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  • 1.
    Afonso, Marco Martins
    et al.
    Univ Porto, Fac Ciencias, Ctr Matemat, Rua Campo Alegre 687, P-4169007 Porto, Portugal..
    Mitra, Dhrubaditya
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Vincenzi, Dario
    Univ Cote dAzur, CNRS, LJAD, F-06100 Nice, France..
    Kazantsev dynamo in turbulent compressible flows2019In: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, E-ISSN 1471-2946, Vol. 475, no 2223, article id 20180591Article in journal (Refereed)
    Abstract [en]

    We consider the kinematic fluctuation dynamo problem in a flow that is random, white-in-time, with both solenoidal and potential components. This model is a generalization of the well-studied Kazantsev model. If both the solenoidal and potential parts have the same scaling exponent, then, as the compressibility of the flow increases, the growth rate decreases but remains positive. If the scaling exponents for the solenoidal and potential parts differ, in particular if they correspond to typical Kolmogorov and Burgers values, we again find that an increase in compressibility slows down the growth rate but does not turn it off. The slow down is, however, weaker and the critical magnetic Reynolds number is lower than when both the solenoidal and potential components display the Kolmogorov scaling. Intriguingly, we find that there exist cases, when the potential part is smoother than the solenoidal part, for which an increase in compressibility increases the growth rate. We also find that the critical value of the scaling exponent above which a dynamo is seen is unity irrespective of the compressibility. Finally, we realize that the dimension d = 3 is special, as for all other values of d the critical exponent is higher and depends on the compressibility.

  • 2.
    Bagheri, Faranggis
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Mitra, Dhrubaditya
    NORDITA.
    Perlekar, Prasad
    Brandt, Luca
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Statistics of polymer extensions in turbulent channel flow2012In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 86, no 5, p. 056314-Article in journal (Refereed)
    Abstract [en]

    We present direct numerical simulations of turbulent channel flow with passive Lagrangian polymers. To understand the polymer behavior we investigate the behavior of infinitesimal line elements and calculate the probability distribution function (PDF) of finite-time Lyapunov exponents and from them the corresponding Cramer's function for the channel flow. We study the statistics of polymer elongation for both the Oldroyd-B model (for Weissenberg number Wi<1) and the FENE model. We use the location of the minima of the Cramer's function to define the Weissenberg number precisely such that we observe coil-stretch transition at Wi1. We find agreement with earlier analytical predictions for PDF of polymer extensions made by Balkovsky, Fouxon, and Lebedev for linear polymers (Oldroyd-B model) with Wi <1 and by Chertkov for nonlinear FENE-P model of polymers. For Wi >1 (FENE model) the polymer are significantly more stretched near the wall than at the center of the channel where the flow is closer to homogenous isotropic turbulence. Furthermore near the wall the polymers show a strong tendency to orient along the streamwise direction of the flow, but near the center line the statistics of orientation of the polymers is consistent with analogous results obtained recently in homogeneous and isotropic flows.

  • 3.
    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.

  • 4.
    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.

  • 5.
    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.

  • 6.
    Bhatnagar, Akshay
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm Univ, Roslagstullsbacken 23, S-10691 Stockholm, Sweden..
    Gustavsson, K.
    Gothenburg Univ, Dept Phys, S-41296 Gothenburg, Sweden..
    Mehlig, B.
    Gothenburg Univ, Dept Phys, S-41296 Gothenburg, Sweden..
    Mitra, Dhrubaditya
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm Univ, Roslagstullsbacken 23, S-10691 Stockholm, Sweden..
    Relative velocities in bidisperse turbulent aerosols: Simulations and theory2018In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 98, no 6, article id 063107Article in journal (Refereed)
    Abstract [en]

    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.

  • 7.
    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.

