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We carry out a detailed study of dynamic multiscaling in the turbulent nonequilibrium, but statistically steady, state of the stochastically forced one-dimensional Burgers equation. We introduce the concept of interval collapse time, which we define as the time taken for a spatial interval, demarcated by a pair of Lagrangian tracers, to collapse at a shock. By calculating the dynamic scaling exponents of the moments of various orders of these interval collapse times, we show that (a) there is not one but an infinity of characteristic time scales and (b) the probability distribution function of the interval collapse times is non-Gaussian and has a power-law tail. Our study is based on (a) a theoretical framework that allows us to obtain dynamic-multiscaling exponents analytically, (b) extensive direct numerical simulations, and (c) a careful comparison of the results of (a) and (b). We discuss possible generalizations of our work to higher dimensions, for the stochastically forced Burgers equation, and to other compressible flows that exhibit turbulence with shocks. [ABSTRACT FROM AUTHOR]

Aim: We present evidence for finite magnetic helicity density in the heliosphere and numerical models thereof, and relate it to the magnetic field properties of the dynamo in the solar convection zone. Methods: We use simulations and solar wind data to compute magnetic helicity either directly from the simulations or indirectly using time series of the skew-symmetric components of the magnetic correlation tensor. Results: We find that the solar dynamo produces negative magnetic helicity at small scales and positive at large scales. However, in the heliosphere these properties are reversed and the magnetic helicity is now positive at small scales and negative at large scales. We explain this by the fact that a negative diffusive magnetic helicity flux corresponds to a positive gradient of magnetic helicity, which leads to a change of sign from negative to positive values at some radius in the northern hemisphere.

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 ~exp(-C/St), in the limit St→0 where C is a non-universal constant. [ABSTRACT FROM AUTHOR]

As expected, we observe Kolmogorov scaling Graph $E(k)\sim k^{-5/3}$ for Graph $k and a pseudo-turbulence scaling Graph $E(k) \sim k^{-3}$ for Graph $k>k {d}$. Hence for both of these cases we obtain Graph $E(k) \sim k^{-3}$ for Graph $k > k {d}$ and Graph $E(k)\sim k^{-5/3}$ for Graph $k. In figure 13 we plot the p.d.f. of Graph ${\rm \pi} {K}(\boldsymbol {x})$ with Graph $K=k {d}$ for Graph $b=0$, Graph $b=0.13$ and Graph $b=\infty$. For all the runs, Graph $L=2{\rm \pi}$ and Graph $d=0.46$, and the dimensionless numbers Graph $Ga= 302$, Graph $Bo =1.8$, Graph $At = 0.04$ and Graph $\varPhi = 1.64\,\%$ are kept fixed. \end{equation} In figure 3( I a i , I b i ) we plot the velocity streamlines of the average velocity field Graph ${\boldsymbol {u}}^{CM}({\boldsymbol {\xi }})$ for Graph $b=\infty$ (Graph ${\texttt {R0}}$) and Graph $b=0.13$ (Graph ${\texttt {R3}}$). [Extracted from the article]

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. [ABSTRACT FROM AUTHOR]

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 Damköhler numbers, where the Damköhler number is defined as the ratio of the turbulent and chemical time scales, and it may totally control the mass transfer rate for Damköhler 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We study the role of turbulence in magnetic reconnection, within the framework of magnetohydrodynamics, using three-dimensional direct numerical simulations. For small turbulent intensity, we find that the reconnection rate obeys Sweet–Parker scaling. For large enough turbulent intensity, reconnection rate departs significantly from Sweet–Parker behaviour, becomes almost a constant as a function of the Lundquist number.We further study energization of test-particles in the same set-up. We find that the speed of the energized particles obeys a Maxwellian distribution, whose variance also obeys Sweet–Parker scaling for small turbulent intensity but depends weakly on the Lundquist number for large turbulent intensity. Furthermore, the variance is found to increase with the strength of the reconnecting magnetic field. [ABSTRACT FROM AUTHOR]

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 > 10³, the reconnection rate is nearly independent of S in agreement with results of recent numerical simulations performed by other groups in simpler settings. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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 Wi ≈ 1. We find agreement with earlier analytical predictions for PDF of polymer extensions made by Balkovsky, Fouxon, and Lebedev [Phys. Rev. Lett. 84, 4765 (2000)] for linear polymers (Oldroyd-B model)-with Wi < 1 and by Chertkov [Phys. Rev. Lett. 84, 4761 (2000)] 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 [ABSTRACT FROM AUTHOR]

The article presents a study which explores the nonmonotonic behavior of elastic range scaling in polymeric turbulence at large Reynolds and Deborah numbers. It mentions the use of direct numerical simulations to study homogeneous and isotropic turbulent flows of dilute polymer solutions at high Reynolds and Deborah numbers.

