Correlation Time Of Turbulence Research Articles

Scaling of Turbulence and Microphysics in a Convection–Cloud Chamber of Varying Height

AbstractThe convection–cloud chamber enables measurement of aerosol and cloud microphysics, as well as their interactions, within a turbulent environment under steady‐state conditions. Increasing the size of a convection–cloud chamber, while holding the imposed temperature difference constant, leads to increased Rayleigh, Reynolds and Nusselt numbers. Large–eddy simulation coupled with a bin microphysics model allows the influence of increased velocity, time, and spatial scales on cloud microphysical properties to be explored. Simulations of a convection–cloud chamber, with fixed aspect ratio and increasing heights of H = 1, 2, 4, and (for dry conditions only) 8 m are performed. The key findings are: Velocity fluctuations scale as H1/3, consistent with the Deardorff expression for convective velocity, and implying that the turbulence correlation time scales as H2/3. Temperature and other scalar fluctuations scale as H−3/7. Droplet size distributions from chambers of different sizes can be matched by adjusting the total aerosol injection rate as the horizontal cross‐sectional area (i.e., as H2 for constant aspect ratio). Injection of aerosols at a point versus distributed throughout the volume makes no difference for polluted conditions, but can lead to cloud droplet size distribution broadening in clean conditions. Cloud droplet growth by collision and coalescence leads to a broader right tail of the distribution compared to condensation growth alone, and this tail increases in magnitude and extent monotonically as the increase of chamber height. These results also have implications for scaling within turbulent, cloudy mixed‐layers in the atmosphere, such as fog layers.

Dust Settling and Clumping in MRI-turbulent Outer Protoplanetary Disks

Abstract Planetesimal formation is a crucial yet poorly understood process in planet formation. It is widely believed that planetesimal formation is the outcome of dust clumping by the streaming instability (SI). However, recent analytical and numerical studies have shown that the SI can be damped or suppressed by external turbulence, and at least the outer regions of protoplanetary disks are likely weakly turbulent due to magneto-rotational instability (MRI). We conduct high-resolution local shearing-box simulations of hybrid particle-gas magnetohydrodynamics (MHD), incorporating ambipolar diffusion as the dominant nonideal MHD effect, applicable to outer disk regions. We first show that dust backreaction enhances dust settling toward the midplane by reducing turbulence correlation time. Under modest level of MRI turbulence, we find that dust clumping is in fact easier than the conventional SI case, in the sense that the threshold of solid abundance for clumping is lower. The key to dust clumping includes dust backreaction and the presence of local pressure maxima, which in our work is formed by the MRI zonal flows overcoming background pressure gradient. Overall, our results support planetesimal formation in the MRI-turbulent outer protoplanetary disks, especially in ring-like substructures.

Measurement and control of turbulence spreading in the scrape-off layer of TJ-II stellarator

In this paper, we report measurements of turbulence drive and spreading in the edge region and scrape-off layer (SOL) of the TJ-II stellarator for plasmas heated by ECRH and NBI. In addition, we show how these and various other relevant quantities can be modulated actively via edge biasing, i.e. by establishing an edge flow shear layer. When the edge shear reaches values close to the inverse of the turbulence correlation time, turbulence spreading and edge-SOL coupling are reduced significantly. The resulting control of SOL spreading via the edge shear is important in view of the issue of understanding and controlling the SOL width in fusion-relevant devices.

Theory of critical balance in plasma turbulence

Critical balance, a statement of the approximate equality of a timescale of motion parallel to the magnetic field with a timescale of turbulent motion perpendicular to the field, is analyzed from a statistical description of the relative motion of two particles consistent with two-point correlation in a nonlinear gyrokinetic system with collisions. Critical balance is understood from a premise that the fastest time to any spatial scale that encounters decorrelated motions sets an overall correlation time for both perpendicular and parallel scales. For a regime of weak collisionality, this leads to the approximate equality of the parallel streaming time and the perpendicular turbulent correlation time, which is a standard statement of critical balance. These two timescales are only approximately equal because of effects in parallel streaming dynamics and collisions, the former producing deviations tied to variations of perpendicular and parallel wavenumbers. Analysis of a collisional regime shows that critical balance also applies in that limit with a modified relation between parallel and perpendicular spatial scales.

