Advection Field Research Articles

Accounting for magnetic diffusion in core flow inversions from geomagnetic secular variation

SUMMARY We use numerical dynamos to investigate the possible role of magnetic diffusion at the top of the core. We find that the contribution of radial magnetic diffusion to the secular variation is correlated with that of tangential magnetic diffusion for a wide range of control parameters. The correlation between the two diffusive terms is interpreted in terms of the variation in the strength of poloidal flow along a columnar flow tube. The amplitude ratio of the two diffusive terms is used to estimate the probable contribution of radial magnetic diffusion to the secular variation at Earth-like conditions. We then apply a model where radial magnetic diffusion is proportional to tangential diffusion to core flow inversions of geomagnetic secular variation data. We find that including magnetic diffusion does not change dramatically the global flow but some significant local variations appear. In the non frozen-flux core flow models (termed ‘diffusive’), the hemispherical dichotomy between the active Atlantic and quiet Pacific is weaker, a cyclonic vortex below North America emerges and the vortex below Asia is stronger. Our results have several important geophysical implications. First, our diffusive flow models contain some flow activity at low latitudes in the Pacific, suggesting a local balance between magnetic field advection and diffusion in that region. Second, the cyclone below North America in our diffusive flows reconciles the difference between mantle-driven thermal wind predictions and frozen-flux core flow models, and is consistent with the prominent intense magnetic flux patch below North America in geomagnetic field models. Finally, we hypothesize that magnetic diffusion near the core surface plays a larger role in the geomagnetic secular variation than usually assumed.

A new fast reconnection model in a collisionless regime

Based on the first principles [i.e., (i) by balancing the magnetic field advection with the term containing electron pressure tensor nongyrotropic components in the generalized Ohm’s law; (ii) using the conservation of mass; and (iii) assuming that the weak magnetic field region width, where electron meandering motion supports electron pressure tensor off-diagonal (nongyrotropic) components, is of the order of electron Larmor radius] a simple model of magnetic reconnection in a collisionless regime is formulated. The model is general, resembling its collisional Sweet–Parker analog in that it is not specific to any initial configuration, e.g., Harris-type tearing unstable current sheet, X-point collapse or otherwise. In addition to its importance from the fundamental point of view, the collisionless reconnection model offers a much faster reconnection rate [Mc′less=(c∕ωpe)2∕(rL,eL)] than Sweet–Parker’s classical one (Msp=S−1∕2). The width of the diffusion region (current sheet) in the collisionless regime is found to be δc′less=(c∕ωpe)2∕rL,e, which is independent of the global reconnection scale L and is only prescribed by microphysics (electron inertial length, c∕ωpe, and electron Larmor radius, rL,e). Amongst other issues, the fastness of the reconnection rate alleviates, e.g., the problem of interpretation of solar flares by means of reconnection, as for the typical solar coronal parameters the obtained collisionless reconnection time can be a few minutes, as opposed to Sweet–Parker’s equivalent value of less than a day. The new theoretical reconnection rate is compared to the Magnetic Reconnection Experiment device experimental data by Yamada et al. [Phys. Plasmas 13, 052119 (2006)] and Ji et al. [Geophys. Res. Lett. 35, 13106 (2008)], and a good agreement is obtained.

Data assimilation for precipitation nowcasting using Bayesian inference

This work introduces a new variational Bayes data assimilation method for the stochastic estimation of precipitation dynamics using radar observations for short term probabilistic forecasting (nowcasting). A previously developed spatial rainfall model based on the decomposition of the observed precipitation field using a basis function expansion captures the precipitation intensity from radar images as a set of ‘rain cells’. The prior distributions for the basis function parameters are carefully chosen to have a conjugate structure for the precipitation field model to allow a novel variational Bayes method to be applied to estimate the posterior distributions in closed form, based on solving an optimisation problem, in a spirit similar to 3D VAR analysis, but seeking approximations to the posterior distribution rather than simply the most probable state. A hierarchical Kalman filter is used to estimate the advection field based on the assimilated precipitation fields at two times. The model is applied to tracking precipitation dynamics in a realistic setting, using UK Met Office radar data from both a summer convective event and a winter frontal event. The performance of the model is assessed both traditionally and using probabilistic measures of fit based on ROC curves. The model is shown to provide very good assimilation characteristics, and promising forecast skill. Improvements to the forecasting scheme are discussed.

