Time-averaged Field Research Articles

Field synergy equation for turbulent heat transfer and its application

A field synergy equation with a set of specified constraints for turbulent heat transfer developed based on the extremum entransy dissipation principle can be used to increase the field synergy between the time-averaged velocity and time-averaged temperature gradient fields over the entire fluid flow domain to optimize the heat transfer in turbulent flow. The solution of the field synergy equation gives the optimal flow field having the best field synergy for a given decrement of the mean kinetic energy, which maximizes the heat transfer. As an example, the field synergy analysis for turbulent heat transfer between parallel plates is presented. The analysis shows that a velocity field with small eddies near the boundary effectively enhances the heat transfer in turbulent flow especially when the eddy height which are perpendicular to the primary flow direction, are about half of the turbulent flow transition layer thickness. With the guide of this optimal velocity field, appropriate internal fins can be attached to the parallel plates to produce a velocity field close to the optimal one, so as to increase the field synergy and optimize the turbulent heat transfer.

Occupational exposure to static and time‐varying gradient magnetic fields in MR units

To assess exposure of MR staff to static and time-varying gradient magnetic fields by direct measurement and questionnaire and to compare these to the action values and exposure limits stated in published guidance. Instantaneous and time-averaged exposure to static magnetic fields were measured on clinical and research MR scanners. A questionnaire was sent to 100 clinical MR centers to estimate the average static field exposure. Instantaneous measurements of the time-varying magnetic field were conducted on a 1.5 T conventional and a 0.6 T open-bore MR system. The 24-hour time-averaged static field exposure was measured to be 1.8 +/- 1 mT and the questionnaire produced a 24-hour time-average of 2.3 mT. The maximum static field strength recorded during patient set up was 554 mT. Time-varying gradient field exposure was found to exceed the action values up to 30 cm from the bore entrance or magnet rim. The time-varying gradient field exposure limit is the only limit to be exceeded. The time-averaged static field exposure to staff was found to be 100 times lower than the recommended guidelines.

Paleomagnetism of the Eastern Alkaline Province (Mexico): contribution to the time-averaged field global database and geomagnetic instability time scale

AbstractWe report a detailed paleomagnetic and rock-magnetic study of 19 independent lava flows belonging to the Eastern Alkaline Province (EAP) in Mexico. In total, 162 oriented samples were collected in four areas (Sierra de Tantima-Alamo, Tlanchinol, Chiconquiaco-Palma Sola and Poza Rica). All sites analyzed in this study were previously dated by means of theunspikedK-Ar geochronological method (Ferrariet al., J. Volcanol. Geotherm. Res.,146, 284–306, 2005) and span from 14.6 to 1.5 Ma. Rock-magnetic experiments point to simple magnetic mineralogy. In most cases, the remanence is carried by Ti-poor titanomagnetite of pseudosingle-domain grain size. In a few cases, Ti-rich titanomagnetites are responsible for the magnetization. The characteristic paleodirections are successfully isolated for all of the studied units. The mean paleodirection, discarding two intermediate polarity sites, isD=359.5°,I=32.9°,n=17,k=30, α95=6.7°. This direction is practically undistinguishable from the expected Mio-Pliocene paleodirections, as derived from reference poles for the North American polar wander curve, and is in agreement with the previously reported directions from the western Trans-Mexican Volcanic Belt. This suggests that no major tectonic rotation occurred in studied area since the middle Miocene to Present. The paleosecular variation is estimated through the study of the scatter of virtual geomagnetic poles, givingSF=12.7 withSU=16.5 andSL=10.3 (upper and lower limits, respectively). These values are consistent with those predicted by the latitude-dependent variation model of McFaddenet al.(Geophys. Res.,93, 11583–11588, 1991) for the last 5 Myr. Eleven sites yielded reverse magnetic polarity, six are normally magnetized and two lava flows provided apparently intermediate paleodirections. An interesting feature of the paleomagnetic record obtained from EAP volcanics is that two independent lava flows, dated as 2.04±0.04 and 1.97±0.04 Ma, respectively, both yield normal paleodirections during the reverse Matuyama period. These sites were apparently formed during the Réunion geomagnetic event worldwide observed.