  • 8. Bonanno, Alfio
    et al.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Del Sordo, Fabio
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Mitra, Dhrubaditya
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Breakdown of chiral symmetry during saturation of the Tayler instability2012In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 86, no 1, p. 016313-Article in journal (Refereed)
    Abstract [en]

    We study spontaneous breakdown of chiral symmetry during the nonlinear evolution of the Tayler instability. We start with an initial steady state of zero helicity. Within linearized perturbation calculations, helical perturbations of this initial state have the same growth rate for either sign of helicity. Direct numerical simulations (DNS) of the fully nonlinear equations, however, show that an infinitesimal excess of one sign of helicity in the initial perturbation gives rise to a saturated helical state. We further show that this symmetry breaking can be described by weakly nonlinear finite-amplitude equations with undetermined coefficients which can be deduced solely from symmetry consideration. By fitting solutions of the amplitude equations to data from DNS, we further determine the coefficients of the amplitude equations.

  • 9.
    Devlen, Ebru
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Mitra, Dhrubaditya
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    A mean field dynamo from negative eddy diffusivity2013In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 432, no 2, p. 1651-1657Article in journal (Refereed)
    Abstract [en]

    Using direct numerical simulations, we verify that Roberts-IV flow exhibits dynamo action dominated by horizontally averaged large-scale magnetic field. With the test-field method, we compute the turbulent magnetic diffusivity and find that it is negative and overcomes the molecular diffusivity, thus explaining quantitatively the large-scale dynamo for magnetic Reynolds numbers above approximate to 8. As expected for a dynamo of this type, but contrary to alpha-effect dynamos, the two horizontal field components grow independently of each other and have arbitrary amplitude ratios and phase differences. Small length-scales of the mean magnetic field are shown to be stabilized by the turbulent magnetic diffusivity becoming positive at larger wavenumbers. Oscillatory decaying or growing solutions have also been found in certain wavenumber intervals and sufficiently large values of the magnetic Reynolds number. For magnetic Reynolds numbers below approximate to 0.5, the turbulent magnetic diffusivity is confirmed to be positive, as expected for all incompressible flows. Earlier claims of a dynamo driven by a modified Taylor-Green flow through negative eddy diffusivity could not be confirmed.

  • 10. Dikpati, Mausumi
    et al.
    Anderson, Jeffrey L.
    Mitra, Dhrubaditya
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    DATA ASSIMILATION IN A SOLAR DYNAMO MODEL USING ENSEMBLE KALMAN FILTERS: SENSITIVITY AND ROBUSTNESS IN RECONSTRUCTION OF MERIDIONAL FLOW SPEED2016In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 828, no 2, article id 91Article in journal (Refereed)
    Abstract [en]

    We implement an Ensemble Kalman Filter procedure using the. Data Assimilation Research Testbed for assimilating "synthetic" meridional flow-speed data in a Babcock-Leighton-type flux-transport solar dynamo model. By performing several "observing system simulation experiments," we reconstruct time. variation in meridional flow. speed and analyze sensitivity and robustness of reconstruction. Using 192 ensemble members including 10 observations, each with 4% error, we find that flow. speed is reconstructed best if observations of near-surface poloidal fields from low. latitudes and tachocline toroidal fields from midlatitudes are assimilated. If observations include a mixture of poloidal and toroidal fields from different latitude locations, reconstruction is reasonably good for. <= 40% error in low-latitude data, even if observational error in polar region data becomes 200%, but deteriorates when observational error increases in low- and midlatitude data. Solar polar region observations are known to contain larger errors than those in low latitudes; our forward operator (a flux-transport dynamo model here) can sustain larger errors in polar region data, but is more sensitive to errors in low- latitude data. An optimal reconstruction is obtained if an assimilation interval of 15 days is used; 10- and 20-day assimilation intervals also give reasonably good results. Assimilation intervals <5 days do not produce faithful reconstructions of flow. speed, because the system requires a minimum time to develop dynamics to respond to flow. variations. Reconstruction also deteriorates if an assimilation interval >45 days is used, because the system's inherent memory interferes with its short-term dynamics during a substantially long run without updating.