Magnetic field distribution in the quiet Sun: a simplified model approach

We simulate the dynamics and the evolution of quiet Sun magnetic elements to produce a probability density function of the field strengths associated with such elements. The dynamics of the magnetic field are simulated through a numerical model in which magnetic elements are passively driven by an advection field presenting spatio-temporal correlations which mimicks the granulation and the mesogranulation scales observed on the solar surface. The field strength can increase due to an amplification process which takes place where the magnetic elements converge. Starting from a delta-like probability density function centered on B=30 G, we obtain magnetic field strengths up to 2 kG (in absolute value). To derive the statistical properties of the magnetic elements several simulation runs are performed. The model is able to produce kG magnetic fields in a time interval of the order of the granulation time scale. The mean unsigned flux density and the mean magnetic energy density of the synthetic quiet Sun reach respectively 100 G and 350 G in the stationary regime. The derived probability density function of the magnetic field strength decreases rapidly from B=30 G to B=100 G and presents a secondary maximum for B=2 kG. From this result it follows that magnetic fields >700 G dominate the unsigned flux density and magnetic energy density although the probability density function of the field strength presents a maximum for B=30 G.

Simulation of direct effects of black carbon aerosol on temperature and hydrological cycle in Asia by a Regional Climate Model

The simulation of direct radiative effect of black carbon (BC) aerosol over Asia is carried out with application of Regional Climate Model RegCM3 over the period of 1993–2003 based on BC emission inventory in 2000. Major findings are as follows. The column burden of BC exceeds 1 mg/m2 in central, eastern, and southern China with the highest value of 2.5 mg/m2 over Sichuan Basin of China, and is of 1–2 mg/m2 in India subcontinent. The column averaged advection field of BC shows an eastward tendency in north of 20° N, whereas an opposite trend is found in south of 10° N. Off-line radiative forcing (RF) induced by BC, which is due to direct absorption or scattering of BC, is positive at the top of the atmosphere (TOA), while maximum effect is found over Sichuan Basin. The RF is of 1–1.5 W/m2 in areas such as the middle and low reaches of the Yangtze River, East China Sea, South China Sea, Indo-China Peninsula and most parts of Indian subcontinent. Surface RF is found to be negative and its absolute value is larger than that at TOA. Based on simulation results, BC’s impacts on temperature, stratification stability, water vapor, precipitation and evaporation etc., are primarily characterized by cold-and-wet change in southern and northwest China, cold-and-dry change in northern and northeast China, warm-and-wet change of India subcontinent, as well as warm-and-dry change of Central Asia.

Stability of scroll ring orientation in an advective field

The stability of the orientation of scroll rings in the excitable Belousov-Zhabotinsky reaction under an applied electrical current was investigated in experiments and simulations. The parallel and antiparallel orientations of the scroll ring unit vector with respect to the current are two stationary states, the first one unstable, the latter stable. For any other orientation, the scroll rings were forced to rotate by the current. At the stable stationary orientation, the scroll rings may contract or expand under the same applied current depending on the radius of the scroll rings. In simulations, delicate adjustments caused a scroll ring to propagate with a constant radius in an advective field.

Numerical investigation of scaling regimes in a model of an anisotropically advected vector field

Influence of strong uniaxial small-scale anisotropy on the stability of inertial-range scaling regimes in a model of a passive transverse vector field advected by an incompressible turbulent flow is investigated by means of the field theoretic renormalization group. Turbulent fluctuations of the velocity field are taken to have the Gaussian statistics with zero mean and defined noise with finite correlations in time. It is shown that stability of the inertial-range scaling regimes in the three-dimensional case is not destroyed by anisotropy, but the corresponding stability of the two-dimensional system can be corrupted by the presence of anisotropy. A borderline dimension dc below which the stability of the scaling regime is not present is calculated as a function of anisotropy parameters.