Evaluation and validation of large-eddy simulation sub-grid spray dispersion models using high-fidelity volume-of-fluid simulation data and engine combustion network experimental data

A sub-grid model accounting for the interaction of spray and sub-grid turbulence was developed and tested. The model predicts the sub-grid scale dispersion velocity used for calculating the slip velocity in Lagrangian–Eulerian Large-eddy simulation spray models. The dispersion velocity is assumed to be decomposed into a deterministic and a stochastic part, and it is updated in every turbulence correlation time for each computational parcel. The model was validated against two datasets: volume-of-fluid simulations and Engine Combustion Network experiments. The volume-of-fluid data showed that dispersion velocities at the centerline are anisotropic. This qualitative feature is well captured by the current model. For the Engine Combustion Network Spray A cases, it was found that sub-grid scale dispersion has profound impact on the prediction of the spatial distribution of liquid mass. Neglecting the sub-grid scale dispersion model results in underprediction of the width of the lateral projected liquid mass density profiles. Also, the prediction of the projected liquid mass density is sensitive to the two model constants determining the sub-grid scale dispersion velocity magnitude and turbulence time scale. However, the predictions of resolved gas-phase statistics are relatively insensitive to different sub-grid scale dispersion model setups. The primary reason for this was investigated. It was found that the motion of high-momentum liquid blobs in the near-nozzle region leading to air entrainment and subsequent gas jet development is minimally influenced by sub-grid scale dispersion. The importance of sub-grid scale dispersion inversely correlates with drag force magnitude: the larger the drag force, the less critical the sub-grid scale dispersion. Moving further downstream, quasi-equilibrium between the two phases is established, resulting in relatively small slip velocity and drag force.

Mean-field theory of differential rotation in density stratified turbulent convection

A mean-field theory of differential rotation in a density stratified turbulent convection has been developed. This theory is based on the combined effects of the turbulent heat flux and anisotropy of turbulent convection on the Reynolds stress. A coupled system of dynamical budget equations consisting in the equations for the Reynolds stress, the entropy fluctuations and the turbulent heat flux has been solved. To close the system of these equations, the spectral$\unicode[STIX]{x1D70F}$approach, which is valid for large Reynolds and Péclet numbers, has been applied. The adopted model of the background turbulent convection takes into account an increase of the turbulence anisotropy and a decrease of the turbulent correlation time with the rotation rate. This theory yields the radial profile of the differential rotation which is in agreement with that for the solar differential rotation.

Theory of ITG turbulent saturation in stellarators: Identifying mechanisms to reduce turbulent transport

A three-field fluid model that allows for general three-dimensional equilibrium geometry is developed to describe ion temperature gradient turbulent saturation processes in stellarators. The theory relies on the paradigm of nonlinear transfer of energy from unstable to damped modes at comparable wavelength as the dominant saturation mechanism. The unstable-to-damped mode interaction is enabled by a third mode that for dominant energy transfer channels primarily serves as a regulator of the nonlinear energy transfer rate. The identity of the third wave in the interaction defines different scenarios for turbulent saturation with the dominant scenario depending upon the properties of the 3D geometry. The nonlinear energy transfer physics is quantified by the product of a turbulent correlation lifetime and a geometric coupling coefficient. The turbulent correlation time is determined by a three-wave frequency mismatch, which at long wavelength can be calculated from the sum of the linear eigenfrequencies of the three modes. Larger turbulent correlation times denote larger levels of nonlinear energy transfer and hence smaller turbulent transport. The theory provides an analytic prediction for how 3D shaping can be tuned to lower turbulent transport through saturation processes.

Aerosol removal and cloud collapse accelerated by supersaturation fluctuations in turbulence

AbstractPrior observations have documented the process of cloud cleansing, through which cloudy, polluted air from a continent is slowly transformed into cloudy, clean air typical of a maritime environment. During that process, cloud albedo changes gradually, followed by a sudden reduction in cloud fraction and albedo as drizzle forms and convection changes from closed to open cellular. Experiments in a cloud chamber that generates a turbulent environment show a similar cloud cleansing process followed by rapid cloud collapse. Observations of (1) cloud droplet size distribution, (2) interstitial aerosol size distribution, (3) cloud droplet residual size distribution, and (4) water vapor supersaturation are all consistent with the hypothesis that turbulent fluctuations of supersaturation accelerate the cloud cleansing process and eventual cloud collapse. Decay of the interstitial aerosol concentration occurs slowly at first then more rapidly. The accelerated cleansing occurs when the cloud phase relaxation time exceeds the turbulence correlation time.