Improved Late Cretaceous and early Cenozoic Paleomagnetic apparent polar wander path for the Pacific plate

Understanding of Pacific plate tectonics and geodynamics is aided by refinement of the plate's apparent polar wander path (APWP). We improved the Late Cretaceous and early Cenozoic APWP by analyzing a large, diverse paleomagnetic data set that combines core sample, seamount magnetic anomaly model, and marine magnetic anomaly skewness data. Our preferred APWP has five mean paleomagnetic poles representing the Oligocene (30 Ma), Late (39 Ma) and Early (49 Ma) Eocene, and Paleocene (61 Ma) epochs and the Maastrichtian (68 Ma) stage. Along with a published 80 Ma pole, the APWP shows a stillstand from ∼ 80 to ∼ 49 Ma punctuating the large overall northward drift of the plate. The two youngest poles imply resumption of northward motion during mid-Eocene time with another change of polar motion after ∼ 30 Ma. If unaffected by other phenomena (e.g., true polar wander or change in time-averaged magnetic field geometry), the stillstand implies negligible northward plate motion during the period of Emperor Seamounts formation, contrary to most accepted plate motion models. The stillstand is consistent with paleomagnetic data from the Emperor Seamounts, which imply southward motion of the Hawaiian melting anomaly. It also implies significant westward drift of the hotspot if the Pacific plate was moving west at rates similar to the later Cenozoic. In addition, changes in polar wander after ∼ 49 Ma are consistent with changes of north Pacific plate boundaries.

Interpretation of Coastal HF Radar–Derived Surface Currents with High-Resolution Drifter Data

Abstract Dense arrays of surface drifters are used to quantify the flow field on time and space scales over which high-frequency (HF) radar observations are measured. Up to 13 drifters were repetitively deployed off the Santa Barbara and San Diego coasts on 7 days during 18 months. Each day a regularly spaced grid overlaid on a 1-km2 (San Diego) or 4-km2 (Santa Barbara) square, located where HF radar radial data are nearly orthogonal, was seeded with drifters. As drifters moved from the square, they were retrieved and replaced to maintain a spatially uniform distribution of observations within the sampling area during the day. This sampling scheme resulted in up to 56 velocity observations distributed over the time (1 h) and space (1 and 4 km2) scales implicit in typical surface current maps from HF radar. Root-mean-square (RMS) differences between HF radar radial velocities obtained using measured antenna patterns, and average drifter velocities, are mostly 3–5 cm s−1. Smaller RMS differences compared with past validation studies that employ current meters are due to drifter resolution of subgrid-scale velocity variance included in time and space average HF radar fields. Roughly 5 cm s−1 can be attributed to sampling on disparate time and space scales. Despite generally good agreement, differences can change dramatically with time. In one instance, the difference increases from near zero to more than 20 cm s−1 within 2 h. The RMS difference and bias (mean absolute difference) for that day exceed 7 and 12 cm s−1, respectively.

Millisecond mixing of two liquid streams in a mixer model

Fast liquid mixing in the flow channels at millimeter size was studied by planar laser induced fluorescence (PLIF) technique in experiments and the large eddy simulation (LES) as well. A simplified mixer model was applied, where two liquid streams impinge into each other in the confined channels. A dynamic kinetic energy sub-grid scale (SGS) model of LES was employed to simulate the fast liquid mixing. The results show that LES predictions with high-density meshes have good agreement with the experimental data in terms of the instantaneous and time-averaged concentration fields, and the probability density function (PDF) of concentration fluctuations. Hence, the mixing quality characterized by the intensity of segregation (IOS) and 95% mixing time can be also predicted reasonably. The LES simulations further predict the significant effect of cross-flow angle on the mixing process. The cross-flow angle of 90 ∘ gives the fastest mixing of two liquids in the millimeter channels at 1–2 ms. The mixing layer between the two liquid streams cannot be observed under the geometry with larger cross-flow angles. This indicates different mixing mechanisms compared with the mixing of two liquids flowing in parallel. Vorticity in the turbulent mixing process is discussed for a better understanding on the physical factors controlling the mixing process.

