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  • 1.
    Bhatnagar, Akshay
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Indian Institute of Science, India.
    Gupta, A.
    Mitra, Dhrubaditya
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Perlekar, P.
    Wilkinson, M.
    Pandit, R.
    Deviation-angle and trajectory statistics for inertial particles in turbulence2016In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 94, no 6, article id 063112Article in journal (Refereed)
    Abstract [en]

    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.

  • 2.
    Bhatnagar, Akshay
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm University, Sweden.
    Gupta, Anupam
    Mitra, Dhrubaditya
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm University, Sweden.
    Pandit, Rahul
    Heavy inertial particles in turbulent flows gain energy slowly but lose it rapidly2018In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 97, no 3, article id 033102Article in journal (Refereed)
    Abstract [en]

    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.

  • 3.
    Bhatnagar, Akshay
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Gupta, Anupam
    Mitra, Dhrubaditya
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Pandit, Rahul
    Perlekar, Prasad
    How long do particles spend in vortical regions in turbulent flows?2016In: PHYSICAL REVIEW E, ISSN 2470-0045, Vol. 94, no 5, article id 053119Article in journal (Refereed)
    Abstract [en]

    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.

  • 4.
    Bhatnagar, Akshay
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm Univ, Roslagstullsbacken 23, S-10691 Stockholm, Sweden.
    Gustavsson, K.
    Mitra, Dhrubaditya
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm Univ, Roslagstullsbacken 23, S-10691 Stockholm, Sweden.
    Statistics of the relative velocity of particles in turbulent flows: Monodisperse particles2018In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 97, no 2, article id 023105Article in journal (Refereed)
    Abstract [en]

    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.

  • 5. Buzzicotti, Michele
    et al.
    Bhatnagar, Akshay
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Biferale, Luca
    Lanotte, Alessandra S.
    Ray, Samriddhi Sankar
    Lagrangian statistics for Navier-Stokes turbulence under Fourier-mode reduction: fractal and homogeneous decimations2016In: New Journal of Physics, ISSN 1367-2630, E-ISSN 1367-2630, Vol. 18, article id 113047Article in journal (Refereed)
    Abstract [en]

    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.

  • 6. Pandit, R.
    et al.
    Banerjee, D.
    Bhatnagar, Akshay
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholms University, Sweden.
    Brachet, M.
    Gupta, A.
    Mitra, Dhrubaditya
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholms University, Sweden.
    Pal, N.
    Perlekar, P.
    Ray, S. S.
    Shukla, V.
    Vincenzi, D.
    An overview of the statistical properties of two-dimensional turbulence in fluids with particles, conducting fluids, fluids with polymer additives, binary-fluid mixtures, and superfluids2017In: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Vol. 29, no 11, article id 111112Article in journal (Refereed)
    Abstract [en]

    We present an overview of the statistical properties of turbulence in two-dimensional (2D) fluids. After a brief recapitulation of well-known results for statistically homogeneous and isotropic 2D fluid turbulence, we give an overview of recent progress in this field for such 2D turbulence in conducting fluids, fluids with polymer additives, binary-fluid mixtures, and superfluids; we also discuss the statistical properties of particles advected by 2D turbulent fluids.

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