  • 11.
    Haugen, Nils Erland L.
    et al.
    Norwegian Univ Sci & Technol, Dept Energy & Proc Engn, Kolbjorn Hejes Vei 1B, NO-7491 Trondheim, Norway.;SINTEF Energy Res, N-7465 Trondheim, Norway..
    Kruger, Jonas
    Norwegian Univ Sci & Technol, Dept Energy & Proc Engn, Kolbjorn Hejes Vei 1B, NO-7491 Trondheim, Norway..
    Mitra, Dhrubaditya
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm Univ, Roslagstullsbacken 23, SE-10691 Stockholm, Sweden..
    Lovas, Terese
    Norwegian Univ Sci & Technol, Dept Energy & Proc Engn, Kolbjorn Hejes Vei 1B, NO-7491 Trondheim, Norway..
    The effect of turbulence on mass transfer rates of small inertial particles with surface reactions2018In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 836, p. 932-951Article in journal (Refereed)
    Abstract [en]

    The effect of turbulence on the mass transfer between a fluid and embedded small heavy inertial particles that experience surface reactions is studied. For simplicity, the surface reaction, which takes place when a gas phase reactant is converted to a gas phase product at the external surface of the particles, is unimolar and isothermal. Two effects are identified. The first effect is due to the relative velocity between the fluid and the particles, and a model for the relative velocity is presented. The second effect is due to the clustering of particles, where the mass transfer rate is inhibited due to the rapid depletion of the consumed species inside the dense particle clusters. This last effect is relevant for large Damkohler numbers, where the Damkohler number is defined as the ratio of the turbulent and chemical time scales, and it may totally control the mass transfer rate for Damkohler numbers larger than unity. A model that describes how this effect should be incorporated into existing simulation tools that utilize the Reynolds averaged Navier-Stokes approach is presented.

  • 12.
    Jabbari, Sarah
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Kleeorin, Nathan
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Mitra, Dhrubaditya
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Rogachevskii, Igor
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    BIPOLAR MAGNETIC SPOTS FROM DYNAMOS IN STRATIFIED SPHERICAL SHELL TURBULENCE2015In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 805, no 2, article id 166Article in journal (Refereed)
    Abstract [en]

    Recent work by Mitra et al. (2014) has shown that in strongly stratified forced two-layer turbulence with helicity and corresponding large-scale dynamo action in the lower layer, and nonhelical turbulence in the upper, a magnetic field occurs in the upper layer in the form of sharply bounded bipolar magnetic spots. Here we extend this model to spherical wedge geometry covering the northern hemisphere up to 75 degrees latitude and an azimuthal extent of 180 degrees. The kinetic helicity and therefore also the large-scale magnetic field are strongest at low latitudes. For moderately strong stratification, several bipolar spots form that eventually fill the full longitudinal extent. At early times, the polarity of spots reflects the orientation of the underlying azimuthal field, as expected from Parker's Omega-shaped flux loops. At late times their tilt changes such that there is a radial field of opposite orientation at different latitudes separated by about 10 degrees. Our model demonstrates the spontaneous formation of spots of sizes much larger than the pressure scale height. Their tendency to produce filling factors close to unity is argued to be reminiscent of highly active stars. We confirm that strong stratification and strong scale separation are essential ingredients behind magnetic spot formation, which appears to be associated with downflows at larger depths.

  • 13.
    Jabbari, Sarah
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Kleeorin, Nathan
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Mitra, Dhrubaditya
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Rogachevskii, Igor
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Surface flux concentrations in a spherical alpha 2 dynamo2013In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 556, p. A106-Article in journal (Refereed)
    Abstract [en]

    Context. In the presence of strong density stratification, turbulence can lead to the large-scale instability of a horizontal magnetic field if its strength is in a suitable range (around a few percent of the turbulent equipartition value). This instability is related to a suppression of the turbulent pressure so that the turbulent contribution to the mean magnetic pressure becomes negative. This results in the excitation of a negative effective magnetic pressure instability (NEMPI). This instability has so far only been studied for an imposed magnetic field. Aims. We want to know how NEMPI works when the mean magnetic field is generated self-consistently by an alpha(2) dynamo, whether it is affected by global spherical geometry, and whether it can influence the properties of the dynamo itself. Methods. We adopt the mean-field approach, which has previously been shown to provide a realistic description of NEMPI in direct numerical simulations. We assume axisymmetry and solve the mean-field equations with the Pencil Code for an adiabatic stratification at a total density contrast in the radial direction of approximate to 4 orders of magnitude. Results. NEMPI is found to work when the dynamo-generated field is about 4% of the equipartition value, which is achieved through strong alpha quenching. This instability is excited in the top 5% of the outer radius, provided the density contrast across this top layer is at least 10. NEMPI is found to occur at lower latitudes when the mean magnetic field is stronger. For weaker fields, NEMPI can make the dynamo oscillatory with poleward migration. Conclusions. NEMPI is a viable mechanism for producing magnetic flux concentrations in a strongly stratified spherical shell in which a magnetic field is generated by a strongly quenched alpha effect dynamo.