Measurement of electric field and gradient in the plasma sheath using clusters of floating microspheres

A method for measuring the time-averaged vertical electric field and its gradient in the plasma sheath using clusters with n = 2 or 3 floating microspheres of known mass is described. The particle charge q is found by determining the ratio of the breathing frequency to the center-of-mass frequency for horizontal (in-plane) oscillations. The electric field at the position of the particles is then calculated using the measured charge-to-mass ratio, and the electric-field gradient is determined from the vertical resonance frequency. The Debye length is also found. Experimental results are in agreement with a simple sheath model.

Low-latitude paleosecular variation and the time-averaged field during the late Pliocene and Quaternary—Paleomagnetic study of the Michoacan-Guanajuato volcanic field, Central Mexico

AbstractWe report paleomagnetic, rock magnetic, and paleointensity studies for 24 volcanic lava flows from the Michoacan-Guanajuato volcanic field (MGVF), erupted between 2.27 Ma to present according to available radiometric ages and historic records. The MGVF located in the central-western sector of the Plio-Quaternary Trans-Mexican volcanic belt is mainly composed by cinder cones and shield volcanoes. Rock magnetic experiments show remanence is carried in most cases by Ti-poor titanomagnetites, resulting from oxy-exsolution of original titanomagnetites during flow cooling. Unblocking temperature spectra and high coercivities point to “small” pseudo-single domain grains for the titanomagnetites. Single component, linear vector plots are obtained after alternating field and thermal demagnetization. Seven flows yield reverse polarity magnetization while sixteen flows are normally magnetized. The overall mean paleodirection obtained (with 14 flows normal and 6 flows reverse) is I=28.4°, D=357.9°, k=21, α95=7.3°, with a paleomagnetic pole position ofPlat=85.7°,Plong= 104.5°, K=27, A95=6.4°. The paleodirection is undistinguishable from expected Plio-Quaternary paleodirections derived from reference poles for the North American polar wander curve, and previously reported paleodirections for central Mexico. Paleointensity experiments give high quality results for only twelve samples from two flows with mean values of 7.3 and 8.1 × 1022Am2, which are close to present geomagnetic field intensity. The combination of new MGVF directional results with currently available paleomagnetic data from central Mexico yield angular dispersion estimates ofSF= 15.4 withSU= 19.6 andSL= 12.7, which are in agreement with the latitude-dependent PSV model of McFaddenet al.(1988, 1991) for the last 5 Ma, and show no significant inclination anomaly.

Simulation of Global Land Surface Conditions from 1948 to 2004. Part I: Forcing Data and Evaluations

Abstract Because of a lack of observations, historical simulations of land surface conditions using land surface models are needed for studying variability and changes in the continental water cycle and for providing initial conditions for seasonal climate predictions. Atmospheric forcing datasets are also needed for land surface model development. The quality of atmospheric forcing data greatly affects the ability of land surface models to realistically simulate land surface conditions. Here a carefully constructed global forcing dataset for 1948–2004 with 3-hourly and T62 (∼1.875°) resolution is described, and historical simulations using the latest version of the Community Land Model version 3.0 (CLM3) are evaluated using available observations of streamflow, continental freshwater discharge, surface runoff, and soil moisture. The forcing dataset was derived by combining observation-based analyses of monthly precipitation and surface air temperature with intramonthly variations from the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis, which is shown to have spurious trends and biases in surface temperature and precipitation. Surface downward solar radiation from the reanalysis was first adjusted for variations and trends using monthly station records of cloud cover anomaly and then for mean biases using satellite observations during recent decades. Surface specific humidity from the reanalysis was adjusted using the adjusted surface air temperature and reanalysis relative humidity. Surface wind speed and air pressure were interpolated directly from the 6-hourly reanalysis data. Sensitivity experiments show that the precipitation adjustment (to the reanalysis data) leads to the largest improvement, while the temperature and radiation adjustments have only small effects. When forced by this dataset, the CLM3 reproduces many aspects of the long-term mean, annual cycle, interannual and decadal variations, and trends of streamflow for many large rivers (e.g., the Orinoco, Changjiang, Mississippi, etc.), although substantial biases exist. The simulated long-term-mean freshwater discharge into the global and individual oceans is comparable to 921 river-based observational estimates. Observed soil moisture variations over Illinois and parts of Eurasia are generally simulated well, with the dominant influence coming from precipitation. The results suggest that the CLM3 simulations are useful for climate change analysis. It is also shown that unrealistically low intensity and high frequency of precipitation, as in most model-simulated precipitation or observed time-averaged fields, result in too much evaporation and too little runoff, which leads to lower than observed river flows. This problem can be reduced by adjusting the precipitation rates using observed-precipitation frequency maps.

