| 1. |
- Bhatnagar, Akshay, et al.
(författare)
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Deviation-angle and trajectory statistics for inertial particles in turbulence
- 2016
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Ingår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics. - : American Physical Society. - 1539-3755 .- 1550-2376. ; 94:6
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Tidskriftsartikel (refereegranskat)abstract
- Small particles in suspension in a turbulent fluid have trajectories that do not follow the pathlines of the flow exactly. We investigate the statistics of the angle of deviation φ between the particle and fluid velocities. We show that, when the effects of particle inertia are small, the probability distribution function (PDF) Pφ of this deviation angle shows a power-law region in which Pφ∼φ-4. We also find that the PDFs of the trajectory curvature κ and modulus θ of the torsion have power-law tails that scale, respectively, as Pκ∼κ-5/2, as κ→∞, and Pθ∼θ-3, as θ→∞: These exponents are in agreement with those previously observed for fluid pathlines. We propose a way to measure the complexity of heavy-particle trajectories by the number NI(t,St) of points (up until time t) at which the torsion changes sign. We present numerical evidence that nI(St)≡limt→∞NI(t,St)t∼St-Δ for large St, with Δ≃0.5.
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| 2. |
- Bhatnagar, Akshay, et al.
(författare)
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Heavy inertial particles in turbulent flows gain energy slowly but lose it rapidly
- 2018
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Ingår i: Physical review. E. - : American Physical Society. - 2470-0045 .- 2470-0053. ; 97:3
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Tidskriftsartikel (refereegranskat)abstract
- We present an extensive numerical study of the time irreversibility of the dynamics of heavy inertial particles in three-dimensional, statistically homogeneous, and isotropic turbulent flows. We show that the probability density function (PDF) of the increment, W(tau), of a particle's energy over a time scale tau is non-Gaussian, and skewed toward negative values. This implies that, on average, particles gain energy over a period of time that is longer than the duration over which they lose energy. We call this slow gain and fast loss. We find that the third moment of W(tau) scales as tau(3) for small values of tau. We show that the PDF of power-input p is negatively skewed too; we use this skewness Ir as a measure of the time irreversibility and we demonstrate that it increases sharply with the Stokes number St for small St; this increase slows down at St similar or equal to 1. Furthermore, we obtain the PDFs of t(+) and t(-), the times over which p has, respectively, positive or negative signs, i.e., the particle gains or loses energy. We obtain from these PDFs a direct and natural quantification of the slow gain and fast loss of the energy of the particles, because these PDFs possess exponential tails from which we infer the characteristic loss and gain times t(loss) and t(gain), respectively, and we obtain t(loss) < t(gain) for all the cases we have considered. Finally, we show that the fast loss of energy occurs with greater probability in the strain-dominated region than in the vortical one; in contrast, the slow gain in the energy of the particles is equally likely in vortical or strain-dominated regions of the flow.
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| 3. |
- Bhatnagar, Akshay, et al.
(författare)
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How long do particles spend in vortical regions in turbulent flows?
- 2016
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Ingår i: Physical Review E. - 2470-0045. ; 94:5
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Tidskriftsartikel (refereegranskat)abstract
- We obtain the probability distribution functions (PDFs) of the time that a Lagrangian tracer or a heavy inertial particle spends in vortical or strain-dominated regions of a turbulent flow, by carrying out direct numerical simulations of such particles advected by statistically steady, homogeneous, and isotropic turbulence in the forced, three-dimensional, incompressible Navier-Stokes equation. We use the two invariants, Q and R, of the velocity-gradient tensor to distinguish between vortical and strain-dominated regions of the flow and partition the Q-R plane into four different regions depending on the topology of the flow; out of these four regions two correspond to vorticity-dominated regions of the flow and two correspond to strain-dominated ones. We obtain Q and R along the trajectories of tracers and heavy inertial particles and find out the time t(pers) for which they remain in one of the four regions of the Q-R plane. We find that the PDFs of tpers display exponentially decaying tails for all four regions for tracers and heavy inertial particles. From these PDFs we extract characteristic time scales, which help us to quantify the time that such particles spend in vortical or strain-dominated regions of the flow.
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| 4. |
- Bhatnagar, Akshay, et al.