Advection of Magnetic Fields in Accretion Disks: Not So Difficult After All

We show that a large-scale, weak magnetic field threading a turbulent accretion disk tends to be advected inward, contrary to previous suggestions that it will be stopped by outward diffusion. The efficient inward transport is a consequence of the diffuse, magnetically-dominated surface layers of the disk, where the turbulence is suppressed and the conductivity is very high. This structure arises naturally in three-dimensional simulations of magnetorotationally unstable disks, and we demonstrate here that it can easily support inward advection and compression of a weak field. The advected field is anchored in the surface layer but penetrates the main body of the disk, where it can generate strong turbulence and produce values of alpha (i.e., the turbulent stress) large enough to match observational constraints; typical values of the vertical magnetic field merely need to reach a few percent of equipartition for this to occur. Overall, these results have important implications for models of jet formation which require strong, large-scale magnetic fields to exist over a region of the inner accretion disk.

Seasonality and scale of the Kerguelen plateau phytoplankton bloom: A remote sensing and modeling analysis of the influence of natural iron fertilization in the Southern Ocean

The phytoplankton bloom that develops over the Kerguelen plateau following natural input of iron is analysed on a regional and seasonal scale. The relation between chlorophyll, bathymetry, and surface advection fields is not as obvious as it first appears from large-scale annual mean field. The high chlorophyll biomass does not always correspond with the shallowest water, and there are portions of the plateau, which persistently exhibit low chlorophyll. Despite this complex dynamic, a one-dimensional model calibrated for HNLC (high-nutrient low-chlorophyll) region is able to capture the observed increase in chlorophyll by increasing the deep iron concentration. The elemental budget shows similarity in terms of carbon, nitrogen, and silicon but differences in terms of iron with the budget calculated during the mission. This discrepancy either has its origin in the structure of the iron cycling in the model or in the temporal scarcity of data that could only be collected during the summer months. In the model, flexibility of the Fe/C ratio associated with high Fe export and input fluxes prevents high carbon sequestration efficiency. This first insight with remote sensing data and the model allows the validation of some of the key mechanisms of natural iron fertilization and exposes problems that will need to be solved to have a complete biogeochemical diagnostic of this natural iron fertilization.

Evidence of Relentless Reconnections at Boundaries of Supergranular Network Lanes in Quiet Sun and Coronal Hole

Doppler-shift properties of the solar transition region (TR) and low corona are investigated in relation to the underlying chromospheric supergranular network, with particular regard to the role of the magnetic field. EUV line properties were obtained from a large raster scan of the solar chromosphere, transition region, and corona acquired by the SUMER spectrometer on board SOHO. The observed region includes an equatorial coronal hole, as well as surrounding quiet-Sun areas. The chromospheric supergranular network pattern is enhanced using a filter defined previously by Aiouaz and coworkers applied to a Lyman continuum image. The filtered continuum image and Dopplergrams are used to produce dispersion plots. We find correlations between the chromospheric network, and the N IV (765.15 Å), O IV (790.19 Å), S V (786.50 Å), O V (760.45 Å) Doppler shifts in quiet Sun and coronal hole. It is established that the maximum inflow (redshift) at transition region temperatures appears statistically toward the center of the network lanes in the quiet-Sun areas and toward the boundary of the network lanes in the coronal hole. Furthermore, while the strong redshifts in the TR lines complement spatially blueshifts from the low corona (Ne VIII 770.41 Å) in a puzzle-like pattern, bidirectional flows (i.e., cospatial strong red- and blueshifts in the TR/Corona) appear predominantly in the coronal hole. The bidirectional flows congregate almost systematically at boundaries of magnetic field concentrations seen in SOHO MDI magnetograms. These results support a coherent interpretation of almost 30 years of unexplained statistical Doppler-shift variations in the transition region and corona for quiet Sun and coronal hole. The proposed scenario involves reconnections between the strong network magnetic field and continuously advected weak field from the supergranular cell interior.

Reorientation of scroll rings in an advective field

When scroll rings in the excitable Belousov-Zhabotinsky reaction are subjected to an applied electrical current, a reorientation of the scroll ring is induced which is accompanied by a linear drift towards the cathode. The findings can be explained using a modified theory of local filament dynamics under parameter gradients. Numerical simulations using the Oregonator model with an additional advective term accounting for the applied electric field reproduce the experimental results and provide insights into the deformation of the structure of the filament during the reorientation.