Some consequences of shear on galactic dynamos with helicity fluxes

Galactic dynamo models sustained by supernova (SN) driven turbulence and differential rotation have revealed that the sustenance of large scale fields requires a flux of small scale magnetic helicity to be viable. Here we generalize a minimalist analytic version of such galactic dynamos to explore some heretofore unincluded contributions from shear on the total turbulent energy and turbulent correlation time, with the helicity fluxes maintained by either winds, diffusion, or magnetic buoyancy. We construct an analytic framework for modeling the turbulent energy and correlation time as functions of SN rate and shear. We compare our prescription with previous approaches that only include rotation. The solutions depend separately on the rotation period and the eddy turnover time and not just on their ratio (the Rossby number). We consider models in which these two time scales are allowed to be independent and also a case in which they are mutually dependent on radius when a radial dependent SN rate model is invoked. For the case of a fixed rotation period (or fixed radius) we show that the influence of shear is dramatic for low Rossby numbers, reducing the correlation time of the turbulence, which in turn, strongly reduces the saturation value of the dynamo compared to the case when the shear is ignored. We also show that even in the absence of winds or diffusive fluxes, magnetic buoyancy may be able to sustain sufficient helicity fluxes to avoid quenching.

STATISTICAL TESTS OF GALACTIC DYNAMO THEORY

ABSTRACT Mean-field galactic dynamo theory is the leading theory to explain the prevalence of regular magnetic fields in spiral galaxies, but its systematic comparison with observations is still incomplete and fragmentary. Here we compare predictions of mean-field dynamo models to observational data on magnetic pitch angle and the strength of the mean magnetic field. We demonstrate that a standard dynamo model produces pitch angles of the regular magnetic fields of nearby galaxies that are reasonably consistent with available data. The dynamo estimates of the magnetic field strength are generally within a factor of a few of the observational values. Reasonable agreement between theoretical and observed pitch angles generally requires the turbulent correlation time τ to be in the range of 10– , in agreement with standard estimates. Moreover, good agreement also requires that the ratio of the ionized gas scale height to root-mean-square turbulent velocity increases with radius. Our results thus widen the possibilities to constrain interstellar medium parameters using observations of magnetic fields. This work is a step toward systematic statistical tests of galactic dynamo theory. Such studies are becoming more and more feasible as larger data sets are acquired using current and up-and-coming instruments.

Characterisation of the turbulent electromotive force and its magnetically-mediated quenching in a global EULAG-MHD simulation of solar convection

We perform a mean-field analysis of the EULAG-MHD millenium simulation of global magnetohydrodynamical convection presented in Passos and Charbonneau (2014). The turbulent electromotive force (emf) operating in the simulation is assumed to be linearly related to the cyclic axisymmetric mean magnetic field and its first spatial derivatives. At every grid point in the simulation’s meridional plane, this assumed relationship involves 27 independent tensorial coefficients. Expanding on Racine et al. (2011), we extract these coefficients from the simulation data through a least-squares minimization procedure based on singular value decomposition. The reconstructed α-tensor shows good agreement with that obtained by Racine et al. (2011), who did not include derivatives of the mean-field in their fit, as well as with the α-tensor extracted by Augustson et al. (2015) from a distinct ASH MHD simulation. The isotropic part of the turbulent magnetic diffusivity tensor β is positive definite and reaches values of 5.0×107m2s−1 in the middle of the convecting fluid layers. The spatial variations of both αϕϕ and βϕϕ component are well reproduced by expressions obtained under the Second Order Correlation Approximation, with a good matching of amplitude requiring a turbulent correlation time about five times smaller than the estimated turnover time of the small-scale turbulent flow. By segmenting the simulation data into epochs of magnetic cycle minima and maxima, we also measure α- and β-quenching. We find the magnetic quenching of the α-effect to be driven primarily by a reduction of the small-scale flow’s kinetic helicity, with variations of the current helicity playing a lesser role in most locations in the simulation domain. Our measurements of turbulent diffusivity quenching are restricted to the βϕϕ component, but indicate a weaker quenching, by a factor of ≃1.36, than of the α-effect, which in our simulation drops by a factor of three between the minimum and maximum phases of the magnetic cycle.

Erratum: sensitivity of the magnetorotational instability to the shear parameter in stratified simulations

The magnetorotational instability (MRI) is a shear instability and thus its sensitivity to the shear parameter $q = - d\ln\Omega/d\ln r $ is of interest to investigate. Motivated by astrophysical disks, most (but not all) previous MRI studies have focused on the Keplerian value of $ q=1.5$. Using simulation with 8 vertical density scale heights, we contribute to the subset of studies addressing the the effect of varying $q$ in stratified numerical simulations. We discuss why shearing boxes cannot easily be used to study $q>2$ and thus focus on $q<2$. As per previous simulations, which were either unstratified or stratified with a smaller vertical domain, we find that the $q$ dependence of stress for the stratified case is not linear, contrary to the Shakura-Sunyaev model. We find that the scaling agrees with \cite{1996MNRAS.281L..21A} who found it to be proportional to the shear to vorticity ratio $q/(2-q)$. We also find however, that the shape of the magnetic and kinetic energy spectra are relatively insensitive to $q$ and that the ratio of Maxwell stress to magnetic energy ratio also remains nearly independent of $q$. This is consistent with a theoretical argument in which the rate of amplification of the azimuthal field depends linearly on $q$ and the turbulent correlation time $\tau$ depends inversely on $q$. As such, we measure the correlation time of the turbulence and find that indeed it is inversely proportional to $q$.