Ideal gas flows with separation zones and time-dependent contact discontinuities of complicated shape

Some examples of flows with separation zones andmovable contact discontinuities obtained as a result of the numerical integration of the time-dependent equations for an ideal gas are presented. The examples concern a steady annular separation zone on the blunt nose of a body in a supersonic flow, periodic shedding of unsteady discontinuities from a cylinder in a steady uniform subsonic flow with a supercritical Mach number, and the complicated deformation of a contact (tangential) discontinuity, namely, the boundaries of a two-dimensional jet, either subsonic or supersonic, flowing into a cocurrent subsonic low-velocity flow. A multiple increase in the difference grid capacity in the numerical integration of the Euler equations indicates the absence of a noticeable scheme viscosity effect in the examples calculated. The inviscid nature of the separation flows obtained is also confirmed by their well-known counterparts constructed in the ideal incompressible fluid approximation. The time-average velocity fields of the two-dimensional jet and the intensity of its sound field are in reasonable agreement with the available data.

Computation of the time-averaged temperature fields and energy fluxes in a thermally isolated thermoacoustic stack at low acoustic Mach numbers

A simplified calculus model to investigate on the transverse heat transport near the edges of a thermally isolated thermoacoustic stack in the low acoustic Mach number regime is presented. The proposed methodology relies on the well-known results of the classical linear thermoacoustic theory which are implemented into an energy balance calculus-scheme through a finite difference technique. Details of the time-averaged temperature and heat flux density distributions along a pore cross-section of the stack are given. It is shown that a net heat exchange between the fluid and the solid walls takes place only near the edges of the stack plates, at distances from the ends not exceeding the peak-to-peak particle displacement amplitude. The structure of the mean temperature field within a stack plate is also investigated; this last results not uniform near its terminations giving rise to a smaller temperature difference between the plate extremities than that predicted by the standard linear theory. This result, when compared with experimental measurements available in literature, suggests that thermal effects localized at the stack edges may play an important role as sources of the deviations found between linear theory predictions and experiments at low and moderate Mach numbers.

Paleosecular variation and the average geomagnetic field at ±20° latitude

We assembled a new paleomagnetic directional data set from lava flows and thin dikes for four regions centered on ±20° latitude: Hawaii, Mexico, the South Pacific, and Reunion. We investigate geomagnetic field behavior over the past 5 Myr and address whether geographical differences are recorded by our data set. We include inclination data from other globally distributed sites with the ±20° data to determine the best fitting time‐averaged field (TAF) for a two‐parameter longitudinally symmetric (zonal) model. Values for our model parameters, the axial quadrupole and octupole terms, are 4% and 6% of the axial dipole, respectively. Our estimate of the quadrupole term is compatible with most previous studies of deviations from a geocentric axial dipole (GAD) field. Our estimated octupole term is larger than that from normal polarity continental and igneous rocks, and oceanic sediments, but consistent with that from reversed polarity continental and igneous rocks. The variance reduction compared with a GAD field is ∼12%, and the remaining signal is attributed to paleosecular variation (PSV). We examine PSV at ±20° using virtual geomagnetic pole (VGP) dispersion and comparisons of directional distributions with simulations from two statistical models. Regionally, the Hawaii and Reunion data sets lack transitional magnetic directions and have similar inclination anomalies and VGP dispersion. In the Pacific hemisphere, Hawaii has a large inclination anomaly, and the South Pacific exhibits high PSV. The deviation of the TAF from a GAD contradicts earlier ideas of a “Pacific dipole window,” and the strong regional PSV in the South Pacific contrasts with the generally low secular variation found on short timescales. The TAF and PSV at Hawaii and Reunion are distinct from values for the South Pacific and Mexico, demonstrating the need for time‐averaged and paleosecular variation models that can describe nonzonal field structures. Investigations of zonal statistical PSV models reveal that recent models are incompatible with the empirical ±20° directional distributions and cannot fit the data by simply adjusting relative variance contributions to the PSV. The ±20° latitude data set also suggests less PSV and smaller persistent deviations from a geocentric axial dipole field during the Brunhes.