  • 14.
    Jabbari, Sarah
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm University, Sweden.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm University, Sweden.
    Mitra, Dhrubaditya
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Kleeorin, Nathan
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Ben-Gurion University of the Negev, Israel.
    Rogachevskii, Igor
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Ben-Gurion University of the Negev, Israel.
    Turbulent reconnection of magnetic bipoles in stratified turbulence2016In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 459, no 4, p. 4046-4056Article in journal (Refereed)
    Abstract [en]

    We consider strongly stratified forced turbulence in a plane-parallel layer with helicity and corresponding large-scale dynamo action in the lower part and non-helical turbulence in the upper. The magnetic field is found to develop strongly concentrated bipolar structures near the surface. They form elongated bands with a sharp interface between opposite polarities. Unlike earlier experiments with imposed magnetic field, the inclusion of rotation does not strongly suppress the formation of these structures. We perform a systematic numerical study of this phenomenon by varying magnetic Reynolds number, scale-separation ratio, and Coriolis number. We focus on the formation of a current sheet between bipolar regions where reconnection of oppositely oriented field lines occurs. We determine the reconnection rate by measuring either the inflow velocity in the vicinity of the current sheet or by measuring the electric field in the reconnection region. We demonstrate that for large Lundquist numbers, S > 10(3), the reconnection rate is nearly independent of S in agreement with results of recent numerical simulations performed by other groups in simpler settings.

  • 15.
    Kemel, Koen
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Kleeorin, Nathan
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Mitra, Dhrubaditya
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Rogachevskii, Igor
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Active Region Formation through the Negative Effective Magnetic Pressure Instability2013In: Solar Physics, ISSN 0038-0938, E-ISSN 1573-093X, Vol. 287, no 1-2, p. 293-313Article in journal (Refereed)
    Abstract [en]

    The negative effective magnetic-pressure instability operates on scales encompassing many turbulent eddies, which correspond to convection cells in the Sun. This instability is discussed here in connection with the formation of active regions near the surface layers of the Sun. This instability is related to the negative contribution of turbulence to the mean magnetic pressure that causes the formation of large-scale magnetic structures. For an isothermal layer, direct numerical simulations and mean-field simulations of this phenomenon are shown to agree in many details, for example the onset of the instability occurs at the same depth. This depth increases with increasing field strength, such that the growth rate of this instability is independent of the field strength, provided the magnetic structures are fully contained within the domain. A linear stability analysis is shown to support this finding. The instability also leads to a redistribution of turbulent intensity and gas pressure that could provide direct observational signatures.

  • 16. Kruger, Jonas
    et al.
    Haugen, Nils E. L.
    Mitra, Dhrubaditya
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Lovas, Terese
    The effect of turbulent clustering on particle reactivity2017In: Proceedings of the Combustion Institute, ISSN 1540-7489, E-ISSN 1873-2704, Vol. 36, no 2, p. 2333-2340Article in journal (Refereed)
    Abstract [en]

    The effect of turbulence on the heterogeneous (solid-fluid) reactions of solid particles is studied numerically with Direct Numerical Simulations (DNS). A simplified reaction system is used, where the solid-fluid reaction is represented by a single isothermal reaction step. It is found that, due to the clustering of particles by the isotropic turbulence, the overall reaction rate is entirely controlled by the turbulence for large Damkohler numbers. The particle clustering significantly slows down the reaction rate for increasing Damkohler numbers which reaches an asymptotic limit that can be analytically derived. This implies that the effect of turbulence on heterogeneously reacting particles should be included in models that are used in CFD simulations of e. g. char burnout in combustors or gasifiers. Such a model, based on the chemical and turbulent time scales, is here proposed for the heterogeneous reaction rate in the presence of turbulence.

