Reynolds number dependence of Lagrangian statistics in large numerical simulations of isotropic turbulence

2006 ◽  
Vol 7 ◽  
pp. N58 ◽  
Author(s):  
P. K. Yeung ◽  
S. B. Pope ◽  
B. L. Sawford
Keyword(s):  
Reynolds Number ◽  
Numerical Simulations ◽  
Isotropic Turbulence ◽  
Lagrangian Statistics ◽  
Reynolds Number Dependence

Reynolds-number dependence of line and surface stretching in turbulence: folding effects

2007 ◽  
Vol 586 ◽  
pp. 59-81 ◽  
Author(s):  
SUSUMU GOTO ◽  
SHIGEO KIDA
Keyword(s):  
Reynolds Number ◽  
Time Scale ◽  
Isotropic Turbulence ◽  
Three Dimensional ◽  
Turnover Time ◽  
Material Object ◽  
Material Objects ◽  
Short Time Scale ◽  
Kolmogorov Scale ◽  
Reynolds Number Dependence

The stretching rate, normalized by the reciprocal of the Kolmogorov time, of sufficiently extended material lines and surfaces in statistically stationary homogeneous isotropic turbulence depends on the Reynolds number, in contrast to the conventional picture that the statistics of material object deformation are determined solely by the Kolmogorov-scale eddies. This Reynolds-number dependence of the stretching rate of sufficiently extended material objects is numerically verified both in two- and three-dimensional turbulence, although the normalized stretching rate of infinitesimal material objects is confirmed to be independent of the Reynolds number. These numerical results can be understood from the following three facts. First, the exponentially rapid stretching brings about rapid multiple folding of finite-sized material objects, but no folding takes place for infinitesimal objects. Secondly, since the local degree of folding is positively correlated with the local stretching rate and it is non-uniformly distributed over finite-sized objects, the folding enhances the stretching rate of the finite-sized objects. Thirdly, the stretching of infinitesimal fractions of material objects is governed by the Kolmogorov-scale eddies, whereas the folding of a finite-sized material object is governed by all eddies smaller than the spatial extent of the objects. In other words, the time scale of stretching of infinitesimal fractions of material objects is proportional to the Kolmogorov time, whereas that of folding of sufficiently extended material objects can be as long as the turnover time of the largest eddies. The combination of the short time scale of stretching of infinitesimal fractions and the long time scale of folding of the whole object yields the Reynolds-number dependence. Movies are available with the online version of the paper.

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.

Reynolds number dependence of relative dispersion statistics in isotropic turbulence

2008 ◽  
Vol 20 (6) ◽  
pp. 065111 ◽  
Author(s):  
Brian L. Sawford ◽  
P. K. Yeung ◽  
Jason F. Hackl
Keyword(s):  
Reynolds Number ◽  
Isotropic Turbulence ◽  
Relative Dispersion ◽  
Reynolds Number Dependence

Collision statistics of inertial particles in two-dimensional homogeneous isotropic turbulence with an inverse cascade

2014 ◽  
Vol 745 ◽  
pp. 279-299 ◽  
Author(s):  
Ryo Onishi ◽  
J. C. Vassilicos
Keyword(s):  
Reynolds Number ◽  
Isotropic Turbulence ◽  
Particle System ◽  
Stochastic Simulations ◽  
Collision Kernel ◽  
Inertial Particles ◽  
Two Dimensional ◽  
Homogeneous Isotropic Turbulence ◽  
Local Flow ◽  
Reynolds Number Dependence

AbstractThis study investigates the collision statistics of inertial particles in inverse-cascading two-dimensional (2D) homogeneous isotropic turbulence by means of a direct numerical simulation (DNS). A collision kernel model for particles with small Stokes number ($\mathit{St}$) in 2D flows is proposed based on the model of Saffman & Turner (J. Fluid Mech., vol. 1, 1956, pp. 16–30) (ST56 model). The DNS results agree with this 2D version of the ST56 model for $\mathit{St}\lesssim 0.1$. It is then confirmed that our DNS results satisfy the 2D version of the spherical formulation of the collision kernel. The fact that the flatness factor stays around 3 in our 2D flow confirms that the present 2D turbulent flow is nearly intermittency-free. Collision statistics for $\mathit{St}= 0.1$, 0.4 and 0.6, i.e. for $\mathit{St}<1$, are obtained from the present 2D DNS and compared with those obtained from the three-dimensional (3D) DNS of Onishi et al. (J. Comput. Phys., vol. 242, 2013, pp. 809–827). We have observed that the 3D radial distribution function at contact ($g(R)$, the so-called clustering effect) decreases for $\mathit{St}= 0.4$ and 0.6 with increasing Reynolds number, while the 2D $g(R)$ does not show a significant dependence on Reynolds number. This observation supports the view that the Reynolds-number dependence of $g(R)$ observed in three dimensions is due to internal intermittency of the 3D turbulence. We have further investigated the local $\mathit{St}$, which is a function of the local flow strain rates, and proposed a plausible mechanism that can explain the Reynolds-number dependence of $g(R)$. Meanwhile, 2D stochastic simulations based on the Smoluchowski equations for $\mathit{St}\ll 1$ show that the collision growth can be predicted by the 2D ST56 model and that rare but strong events do not play a significant role in such a small-$\mathit{St}$ particle system. However, the probability density function of local $\mathit{St}$ at the sites of colliding particle pairs supports the view that powerful rare events can be important for particle growth even in the absence of internal intermittency when $\mathit{St}$ is not much smaller than unity.

517 Reynolds Number Dependence of Coherent Fine Scale Eddies in Homogeneous Isotropic Turbulence

2001 ◽  
Vol 2001.14 (0) ◽  
pp. 567-568
Author(s):  
Mamoru TANAHASHI ◽  
Shinichiro KIKUCHI ◽  
Shiki IWASE ◽  
Toru YANAGAWA ◽  
Toshio MIYAUCHI
Keyword(s):  
Reynolds Number ◽  
Isotropic Turbulence ◽  
Fine Scale ◽  
Homogeneous Isotropic Turbulence ◽  
Reynolds Number Dependence

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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