Evolution of non-uniformly seeded warm clouds in idealized turbulent conditions

Derevyanko, Stanislav A.; Falkovich, Gregory; Turitsyn, Sergei K.

doi:10.1088/1367-2630/10/7/075019

Cited by 10 publications

(12 citation statements)

References 40 publications

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“…In figures 6 and 7 we plot c g data from our simulations and compare with theoretical estimations. Overall, our results without gravity are consistent with theoretical predictions derived in [28,31,37] and other independent numerical studies reported in [22,29,33]. Several important observations can be made.…”

Section: Scaling Exponentsupporting

confidence: 92%

“…For the cases without gravity, c g reaches a maximum value at St ∼ 0.6 and then decreases with the Stokes number. The empirical formula of Derevyanko et al [37] appears to overestimate c g for intermediate Stokes numbers, and underestimates c g for large Stokes numbers.…”

Section: Scaling Exponentmentioning

confidence: 86%

“…Theoretical analysis of clustering of the inertial particles at small distances, limited to small Stokes numbers, has been developed by Chun et al [28] where they showed analytically that in the limit St 1, c g is proportional to St 2 . Other studies have extended the expression for c g to cover larger Stokes numbers; see [37] for example. However, these theoretical analyses often involved various assumptions and their predictive capability must be checked against DNS and experimental data.…”

Section: Scaling Exponentmentioning

confidence: 99%

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Kinematic and dynamic collision statistics of cloud droplets from high-resolution simulations

et al. 2013

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We study the dynamic and kinematic collision statistics of cloud droplets for a range of flow Taylor microscale Reynolds numbers (up to 500), using a highly scalable hybrid direct numerical simulation approach. Accurate results of radial relative velocity (RRV) and radial distribution function (RDF) at contact have been obtained by taking advantage of their power-law scaling at short separation distances. Three specific but inter-related questions have been addressed in a systematic manner for geometric collisions of same-size droplets (of radius from 10 to 60 µm) in a typical cloud turbulence (dissipation rate at 400 cm 2 s −3 ). Firstly, both deterministic and stochastic forcing schemes were employed to test the sensitivity of the simulation results on the largescale driving mechanism. We found that, in general, the results are quantitatively similar, with the deterministic forcing giving a slightly larger RDF and collision 6

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Section: Scaling Exponentsupporting

confidence: 92%

Section: Scaling Exponentmentioning

confidence: 86%

Section: Scaling Exponentmentioning

confidence: 99%

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Kinematic and dynamic collision statistics of cloud droplets from high-resolution simulations

et al. 2013

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“…They observed that the clustering effect, and consequently the collision kernel, decreases as R λ increases for R λ > 100 and St = 0.4, while no significant Reynolds-number dependence was observed for St = 0.1. This is a relevant and significant observation, since many authors ignore this Reynolds-number dependence and assume a constant collision kernel irrespective of R λ (Saffman & Turner 1956;Derevyanko, Falkovich & Turitsyn 2008;Zaichik & Alipchenkov 2009) or assume a convergence to a constant collision kernel with increasing R λ (Ayala, Rosa & Wang 2008). A similar Reynolds-number dependence for St < 1 has now been confirmed by Rosa et al (2013).…”

Section: Introductionmentioning

confidence: 62%

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

Onishi

Vassilicos

2014

J. Fluid Mech.

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This 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 (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 St 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 St = 0.1, 0.4 and 0.6, i.e. for 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 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 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 St 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-St particle system. However, the probability density function of local 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 St is not much smaller than unity.

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“…how they depend on the Taylor-scale Reynolds number Re λ of the flow (see e.g. Derevyanko, Falkovich & Turitsyn 2008;Xue, Wang & Grabowski 2008). We consider suspensions of small, heavy and dilute particles, neglecting gravity.…”

Section: Introductionmentioning

confidence: 99%

Intermittency in the velocity distribution of heavy particles in turbulence

Bec

Biferale

Cencini³

et al. 2010

J. Fluid Mech.

115

152

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The statistics of velocity differences between pairs of heavy inertial point particles suspended in an incompressible turbulent flow is studied and found to be extremely intermittent. The problem is particularly relevant to the estimation of the efficiency of collisions among heavy particles in turbulence. We found that when particles are separated by distances within the dissipative subrange, the competition between regions with quiet regular velocity distributions and regions where very close particles have very different velocities (caustics) leads to a quasi bi-fractal behaviour of the particle velocity structure functions. Contrastingly, we show that for particles separated by inertial-range distances, the velocity-difference statistics can be characterized in terms of a local roughness exponent, which is a function of the scaledependent particle Stokes number only. Results are obtained from high-resolution direct numerical simulations up to 2048 3 collocation points and with millions of particles for each Stokes number.

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Evolution of non-uniformly seeded warm clouds in idealized turbulent conditions

Cited by 10 publications

References 40 publications

Kinematic and dynamic collision statistics of cloud droplets from high-resolution simulations

Kinematic and dynamic collision statistics of cloud droplets from high-resolution simulations

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

Intermittency in the velocity distribution of heavy particles in turbulence

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