  • 17. Losada, I. R.
    et al.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Kleeorin, Nathan
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Mitra, Dhrubaditya
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Rogachevskii, Igor
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Rotational effects on the negative magnetic pressure instability2012In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 548, p. A49-Article in journal (Refereed)
    Abstract [en]

    Context. The surface layers of the Sun are strongly stratified. In the presence of turbulence with a weak mean magnetic field, a large-scale instability resulting in the formation of nonuniform magnetic structures, can be excited on the scale of many (more than ten) turbulent eddies (or convection cells). This instability is caused by a negative contribution of turbulence to the effective (mean-field) magnetic pressure and has previously been discussed in connection with the formation of active regions. Aims. We want to understand the effects of rotation on this instability in both two and three dimensions. Methods. We use mean-field magnetohydrodynamics in a parameter regime in which the properties of the negative effective magnetic pressure instability have previously been found to agree with properties of direct numerical simulations. Results. We find that the instability is already suppressed for relatively slow rotation with Coriolis numbers (i.e. inverse Rossby numbers) around 0.2. The suppression is strongest at the equator. In the nonlinear regime, we find traveling wave solutions with propagation in the prograde direction at the equator with additional poleward migration away from the equator. Conclusions. We speculate that the prograde rotation of the magnetic pattern near the equator might be a possible explanation for the faster rotation speed of magnetic tracers relative to the plasma velocity on the Sun. In the bulk of the domain, kinetic and current helicities are negative in the northern hemisphere and positive in the southern.

  • 18.
    Mitra, Dhrubaditya
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm University, Sweden.
    Dasgupta, B.
    Niklasson, E.
    Ram, A.
    Particle energization through time-periodic helical magnetic fields2014In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 89, no 4, article id 042919Article in journal (Refereed)
    Abstract [en]

    We solve for the motion of charged particles in a helical time-periodic ABC (Arnold-Beltrami-Childress) magnetic field. The magnetic field lines of a stationary ABC field with coefficients A=B=C=1 are chaotic, and we show that the motion of a charged particle in such a field is also chaotic at late times with positive Lyapunov exponent. We further show that in time-periodic ABC fields, the kinetic energy of a charged particle can increase indefinitely with time. At late times the mean kinetic energy grows as a power law in time with an exponent that approaches unity. For an initial distribution of particles, whose kinetic energy is uniformly distributed within some interval, the probability density function of kinetic energy is, at late times, close to a Gaussian but with steeper tails.

  • 19.
    Mitra, Dhrubaditya
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm Univ, Sweden.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm Univ, Sweden.
    Kleeorin, Nathan
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm Univ, Sweden; Ben Gurion Univ Negev, Israel; NI Lobachevsky State Univ Nizhny Novgorod, Russia.
    Rogachevskii, Igor
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm Univ, Sweden; Ben Gurion Univ Negev, Israel; NI Lobachevsky State Univ Nizhny Novgorod, Russia.
    Intense bipolar structures from stratified helical dynamos2014In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 445, no 1, p. 761-769Article in journal (Refereed)
    Abstract [en]

    We perform direct numerical simulations of the equations of magnetohydrodynamics with external random forcing and in the presence of gravity. The domain is divided into two parts: a lower layer where the forcing is helical and an upper layer where the helicity of the forcing is zero with a smooth transition in between. At early times, a large-scale helical dynamo develops in the bottom layer. At later times the dynamo saturates, but the vertical magnetic field continues to develop and rises to form dynamic bipolar structures at the top, which later disappear and reappear. Some of the structures look similar to delta spots observed in the Sun. This is the first example of magnetic flux concentrations, owing to strong density stratification, from self-consistent dynamo simulations that generate bipolar, super-equipartition strength, magnetic structures whose energy density can exceeds the turbulent kinetic energy by even a factor of 10.