(författare)
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Rate of formation of caustics in heavy particles advected by turbulence
- 2022
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Ingår i: Philosophical Transactions. Series A. - : The Royal Society. - 1364-503X .- 1471-2962. ; 380:2219
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Tidskriftsartikel (refereegranskat)abstract
- The rate of collision and the relative velocities of the colliding particles in turbulent flows are a crucial part of several natural phenomena, e.g. rain formation in warm clouds and planetesimal formation in protoplanetary discs. The particles are often modelled as passive, but heavy and inertial. Within this model, large relative velocities emerge due to formation of singularities (caustics) of the gradient matrix of the velocities of the particles. Using extensive direct numerical simulations of heavy particles in both two (direct and inverse cascade) and three-dimensional turbulent flows, we calculate the rate of formation of caustics, J as a function of the Stokes number (St). The best approximation to our data is J similar to exp(-C/St), in the limit St -> 0 where C is a non-universal constant. This article is part of the theme issue 'Scaling the turbulence edifice (part 2)'.
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| 5. |
- Bhatnagar, Akshay, et al.
(författare)
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Relative velocities in bidisperse turbulent aerosols : Simulations and theory
- 2018
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Ingår i: Physical review. E. - : American Physical Society. - 2470-0045 .- 2470-0053. ; 98:6
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Tidskriftsartikel (refereegranskat)abstract
- We perform direct numerical simulations of a bidisperse suspension of heavy spherical particles in forced, homogeneous, and isotropic three-dimensional turbulence. We compute the joint distribution of relative particle distances and longitudinal relative velocities between particles of different inertia. For a pair of particles with small difference in their inertias we compare our results with recent theoretical predictions [Meibohm et al., Phys. Rev. E 96, 061102 (2017)] for the shape of this distribution. We also compute the moments of relative velocities as a function of particle separation and compare with the theoretical predictions. We observe good agreement. For a pair of particles that are very different from each other-one is heavy and the other one has negligible inertia-we give a theory to calculate their root-mean-square relative velocity. This theory also agrees well with the results of our simulations.
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| 6. |
- Bhatnagar, Akshay
(författare)
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Statistics of relative velocity for particles settling under gravity in a turbulent flow
- 2020
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Ingår i: Physical review. E. - : AMER PHYSICAL SOC. - 2470-0045 .- 2470-0053. ; 101:3
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Tidskriftsartikel (refereegranskat)abstract
- We study the joint probability distributions of separation R and radial component of the relative velocity V-R of particles settling under gravity in a turbulent flow. We also obtain the moments of these distributions and analyze their anisotropy using spherical harmonics. We find that the qualitative nature of the joint distributions remains the same as no-gravity case. Distributions of V-R for fixed values of R show a power-law dependence on V-R for a range of V-R; the exponent of the power law depends on the gravity. Effects of gravity are also manifested in the following ways: (a) Moments of the distributions are anisotropic; degree of anisotropy depends on particle's Stokes number, but does not depend on R for small values of R. (b) Mean velocity of collision between two particles is decreased for particles having equal Stokes numbers but increased for particles having different Stokes numbers. For the later, collision velocity is set by the difference in their settling velocities.
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| 7. |
- Bhatnagar, Akshay, et al.
(författare)
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Statistics of the relative velocity of particles in turbulent flows: Monodisperse particles
- 2018
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Ingår i: Physical Review E. - : AMER PHYSICAL SOC. - 2470-0045 .- 2470-0053. ; 97:2
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Tidskriftsartikel (refereegranskat)abstract
- We use direct numerical simulations to calculate the joint probability density function of the relative distance R and relative radial velocity component V-R for a pair of heavy inertial particles suspended in homogeneous and isotropic turbulent flows. At small scales the distribution is scale invariant, with a scaling exponent that is related to the particle-particle correlation dimension in phase space, D-2. It was argued [K. Gustavsson and B. Mehlig, Phys. Rev. E 84, 045304 (2011); J. Turbul. 15, 34 (2014)] that the scale invariant part of the distribution has two asymptotic regimes: (1) vertical bar V-R vertical bar << R, where the distribution depends solely on R, and (2) vertical bar V-R vertical bar >> R, where the distribution is a function of vertical bar V-R vertical bar alone. The probability distributions in these two regimes are matched along a straight line: vertical bar V-R vertical bar = z*R. Our simulations confirm that this is indeed correct. We further obtain D-2 and z* as a function of the Stokes number, St. The former depends nonmonotonically on St with aminimum at about St approximate to 0.7 and the latter has only a weak dependence on St.