Sensitivity of the magnetorotational instability to the shear parameter in stratified simulations

The magnetorotational instability (MRI) is a shear instability and thus its sensitivity to the shear parameter q = −d ln Ω/d ln r is of interest to investigate. Motivated by astrophysical discs, most (but not all) previous MRI studies have focused on the Keplerian value of q = 1.5. Using simulation with eight vertical density scaleheights, we contribute to the subset of studies addressing the effect of varying q in stratified numerical simulations. We discuss why shearing boxes cannot easily be used to study q > 2 and thus focus on q < 2. As per previous simulations, which were either unstratified or stratified with a smaller vertical domain, we find that the q dependence of stress for the stratified case is not linear, contrary to the Shakura–Sunyaev model. We find that the scaling agrees with Abramowicz, Brandenburg & Lasota who found it to be proportional to the shear to vorticity ratio q/(2 − q). We also find however that the shape of the magnetic and kinetic energy spectra are relatively insensitive to q and that the ratio of Maxwell stress to magnetic energy ratio also remains nearly independent of q. This is consistent with a theoretical argument in which the rate of amplification of the azimuthal field depends linearly on q and the turbulent correlation time τ depends inversely on q. As such, we measure the correlation time of the turbulence and find that indeed it is inversely proportional to q.

Galactic spiral patterns and dynamo action – II. Asymptotic solutions

The exploration of mean-field galactic dynamos affected by a galactic spiral pattern, begun in Chamandy et al. (2013, hereafter Paper I) with numerical simulations, is continued here with an asymptotic solution. The mean-field dynamo model used generalizes the standard theory to include the delayed response of the mean electromotive force to variations of the mean magnetic field and turbulence parameters (the temporal non-locality, or {\tau} effect). The effect of the spiral pattern on the dynamo considered is the enhancement of the {\alpha}-effect in spiral-shaped regions (which may overlap the gaseous spiral arms or be located in the interarm regions). The axisymmetric and enslaved non-axisymmetric modes of the mean magnetic field are studied semi-analytically to clarify and strengthen the numerical results. Good qualitative agreement is obtained between the asymptotic solution and numerical solutions of Paper I for a global, rigidly rotating material spiral (density wave). At all galactocentric distances except for the co-rotation radius, we find magnetic arms displaced in azimuth from the {\alpha}-arms, so that the ridges of magnetic field strength are more tightly wound than the {\alpha}-arms. Moreover, the effect of a finite dynamo relaxation time {\tau} (related to the turbulence correlation time) is to phase-shift the magnetic arms in the direction opposite to the galactic rotation even at the co-rotation radius. This mechanism can be used to explain the phase shifts between magnetic and material arms observed in some spiral galaxies.

Kinetic theory of weak turbulence in plasmas

From the nonlinear Vlasov equation, a nonlinear turbulence scattering term is found to describe stochastic dissipation on a time scale longer than the turbulence correlation time. The evolution of the plasma distribution is determined by the well-understood unperturbed motion of charged particles, with the effects of the fluctuating part of fields described by the turbulence scattering term. In the present framework, one can identify various important physics, from the linear and quasilinear regimes to the nonlinear regime, in particular, the connections between the widely used Kadomtsev-Pogutse equation [B. B. Kadomtsev and O. P. Pogutse, in Reviews of Plasma Physics, edited by M. A. Leontovich (Consultants Bureau, New York, 1970), pp. 368-387] and the Frieman-Chen equation [Frieman and Chen, Phys. Fluids 25, 502 (1982)]. The nonlinear scattering term indicates the Onsager symmetry relation of turbulent transport and a nonlinear frequency or k spectrum shift of a resonantly excited wave.

Experimental signatures of critically balanced turbulence in MAST.