  • 20.
    Mitra, Dhrubaditya
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Haugen, Nils Erland L.
    Rogachevskii, Igor
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Turbophoresis in forced inhomogeneous turbulence2018In: The European Physical Journal Plus, ISSN 2190-5444, E-ISSN 2190-5444, Vol. 133, no 2, article id 35Article in journal (Refereed)
    Abstract [en]

    We show, by direct numerical simulations, that heavy inertial particles (characterized by Stokes number St) in inhomogeneously forced statistically stationary isothermal turbulent flows cluster at the minima of mean-square turbulent velocity. Two turbulent transport processes, turbophoresis and turbulent diffusion together determine the spatial distribution of the particles. If the turbulent diffusivity is assumed to scale with turbulent root-mean-square velocity, as is the case for homogeneous turbulence, the turbophoretic coefficient can be calculated. Indeed, for the above assumption, the non-dimensional product of the turbophoretic coefficient and the rms velocity is shown to increase with St for small St, reach a maxima for St approximate to 10 and decrease as similar to St(-0.33) for large St.

  • 21.
    Mitra, Dhrubaditya
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm Univ, Roslagstullsbacken 23, S-10691 Stockholm, Sweden.
    Perlekar, Prasad
    Tata Inst Fundamental Res, Ctr Interdisciplinary Sci, Hyderabad 500107, Andhra Pradesh, India..
    Topology of two-dimensional turbulent flows of dust and gas2018In: Physical Review Fluids, E-ISSN 2469-990X, Vol. 3, no 4, article id 044303Article in journal (Refereed)
    Abstract [en]

    We perform direct numerical simulations (DNS) of passive heavy inertial particles (dust) in homogeneous and isotropic two-dimensional turbulent flows (gas) for a range of Stokes number, St < 1. We solve for the particles using both a Lagrangian and an Eulerian approach (with a shock-capturing scheme). In the latter, the particles are described by a dust-density field and a dust-velocity field. We find the following: the dust-density field in our Eulerian simulations has the same correlation dimension d(2) as obtained from the clustering of particles in the Lagrangian simulations for St < 1; the cumulative probability distribution function of the dust density coarse grained over a scale r, in the inertial range, has a left tail with a power-law falloff indicating the presence of voids; the energy spectrum of the dust velocity has a power-law range with an exponent that is the same as the gas-velocity spectrum except at very high Fourier modes; the compressibility of the dust-velocity field is proportional to St(2). We quantify the topological properties of the dust velocity and the gas velocity through their gradient matrices, called A and B, respectively. Our DNS confirms that the statistics of topological properties of B are the same in Eulerian and Lagrangian frames only if the Eulerian data are weighed by the dust density. We use this correspondence to study the statistics of topological properties of A in the Lagrangian frame from our Eulerian simulations by calculating density-weighted probability distribution functions. We further find that in the Lagrangian frame, the mean value of the trace of A is negative and its magnitude increases with St approximately as exp(-C/St) with a constant C approximate to 0.1. The statistical distribution of different topological structures that appear in the dust flow is different in Eulerian and Lagrangian (density-weighted Eulerian) cases, particularly for St close to unity. In both of these cases, for small St the topological structures have close to zero divergence and are either vortical (elliptic) or strain dominated (hyperbolic, saddle). As St increases, the contribution to negative divergence comes mostly from saddles and the contribution to positive divergence comes from both vortices and saddles. Compared to the Eulerian case, the Lagrangian (density-weighted Eulerian) case has less outward spirals and more converging saddles. Inward spirals are the least probable topological structures in both cases.

  • 22.
    Mitra, Dhrubaditya
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Wettlaufer, John S.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Can planetesimals form by collisional fusion?2013In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 773, no 2, p. 120-Article in journal (Refereed)
    Abstract [en]

    As a test bed for the growth of protoplanetary bodies in a turbulent circumstellar disk, we examine the fate of a boulder using direct numerical simulations of particle seeded gas flowing around it. We provide an accurate description of the flow by imposing no-slip and non-penetrating boundary conditions on the boulder surface using the immersed boundary method pioneered by Peskin. Advected by the turbulent disk flow, the dust grains collide with the boulder and we compute the probability density function of the normal component of the collisional velocity. Through this examination of the statistics of collisional velocities, we test the recently developed concept of collisional fusion which provides a physical basis for a range of collisional velocities exhibiting perfect sticking. A boulder can then grow sufficiently rapidly to settle into a Keplerian orbit on disk evolution timescales.

