented. The model consists of a set of Langevin (stochastic) equations for the droplet area, supersaturation, and temperature surrounding the droplets. These equations yield corresponding ordinary differential equations for various moments and correlations. The statistics predicted by the model, for instance, the droplet area–supersaturation correlation, reproduce the simulations well.

scholarly journals Diffusional growth of cloud droplets in homogeneous isotropic turbulence: DNS, scaled-up DNS, and stochastic model

2020 ◽  
Author(s):  
Lois Thomas ◽  
Wojciech W. Grabowski ◽  
Bipin Kumar
Keyword(s):  
Stochastic Model ◽  
Vertical Velocity ◽  
Molecular Transport ◽  
Domain Size ◽  
Scale Model ◽  
Computational Domain ◽  
Diffusional Growth ◽  
Spectral Evolution ◽  
Cloud Droplets ◽  
The Impact

Abstract. This paper presents a novel methodology to use the 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 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 mean 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 as in 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 large-eddy simulation model.

scholarly journals Diffusional growth of cloud droplets in homogeneous isotropic turbulence: DNS, scaled-up DNS, and stochastic model

2020 ◽  
Vol 20 (14) ◽  
pp. 9087-9100 ◽  
Author(s):  
Lois Thomas ◽  
Wojciech W. Grabowski ◽  
Bipin Kumar
Keyword(s):  
Stochastic Model ◽  
Vertical Velocity ◽  
Molecular Transport ◽  
Domain Size ◽  
Scale Model ◽  
Computational Domain ◽  
Diffusional Growth ◽  
Spectral Evolution ◽  
Cloud Droplets ◽  
The Impact

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.

scholarly journals Reynolds-number dependence of turbulence enhancement on collision growth

2016 ◽  
Author(s):  
Ryo Onishi ◽  
Axel Seifert
Keyword(s):  
Reynolds Number ◽  
Isotropic Turbulence ◽  
Reynolds Numbers ◽  
Stokes Number ◽  
Homogeneous Isotropic Turbulence ◽  
Collision Efficiency ◽  
Cloud Droplets ◽  
Clustering Effect ◽  
Reynolds Number Dependence ◽  
Coagulation Kernel

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 (Reλ) up to 1,140. 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 μm and r2 > 40 μm; r1 > 40 μm and r2 < 40 μm) as Reλ 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 Reλ. The two SCE simulations, however, show different Reynolds-number dependences, indicating possible large differences in atmospheric turbulent clouds with large Reλ.

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