Beam emission spectroscopy (BES) measurements of ion-scale density fluctuations in the MAST tokamak are used to show that the turbulence correlation time, the drift time associated with ion temperature or density gradients, the particle (ion) streaming time along the magnetic field, and the magnetic drift time are consistently comparable, suggesting a "critically balanced" turbulence determined by the local equilibrium. The resulting scalings of the poloidal and radial correlation lengths are derived and tested. The nonlinear time inferred from the density fluctuations is longer than the other times; its ratio to the correlation time scales as ν(*i)(-0.8 ± 0.1), where ν(*i) = ion collision rate/streaming rate. This is consistent with turbulent decorrelation being controlled by a zonal component, invisible to the BES, with an amplitude exceeding those of the drift waves by ∼ ν(*i)(-0.8).

Derivation of stochastic differential equations for scrape-off layer plasma fluctuations from experimentally measured statistics

A stochastic differential equation for intermittent plasma density dynamics in magnetic fusion edge plasma is derived, which is consistent with the experimentally measured gamma distribution and the theoretically expected quadratic nonlinearity. The plasma density is driven by a multiplicative Wiener process and evolves on the turbulence correlation time scale, while the linear growth is quadratically damped by the fluctuation level. The sensitivity of intermittency to the nonlinear dynamics is investigated by analyzing the nonlinear Langevin representation of the beta process, which leads to a root-square nonlinearity.

A coarse-grained kinetic equation for neutral particles in turbulent fusion plasmas

A coarse-grained kinetic equation for neutral particles (atoms, molecules) in magnetized fusion plasmas, valid on time scales large compared to the turbulence correlation time, is presented. This equation includes the effects of plasma density fluctuations, described by gamma statistics, on the transport of neutral particles. These effects have so far been neglected in plasma edge modeling, in spite of the fact that the amplitude of fluctuations can be of order unity. Density fluctuations are shown to have a marked effect on the screening of neutrals and on the spatial localization of the ionization source, in particular at high density. The coarse-grained equations obtained in this work are readily implemented in edge code suites currently used for fusion plasma analysis and future divertor design (ITER, DEMO).

Coronal heating in coupled photosphere-chromosphere-coronal systems: turbulence and leakage

Coronal loops act as resonant cavities for low frequency fluctuations that are transmitted from the deeper layers of the solar atmosphere and are amplified in the corona, triggering nonlinear interactions. However trapping is not perfect, some energy leaks down to the chromosphere, thus limiting the turbulence development and the associated heating. We consider the combined effects of turbulence and leakage in determining the energy level and associated heating rate in models of coronal loops which include the chromosphere and transition region. We use a piece-wise constant model for the Alfven speed and a Reduced MHD - Shell model to describe the interplay between turbulent dynamics in the direction perpendicular to the mean field and propagation along the field. Turbulence is sustained by incoming fluctuations which are equivalent, in the line-tied case, to forcing by the photospheric shear flows. While varying the turbulence strength, we compare systematically the average coronal energy level (E) and dissipation rate (D) in three models with increasing complexity: the classical closed model, the semi-open corona model, and the corona-chromosphere (or 3-layer) model, the latter two models allowing energy leakage. We find that: (i) Leakage always plays a role (even for strong turbulence), E and D are systematically lower than in the line-tied model. (ii) E is close to the resonant prediction, i.e., assuming effective turbulent correlation time longer than the Alfven coronal crossing time (Ta). (iii) D is close to the value given by the ratio of photospheric energy divided by Ta (iv) The coronal spectra exibits an inertial range with 5/3 spectral slope, and a large scale peak of trapped resonant modes that inhibit nonlinear couplings. (v) In the realistic 3-layer model, the two-component spectrum leads to a damping time equal to the Kolmogorov time reduced by a factor u_rms/Va_corona

Nonperturbative quasilinear approach to the shear dynamo problem

We study large-scale dynamo action due to turbulence in the presence of a linear shear flow. Our treatment is quasilinear and equivalent to the standard "first-order smoothing approximation." However it is non perturbative in the shear strength. We first derive an integrodifferential equation for the evolution of the mean magnetic field, by systematic use of the shearing coordinate transformation and the Galilean invariance of the linear shear flow. We show that, for nonhelical turbulence, the time evolution of the cross-shear components of the mean field do not depend on any other components excepting themselves; this is valid for any Galilean-invariant velocity field, independent of its dynamics. Hence, to all orders in the shear parameter, there is no shear-current-type effect for non helical turbulence in a linear shear flow in quasilinear theory in the limit of zero resistivity. We then develop a systematic approximation of the integro-differential equation for the case when the mean magnetic field varies slowly compared to the turbulence correlation time. For nonhelical turbulence, the resulting partial differential equations can again be solved by making a shearing coordinate transformation in Fourier space. The resulting solutions are in the form of shearing waves, labeled by the wave number in the sheared coordinates. These shearing waves can grow at early and intermediate times but are expected to decay in the long time limit.