The Meridional Flow of Source-Driven Abyssal Currents in a Stratified Basin with Topography. Part II: Numerical Simulation

Abstract A numerical simulation is described for source-driven abyssal currents in a 3660 km × 3660 km stratified Northern Hemisphere basin with zonally varying topography. The model is the two-layer quasigeostrophic equations, describing the overlying ocean, coupled to the finite-amplitude planetary geostrophic equations, describing the abyssal layer, on a midlatitude β plane. The source region is a fixed 75 km × 150 km area located in the northwestern sector of the basin with a steady downward volume transport of about 5.6 Sv (Sv ≡ 106 m3 s−1) corresponding to an average downwelling velocity of about 0.05 cm s−1. The other parameter values are characteristic of the North Atlantic Ocean. It takes about 3.2 yr for the abyssal water mass to reach the southern boundary and about 25 yr for a statistical state to develop. Time-averaged and instantaneous fields at a late time are described. The time-averaged fields show an equatorward-flowing abyssal current with distinct up- and downslope groundings with decreasing height in the equatorward direction. The average equatorward abyssal transport is about 8 Sv, and the average abyssal current thickness is about 500 m and is about 400 km wide. The circulation in the upper layers is mostly cyclonic and is western intensified, with current speeds about 0.6 cm s−1. The upper layer cyclonic circulation intensifies in the source region with speeds about 4 cm s−1, and there is an anticyclonic circulation region immediately adjacent to the western boundary giving rise to a weak barotropic poleward current in the upper layers with a speed of about 0.6 cm s−1. The instantaneous fields are highly variable. Even though the source is steady, there is a pronounced spectral peak at the period of about 54 days. The frequency associated with the spectral peak is an increasing function of the downwelling volume flux. The periodicity is associated with the formation of transient cyclonic eddies in the overlying ocean in the source region and downslope propagating plumes and boluses in the abyssal water mass. The cyclonic eddies have a radii about 100–150 km and propagation speeds about 5–10 cm s−1. The eddies are formed initially because of stretching associated with the downwelling in the source region. Once detached from the source region, the cyclonic eddies are phase locked with the boluses or plumes that form on the downslope grounding of the abyssal current, which themselves form because of baroclinic instability. Eventually, the background vorticity gradients associated with β and the sloping bottom arrest the downslope (eastward) motion, the abyssal boluses diminish in amplitude, the abyssal current flows preferentially equatorward, the upper layer eddies disperse and diminish in amplitude, and westward intensification develops.

Coherent Structures in a Jet Indicating Edgetone Oscillation (2nd Report, Eduction of Coherent Structures by Using Low Pressure Region and Velocity Gradient Tensor)

Coherent vortical structures in a high-Reynolds number turbulent jet indicating edgetone oscillations were extracted from velocity and pressure data. Three quantities were chosen as candidate indicators of the coherent structures : (i) phase-averaged vorticity, (ii) phase-averaged pressure, and (iii) the phase-averaged velocity gradient tensor. All these quantities worked well in extracting coherent structures in a test case of a low-Reynolds number wake of a cylinder. However, when applied to the high-Reynolds number edgetone flow, (ii) and (iii) indicated much better performance than (i), since (i) was affected by the background time-averaged vorticity field. The advection of the coherent structures was well captured by using (ii) and (iii).