  • 23. Pandey, V.
    et al.
    Perlekar, P.
    Mitra, Dhrubaditya
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Clustering and energy spectra in two-dimensional dusty gas turbulence2019In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 100, no 1, article id 013114Article in journal (Refereed)
    Abstract [en]

    We present direct numerical simulation of heavy inertial particles (dust) immersed in two-dimensional turbulent flow (gas). The dust particles are modeled as monodispersed heavy particles capable of modifying the flow through two-way coupling. By varying the Stokes number (St) and the mass-loading parameter (φm), we study the clustering phenomenon and the gas phase kinetic energy spectra. We find that the dust-dust correlation dimension (d2) also depends on φm. In particular, clustering decreases as mass loading (φm) is increased. In the kinetic energy spectra of gas we show (i) the emergence of a different scaling regime and that (ii) the scaling exponent in this regime is not universal but a function of both St and φm. Using a scale-by-scale enstrophy budget analysis we show that in this emerged scaling regime, which we call the dust-dissipative range, viscous dissipation due to the gas balances the back-reaction from the dust.

  • 24.
    Picano, Francesco
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Breugem, Wim-Paul
    Mitra, Dhrubaditya
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Brandt, Luca
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Shear Thickening in Non-Brownian Suspensions: An Excluded Volume Effect2013In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 111, no 9, p. 098302-Article in journal (Refereed)
    Abstract [en]

    Shear thickening appears as an increase of the viscosity of a dense suspension with the shear rate, sometimes sudden and violent at high volume fraction. Its origin for noncolloidal suspension with non-negligible inertial effects is still debated. Here we consider a simple shear flow and demonstrate that fluid inertia causes a strong microstructure anisotropy that results in the formation of a shadow region with no relative flux of particles. We show that shear thickening at finite inertia can be explained as an increase of the effective volume fraction when considering the dynamically excluded volume due to these shadow regions.

  • 25. Ram, Abhay K.
    et al.
    Dasgupta, Brahmananda
    Krishnamurthy, V.
    Mitra, Dhrubaditya
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Anomalous diffusion of field lines and charged particles in Arnold-Beltrami-Childress force-free magnetic fields2014In: Physics of Plasmas, ISSN 1070-664X, E-ISSN 1089-7674, Vol. 21, no 7, p. 072309-Article in journal (Refereed)
    Abstract [en]

    The cosmic magnetic fields in regions of low plasma pressure and large currents, such as in interstellar space and gaseous nebulae, are force-free in the sense that the Lorentz force vanishes. The three-dimensional Arnold-Beltrami-Childress (ABC) field is an example of a force-free, helical magnetic field. In fluid dynamics, ABC flows are steady state solutions of the Euler equation. The ABC magnetic field lines exhibit a complex and varied structure that is a mix of regular and chaotic trajectories in phase space. The characteristic features of field line trajectories are illustrated through the phase space distribution of finite-distance and asymptotic-distance Lyapunov exponents. In regions of chaotic trajectories, an ensemble-averaged variance of the distance between field lines reveals anomalous diffusion-in fact, superdiffusion-of the field lines. The motion of charged particles in the force-free ABC magnetic fields is different from the flow of passive scalars in ABC flows. The particles do not necessarily follow the field lines and display a variety of dynamical behavior depending on their energy, and their initial pitch-angle. There is an overlap, in space, of the regions in which the field lines and the particle orbits are chaotic. The time evolution of an ensemble of particles, in such regions, can be divided into three categories. For short times, the motion of the particles is essentially ballistic; the ensemble-averaged, mean square displacement is approximately proportional to t(2), where t is the time of evolution. The intermediate time region is defined by a decay of the velocity autocorrelation function-this being a measure of the time after which the collective dynamics is independent of the initial conditions. For longer times, the particles undergo superdiffusion-the mean square displacement is proportional to t(alpha), where alpha > 1, and is weakly dependent on the energy of the particles. These super-diffusive characteristics, both of magnetic field lines and of particles moving in these fields, strongly suggest that theories of transport in three-dimensional chaotic magnetic fields need a shift from the usual paradigm of quasilinear diffusion.