On the theory of advective effects on biological dynamics in the sea. III. The role of turbulence in biological–physical interactions

A nonlinear model for biological and physical dynamical interactions in a laminar upwelling flow field in parts I and II of this study is extended to turbulent flow. In the previous studies, a prescription for obtaining quadrature solutions to the fundamental biodynamical equations was developed. In this study, we use a probability density function approach on these solutions to obtain statistics of the biodynamical state variables and their self-interaction for the case of turbulent advection. To illustrate the theory, a simple nutrient ( N ), phytoplankton ( P ) problem is considered, that of upwelling into a surface turbulent layer. Biological interaction is modelled as bilinear, representing the uptake of N by P in a uniform light euphotic zone. A random walk model is used to obtain the appropriate probability density function for the advective turbulent field. The mean quantities, , , as well as the biological interaction term are calculated. The term has two contributions, , and the turbulence-induced interaction term, . It is shown that the often neglected turbulence-induced coupling term is of the order and opposite in sign. This results in, over a wide range of Peclet numbers, the mean interaction term being significantly smaller than either of its constituent terms, and .

A new model of volatile bubble growth in a magmatic system: Isobaric case

The nucleation, growth, and, ultimately, coalescence of volatile bubbles in a silicate melt (magma chamber) play a crucial role in the processes leading to volcanic eruptions. A new diffusion‐limited nonlinear growth and nucleation model of volatile bubbles in such a system is proposed here. In contrast to previously existing models, the present one treats the competitive effects of the other randomly located bubbles on the growth dynamics in presence of a hydrodynamic coupling with the melt advection field through its viscous resistance. I consider here cases where the fluid pressure is kept constant. Numerical results pertaining to a basaltic and a rhyolitic melt suggest that for small volatile supersaturations and for small times, bubble growth occurs essentially as in the single‐bubble problem. However, for longer times, the influence of the other bubbles is important. I find that bubble growth rate decreases exponentially with time and propose an approximate expression for the decay rate. Finally, for larger volatile supersaturations, the bubble growth is subjected to transitions to and from an inflationary regime, whereby the bubble radius increases very rapidly during a small time interval.

Transport and Mixing in Kinematic and Dynamically Consistent Flows

Abstract The interplay between dynamics and transport in two-dimensional flows is examined by comparing the transport and mixing in a kinematic flow in which the velocity field is imposed as a given function of time with that in an analogous dynamically consistent flow in which the advected vorticity field controls the flow evolution. In both cases the variation of the transport and mixing behavior with a parameter ε governing the strength of the time dependence is considered. It is shown that dynamical consistency has the effect of (i) postponing the breaking of a central transport barrier as ε increases and (ii) removing the property of the kinematic flow that, for a large range of ε, a weakly permeable central barrier persists. The first effect is associated with the development of a strong vorticity gradient and the associated jet along the central transport barrier. The second effect is associated with the fact that, in the dynamically consistent flow, the breaking of the central barrier is accompanied by a drastic change in the vorticity field and hence in the structure of the flow. The relation between the vorticity field and transport barriers is further examined using a range of simple kinematic and dynamically consistent models. Implications for formulation of predictive models that represent the interactions between dynamics, transport, and mixing (and might be suggested as a basis for parameterizing eddies in flows that form multiple jets) are discussed.

Diurnally varying structure of stationary waves encircling the summer southern pole of Mars observed by MGS TES

The diurnal variation in the vertical structure of the wavenumber‐1 stationary planetary wave observed in the summer southern polar region of Mars was investigated by using temperature data on the dayside and nightside taken by Thermal Emission Spectrometer onboard Mars Global Surveyor. It was found that the westward phase tilt with height during this period tends to be obvious on the dayside, while it is much less on the nightside. A possible explanation for the diurnally‐varying wave structure is the advection of wave fields by the tidal wind: the wave fields away from the ground surface are carried westward by the tidal wind during the local time from midnight to noon, and the process is reversed from noon to midnight. The slow vertical propagation of the wave with a time constant much longer than a sol will allow the tidal wind to influence the wave structure.