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| 8. |
- Buzzicotti, Michele, et al.
(författare)
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Lagrangian statistics for Navier-Stokes turbulence under Fourier-mode reduction : fractal and homogeneous decimations
- 2016
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Ingår i: New Journal of Physics. - : Institute of Physics Publishing (IOPP). - 1367-2630. ; 18
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Tidskriftsartikel (refereegranskat)abstract
- We study small-scale and high-frequency turbulent fluctuations in three-dimensional flows under Fourier-mode reduction. The Navier-Stokes equations are evolved on a restricted set of modes, obtained as a projection on a fractal or homogeneous Fourier set. We find a strong sensitivity (reduction) of the high-frequency variability of the Lagrangian velocity fluctuations on the degree of mode decimation, similarly to what is already reported for Eulerian statistics. This is quantified by a tendency towards a quasi-Gaussian statistics, i.e., to a reduction of intermittency, at all scales and frequencies. This can be attributed to a strong depletion of vortex filaments and of the vortex stretching mechanism. Nevertheless, we found that Eulerian and Lagrangian ensembles are still connected by a dimensional bridge-relation which is independent of the degree of Fourier-mode decimation.
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| 9. |
- Grujić, Anđela, et al.
(författare)
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Collisions among elongated settling particles: The twofold role of turbulence
- 2024
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Ingår i: Physics of Fluids. - : AIP Publishing. - 1089-7666 .- 1070-6631. ; 36:1
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Tidskriftsartikel (refereegranskat)abstract
- We study the collision rates of settling spheres and elongated spheroids in homogeneous, isotropic turbulence by means of direct numerical simulations aiming to understand microscale-particle encounters in oceans and lakes. We explore a range of aspect ratios and sizes relevant to the dynamics of plankton and microplastics in water environments. The results presented here confirm that collision rates between elongated particles in a quiescent fluid are more frequent than those among spherical particles in turbulence due to oblique settling. We also demonstrate that turbulence generally enhances collisions among elongated particles as compared to those expected for a random distribution of the same particles settling in a quiescent fluid, although we also find a decrease in collision rates in turbulence for particles of the highest density and moderate aspect ratios ( A = 5 ) . The increase in the collision rate due to turbulence is found to quickly decrease with aspect ratio, reach a minimum for aspect ratios approximately equal to 5, and then slowly increase again, with an increase up to 50% for the largest aspect ratios investigated. This non-monotonic trend is explained as the result of two competing effects: the increase in the surface area with aspect ratio (beneficial to increase encounter rates) and the alignment of nearby prolate particles in turbulence (reducing the probability of collision). Turbulence mixing is, therefore, partially balanced by rod alignment at high particle aspect ratios.
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| 10. |
- Mattsson, Lars, et al.
(författare)
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Clustering and dynamic decoupling of dust grains in turbulent molecular clouds
- 2019
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Ingår i: Monthly notices of the Royal Astronomical Society. - : Oxford University Press. - 0035-8711 .- 1365-2966. ; 483:4, s. 5623-5641
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Tidskriftsartikel (refereegranskat)abstract
- We present high-resolution (1024 3) simulations of super-/hypersonic isothermal hydrodynamic turbulence inside an interstellar molecular cloud (resolving scales of typically 20-100 au), including a multidisperse population of dust grains, i.e. a range of grain sizes is considered. Due to inertia, large grains (typical radius a ≳ 1.0μm) will decouple from the gas flow, while small grains (al∼ 0.1μm) will tend to better trace the motions of the gas. We note that simulations with purely solenoidal forcing show somewhat more pronounced decoupling and less clustering compared to simulations with purely compressive forcing. Overall, small and large grains tend to cluster, while intermediate-size grains show essentially a random isotropic distribution. As a consequence of increased clustering, the grain-grain interaction rate is locally elevated; but since small and large grains are often not spatially correlated, it is unclear what effect this clustering would have on the coagulation rate. Due to spatial separation of dust and gas, a diffuse upper limit to the grain sizes obtained by condensational growth is also expected, since large (decoupled) grains are not necessarily located where the growth species in the molecular gas is.
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