  • 26.
    Rosti, Marco E.
    et al.
    KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Mechanics.
    Brandt, L.uca
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Mitra, Dhrubaditya
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Rheology of suspensions of viscoelastic spheres: Deformability as an effective volume fraction2018In: Physical Review Fluids, E-ISSN 2469-990X, Vol. 3, no 1, article id 012301Article in journal (Refereed)
    Abstract [en]

    We study suspensions of deformable (viscoelastic) spheres in a Newtonian solvent in planeCouette geometry, by means of direct numerical simulations. We find that in the limit of vanishing inertia, the effective viscosity mu of the suspension increases as the volume fraction occupied by the spheres Phi increases and decreases as the elastic modulus of the spheres G decreases; the function mu(Phi,G) collapses to a universal function mu(Phi(e)) with a reduced effective volume fraction Phi(e)(Phi,G). Remarkably, the function mu(Phi(e)) is the well- known Eilers fit that describes the rheology of suspension of rigid spheres at all Phi. Our results suggest different ways to interpret the macrorheology of blood.

  • 27. Väisälä, M. S.
    et al.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Mitra, Dhrubaditya
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Käpylä, Petri J.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Mantere, M. J.
    Quantifying the effect of turbulent magnetic diffusion on the growth rate of the magneto-rotational instability2014In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 567, p. A139-Article in journal (Refereed)
    Abstract [en]

    Context. In astrophysics, turbulent diffusion is often used in place of microphysical diffusion to avoid resolving the small scales. However, we expect this approach to break down when time and length scales of the turbulence become comparable with other relevant time and length scales in the system. Turbulent diffusion has previously been applied to the magneto-rotational instability (MRI), but no quantitative comparison of growth rates at different turbulent intensities has been performed. Aims. We investigate to what extent turbulent diffusion can be used to model the effects of small-scale turbulence on the kinematic growth rates of the MRI, and how this depends on angular velocity and magnetic field strength. Methods. We use direct numerical simulations in three-dimensional shearing boxes with periodic boundary conditions in the spanwise direction and additional random plane-wave volume forcing to drive a turbulent flow at a given length scale. We estimate the turbulent diffusivity using a mixing length formula and compare with results obtained with the test-field method. Results. It turns out that the concept of turbulent diffusion is remarkably accurate in describing the effect of turbulence on the growth rate of the MRI. No noticeable breakdown of turbulent diffusion has been found, even when time and length scales of the turbulence become comparable with those imposed by the MRI itself. On the other hand, quenching of turbulent magnetic diffusivity by the magnetic field is found to be absent. Conclusions. Turbulence reduces the growth rate of the MRI in the same way as microphysical magnetic diffusion does.

  • 28.
    Zhu, Lailai
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, Centres, SeRC - Swedish e-Science Research Centre. Laboratory of Fluid Mechanics and Instabilities, Switzerland .
    Rorai, Cecilia
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Mitra, Dhrubaditya
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Brandt, Luca
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    A microfluidic device to sort capsules by deformability: a numerical study2014In: Soft Matter, ISSN 1744-683X, E-ISSN 1744-6848, Vol. 10, no 39, p. 7705-7711Article in journal (Refereed)
    Abstract [en]

    Guided by extensive numerical simulations, we propose a microfluidic device that can sort elastic capsules by their deformability. The device consists of a duct embedded with a semi-cylindrical obstacle, and a diffuser which further enhances the sorting capability. We demonstrate that the device can operate reasonably well under changes in the initial position of the capsule. The efficiency of the device remains essentially unaltered under small changes of the obstacle shape (from semi-circular to semi-elliptic cross-section). Confinement along the direction perpendicular to the plane of the device increases its efficiency. This work is the first numerical study of cell sorting by a realistic microfluidic device.

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