Monte Carlo evaluation of FADE approach to anomalous kinetics

In a wide range of transport phenomena in complex systems, the mean squared displacement of a particles plume has been often found to follow a non-linear relationship of the kind 〈 x 2( t) ∝ t α 〉, where α may be greater or smaller than 1: these evidences have been described under the generic term of anomalous diffusion. In this paper we focus on subdiffusion, i.e. the case 0 < α < 1, in presence of an external advective field. Widely adopted models to describe anomalous kinetics are continuous time random walk (CTRW) and its fractional advection–dispersion equation (FADE) asymptotic approximation, which accurately account for experimental results, e.g. in the transport of contaminant particles in porous or fractured media. FADE approximated equations, in particular, admit elegant analytical closed-form solutions for the particle concentration P( x, t). To evaluate the relevance of the approximations which allow to derive the asymptotic FADE equations, we resort to Monte Carlo simulation (which may be regarded as an exact solution of the CTRW model): this comparison shows that the FADE equations represent a less and less accurate asymptotic description of the exact CTRW model as α becomes close to 1. We propose higher-order corrections which lead to modified integral–differential equations and derive new expressions for the moments of P( x, t). These results are validated through comparison with those of Monte Carlo simulation, assumed as reference curves.

Modeling breakup and relaxation of Newtonian droplets using the advected phase-field approach

The relaxation and breakup of Newtonian droplets is considered using the advected field approach. This method allows one to follow the deformation of interfaces using an order parameter field [Biben, Europhys. Lett. 63, 623 (2003)] based on a Ginzburg-Landau equation. Using this method, it is possible to follow the breakup of droplets and stability curves can be obtained in both two- and three-dimensional shear and elongational flows. Finally, relaxation of a droplet is considered, following the application of an elongational flow. The results are compared with previous experimental data [Ha and Leal, Phys. Fluids 13, 1568 (2001)], and are found to be in satisfactory agreement. The method is general enough to be applied to other non-Newtonian fluids, such as Oldroyd-B fluids or viscoplastic materials.

Finite element evaluation of diffusion and dispersion tensors in periodic porous media with advection

This paper presents three-dimensional finite element simulations to evaluate diffusion and dispersion tensors in periodic porous media in the presence of an advective velocity field. These tensors are evaluated in the framework of the double-scale expansion technique. Two problems, a Newtonian flow and a vector-valued advection–diffusion equation, have to be sequentially solved at the pore scale. Finite element techniques to approximate these problems are proposed and analyzed. Numerical results in three-dimensional networks of spheres are presented to quantitatively assess the impact of the pore morphology and of the advection velocity on the diffusion and dispersion tensors.

Current distribution in systems with anomalous diffusion: renormalization group approach

We investigate the asymptotic properties of the large deviation function of the integrated particle current in systems, in or out of thermal equilibrium, whose dynamics exhibits anomalous diffusion. The physical systems covered by our study include mutually repelling particles with a drift, a driven lattice gas displaying a continuous nonequilibrium phase transition and particles diffusing in an anisotropic random advective field. It is exemplified how renormalization group techniques allow for a systematic determination of power laws in the corresponding current large deviation functions. We show that the latter are governed by known universal scaling exponents, specifically the anomalous dimension of the noise correlators.

Monte Carlo investigation of anomalous transport in presence of a discontinuity and of an advection field

Anomalous diffusion has recently turned out to be almost ubiquitous in transport problems. When the physical properties of the medium where the transport process takes place are stationary and constant at each spatial location, anomalous transport has been successfully analysed within the Continuous Time Random Walk (CTRW) model. In this paper, within a Monte Carlo approach to CTRW, we focus on the particle transport through two regions characterized by different physical properties, in presence of an external driving action constituted by an additional advective field, modelled within both the Galilei invariant and Galilei variant schemes. Particular attention is paid to the interplay between the distributions of space and time across the discontinuity. The resident concentration and the flux of the particles are finally evaluated and it is shown that at the interface between the two regions the flux is continuous as required by mass conservation, while the concentration may reveal a neat discontinuity. This result could open the route to the Monte Carlo investigation of the effectiveness of a physical discontinuity acting as a filter on particle concentration.