Relationships between Tracer Ages and Potential Vorticity in Unsteady Wind-Driven Circulations

AbstractThe relationships between different tracer ages and between tracer age and potential vorticity are examined by simulating barotropic double-gyre circulations. The unsteady model flow crudely represents aspects of the midlatitude, middepth ocean circulation including inhomogeneous and anisotropic variability. Temporal variations range in scale from weeks to years, although the statistics are stationary. These variations have a large impact on the time-averaged tracer age fields. Transport properties of the tracer age fields that have been proved for steady flow are shown to also apply to unsteady flow and are illustrated in this circulation. Variability of tracer ages from ideal age tracer, linear, and exponential transient tracers is highly coordinated in phase and amplitude and is explained using simple theory. These relationships between different tracer ages are of practical benefit to the problem of interpreting tracer ages from the real ocean or from general circulation models. There is also a close link between temporal anomalies of tracer age and potential vorticity throughout a significant fraction of the domain. There are highly significant anticorrelations between ideal age and potential vorticity in the subtropical gyre and midbasin jet region, but correlation in the central subpolar gyre and eastern part of the domain is not significant. The existence of the relationship is insensitive to the character of the flow, the tracer sources, and the potential vorticity dynamics. Its structure may be understood by considering the different time-mean states of the tracer age and potential vorticity, the different tracer sources and sinks, and the effect of variability in the flow. Prediction of the correlation without knowledge of the time-mean fields is a harder problem, however. Detecting the correlation between potential vorticity and tracer age in the real ocean will be difficult with typical synoptic oceanographic transect data that are well-sampled in space, but sparse in time. Nevertheless, it is reasonable to suppose the correlation exists in some places.

Bench-Scale Investigation of Inclined Dense Jets

In this work experimental data on the geometry of dense inclined jets issuing in a lab-scale glass rectangular tank are presented. The surrounding fluid was always tap water at room temperature while the dense jets were water solutions of NaCl. Four parameters were changed in the experiments, namely nozzle diameter and inclination, and jet density and flow rate. Jet trajectories were revealed by a colored tracer. Images of the jet were recorded by a digital camera and then further digitally processed, eventually resulting in a time-averaged tracer intensity field. All the jet geometrical parameters, once normalized, were found to be very well correlated to the densimetric Froude number. Moderate jet viscosity variations were found to not significantly affect jet behavior. The reported data allow a quick and easy estimation of maximum rise level, position of the trajectory maximum, and impact point distance of dense jets issued at different angles above the horizontal.

Paleomagnetism and 40Ar / 39Ar Geochronology of Yemeni Oligocene volcanics: Implications for timing and duration of Afro-Arabian traps and geometry of the Oligocene paleomagnetic field

A combined paleomagnetic and 40Ar / 39Ar study was carried out along eight stratigraphically overlapping sections in the Oligocene Afro-Arabian flood volcanic province in Yemen (73 sites). The composite section covers the entire volcanic stratigraphy in the sampling region and represents five polarity zones that are correlated to the geomagnetic polarity time scale based on 40Ar / 39Ar ages from this and previous studies. The resulting magnetostratigraphy is similar to that of the conjugate margin in Ethiopia. The earliest basaltic volcanism took place in a reverse polarity chron that appears to correspond to C11r, while the massive rhyolitic ignimbrite eruptions correlated to ash layers in Oligocene Indian Ocean sediment 2700 km away from the Afro-Arabian traps, appear to have taken place during magnetochron C11n. The youngest ignimbrite was emplaced during magnetochron C9n. Both 40Ar / 39Ar and paleomagnetic data suggest rapid < 1 Ma eruption of the basal basalt units and punctuated eruption of the upper silicic units over a duration potentially as long as 3 Ma with interspersed eruptive hiatuses. Eruption of the basal basalts may have preceded the Oi2 cooling event. The paleomagnetic pole λ = 74.2°N, φ = 249.1°E (A95 = 3.6°; N = 48) is supported by a positive reversal test. Paleosecular variation, estimated as the angular standard deviation of the VGP distribution 14.2° + 2.3° / − 1.7°, is close to expected, suggesting that the paleomagnetic pole represents a time-averaged field. The pole is in excellent accord with the paleomagnetic poles obtained from the Ethiopian part of the Afro-Arabian province, after closure of the Red Sea. By analyzing Afro-Arabian paleomagnetic data in conjunction with contemporaneous paleomagnetic poles available from different latitudes we argue that the Oligocene paleomagnetic field was dominated by the axial dipole with insignificant non-dipole field contributions.