In two-dimensional forced Navier-Stokes turbulence, energy cascades to the largest scales in the system to form a pair of coherent vortices known as the Bose condensate. We show, both numerically and analytically, that the energy condensation saturates and the system reaches a statistically stationary state. The time scale of saturation is inversely proportional to the viscosity and the saturation energy level is determined by both the viscosity and the force. We further show that, without sufficient resolution to resolve the small-scale enstrophy spectrum, numerical simulations can give a spurious result for the saturation energy level. We also find that the movement of the condensate is similar to the motion of an inertial particle with an effective drag force. Furthermore, we show that the profile of the saturated coherent vortices can be described by a Gaussian core with exponential wings. [ABSTRACT FROM AUTHOR]

We obtain, by extensive direct numerical simulations, time-dependent and equal-time structure functions for the vorticity, in both quasi-Lagrangian and Eulerian frames, for the direct-cascade regime in two-dimensional fluid turbulence with air-drag-induced friction. We show that different ways of extracting time scales from these time-dependent structure functions lead to different dynamic-multiscaling exponents, which are related to equal-time multiscaling exponents by different classes of bridge relations; for a representative value of the friction we verify that, given our error bars, these bridge relations hold. [ABSTRACT FROM AUTHOR]

Magnetic helicity fluxes are investigated in a family of gauges in which the contribution from ideal magnetohydrodynamics takes the form of a purely advective flux. Numerical simulations of magnetohydrodynamic turbulence in this advective gauge family exhibit instabilities triggered by the build-up of unphysical irrotational contributions to the magnetic vector potential. As a remedy, the vector potential is evolved in a numerically well behaved gauge, from which the advective vector potential is obtained by a gauge transformation. In the kinematic regime, the magnetic helicity density evolves similarly to a passive scalar when resistivity is small and turbulent mixing is mild, i.e., when the fluid Reynolds number is not too large. In the dynamical regime, resistive contributions to the magnetic helicity flux in the advective gauge are found to be significant owing to the development of small length scales in the irrotational part of the magnetic vector potential. [ABSTRACT FROM AUTHOR]

We present a unified three-dimensional model of the convection zone and upper atmosphere of the Sun in spherical geometry. In this model, magnetic fields, generated by a helically forced dynamo in the convection zone, emerge without the assistance of magnetic buoyancy. We use an isothermal equation of state with gravity and density stratification. Recurrent plasmoid ejections, which rise through the outer atmosphere, is observed. In addition, the current helicity of the small–scale field is transported outwards and form large structures like magnetic clouds. [ABSTRACT FROM PUBLISHER]

We give an overview of the progress that has been made in recent years in understanding dynamic multiscaling in homogeneous, isotropic turbulence and related problems. We emphasise the similarity of this problem with the dynamic scaling of time-dependent correlation functions in the vicinity of a critical point in, e.g., a spin system. The universality of dynamic-multiscaling exponents in fluid turbulence is explored by detailed simulations of the GOY shell model for fluid turbulence. [ABSTRACT FROM AUTHOR]

We systematize the study of dynamic multiscaling of timedependent structure functions in different models of passive-scalar and fluid turbulence. We show that, by suitably normalizing these structure functions, we can eliminate their dependence on the origin of time at which we start our measurements and that these normalized structure functions yield the same linear bridge relations that relate the dynamic-multiscaling and equal-time exponents for statistically steady turbulence. We show analytically, for both the Kraichnan model of passive-scalar turbulence and its shell model analogue, and numerically, for the Gledzer-Ohkitani-Yamada (GOY) shell model of fluid turbulence and a shell model for passive-scalar turbulence, that these exponents and bridge relations are the same for statistically steady and decaying turbulence. Thus, we provide strong evidence for dynamic universality, i.e. dynamic-multiscaling exponents do not depend on whether the turbulence decays or is statistically steady. [ABSTRACT FROM AUTHOR]

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 (d 2) 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. [ABSTRACT FROM AUTHOR]

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 ɸ between the particle and fluid velocities. We show that, when the effects of particle inertia are small, the probability distribution function (PDF) Pɸ of this deviation angle shows a power-law region in which Pɸ~ɸ-4. We also find that the PDFs of the trajectory curvature κ and modulus θ of the torsion ϑ 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. [ABSTRACT FROM AUTHOR]