Geomagnetic dipole strength and reversal rate over the past two million years

Independent records of relative magnetic palaeointensity from sediment cores in different areas of the world can be stacked together to extract the evolution of the geomagnetic dipole moment and thus provide information regarding the processes governing the geodynamo. So far, this procedure has been limited to the past 800,000 years (800 kyr; ref. 3), which does not include any geomagnetic reversals. Here we present a composite curve that shows the evolution of the dipole moment during the past two million years. This reconstruction is in good agreement with the absolute dipole moments derived from volcanic lavas, which were used for calibration. We show that, at least during this period, the time-averaged field was higher during periods without reversals but the amplitude of the short-term oscillations remained the same. As a consequence, few intervals of very low intensity, and thus fewer instabilities, are expected during periods with a strong average dipole moment, whereas more excursions and reversals are expected during periods of weak field intensity. We also observe that the axial dipole begins to decay 60-80 kyr before reversals, but rebuilds itself in the opposite direction in only a few thousand years.

Statistical palaeomagnetic field modelling and dynamo numerical simulation

By relying on two numerical dynamo simulations for which such investigations are possible, we test the validity and sensitivity of a statistical palaeomagnetic field modelling approach known as the giant gaussian process (GGP) modelling approach. This approach is currently used to analyse palaeomagnetic data at times of stable polarity and infer some information about the way the main magnetic field (MF) of the Earth has been behaving in the past and has possibly been influenced by core–mantle boundary (CMB) conditions. One simulation has been run with homogeneous CMB conditions, the other with more realistic non-homogeneous symmetry breaking CMB conditions. In both simulations, it is found that, as required by the GGP approach, the field behaves as a short-term memory process. Some severe non-stationarity is however found in the non-homogeneous case, leading to very significant departures of the Gauss coefficients from a Gaussian distribution, in contradiction with the assumptions underlying the GGP approach. A similar but less severe non-stationarity is found in the case of the homogeneous simulation, which happens to display a more Earth-like temporal behaviour than the non-homogeneous case. This suggests that a GGP modelling approach could nevertheless be applied to try and estimate the mean µ and covariance matrix γ(τ) (first-and second-order statistical moments) of the field produced by the geodynamo. A detailed study of both simulations is carried out to assess the possibility of detecting statistical symmetry breaking properties of the underlying dynamo process by inspection of estimates of µ and γ(τ). As expected (because of the role of the rotation of the Earth in the dynamo process), those estimates reveal spherical symmetry breaking properties. Equatorial symmetry breaking properties are also detected in both simulations, showing that such symmetry breaking properties can occur spontaneously under homogeneous CMB conditions. By contrast axial symmetry breaking is detected only in the non-homogenous simulation, testifying for the constraints imposed by the CMB conditions. The signature of this axial symmetry breaking is however found to be much weaker than the signature of equatorial symmetry breaking. We note that this could be the reason why only equatorial symmetry breaking properties (in the form of the well-known axial quadrupole term in the time-averaged field) have unambiguously been found so far by analysing the real data. However, this could also be because those analyses have all assumed to simple a form for γ(τ) when attempting to estimate µ. Suggestions are provided to make sure future attempts of GGP modelling with real data are being carried out in a more consistent and perhaps more efficient way.

Space–time scaling behavior of rain statistics in a stochastic fractional diffusion model

Statistical properties of rain exhibit the interesting feature that they depend in a nontrivial way on the length and time scales over which rain rate is averaged. A quantitative understanding of this dependence can be utilized to relate statistics at different scales and is important for inter-comparison of rainfall data obtained from measuring devices with differing space–time resolutions. A stochastic dynamical model of rainfall based on a fractional diffusion type kinetic equation introduced earlier by the authors describes fairly well how the second moment statistics of area-averaged rain rate depend on the averaging length L and predicts a power law scaling behavior as L→0. The model pictures the correlation of the precipitation field as arising from two-dimensional Lévy flights. The present paper extends the investigation to the full space–time covariance function of the precipitation field. In particular, a scaling regime is identified in which the various second moment statistics of area- and/or time-averaged rain field exhibit invariance under a combined rescaling of the space and time variables—a property known as dynamic scaling, the scaling exponent being identified with the Lévy index. Although the space and time scales resolved in the radar data used to establish the model turn out to be too coarse for the dynamic scaling behavior to be experimentally demonstrated, we predict that it should be observable in high frequency rain gauge data from dense gauge networks.