Spatial Intermittency Research Articles

Heater‐induced ionization inferred from spectrometric airglow measurements

AbstractSpectrographic airglow measurements were made during an ionospheric modification experiment at High Frequency Active Auroral Research Program on 12 March 2013. Artificial airglow enhancements at 427.8, 557.7, 630.0, 777.4, and 844.6 nm were observed. On the basis of these emissions and using a methodology based on the method of Backus and Gilbert (1968, 1970), we estimate the suprathermal electron population and the subsequent equilibrium electron density profile, including contributions from electron impact ionization. We find that the airglow is consistent with heater‐induced ionization in view of the spatial intermittency of the airglow.

A Unified Approach to Regularity Problems for the 3D Navier-Stokes and Euler Equations: the Use of Kolmogorov’s Dissipation Range

Motivated by Kolmogorov’s theory of turbulence we present a unified approach to the regularity problems for the 3D Navier-Stokes and Euler equations. We introduce a dissipation wavenumber $${\Lambda(t)}$$ that separates low modes where the Euler dynamics is predominant from the high modes where the viscous forces take over. Then using an indifferent to the viscosity technique we obtain a new regularity criterion which is weaker than every Ladyzhenskaya-Prodi-Serrin condition in the viscous case, and reduces to the Beale-Kato-Majda criterion in the inviscid case. In the viscous case we prove that Leray-Hopf solutions are regular provided $${\Lambda \in L^{5/2}}$$ , which improves our previous $${\Lambda \in L^\infty}$$ condition. We also show that $${\Lambda \in L^1}$$ for all Leray-Hopf solutions. Finally, we prove that Leray-Hopf solutions are regular when the time-averaged spatial intermittency is small, i.e., close to Kolmogorov’s regime.

Large eddy simulation of soot evolution in an aircraft combustor

An integrated kinetics-based Large Eddy Simulation (LES) approach for soot evolution in turbulent reacting flows is applied to the simulation of a Pratt & Whitney aircraft gas turbine combustor, and the results are analyzed to provide insights into the complex interactions of the hydrodynamics, mixing, chemistry, and soot. The integrated approach includes detailed models for soot, combustion, and the unresolved interactions between soot, chemistry, and turbulence. The soot model is based on the Hybrid Method of Moments and detailed descriptions of soot aggregates and the various physical and chemical processes governing their evolution. The detailed kinetics of jet fuel oxidation and soot precursor formation is described with the Radiation Flamelet/Progress Variable model, which has been modified to account for the removal of soot precursors from the gas-phase. The unclosed filtered quantities in the soot and combustion models, such as source terms, are closed with a novel presumed subfilter PDF approach that accounts for the high subfilter spatial intermittency of soot. For the combustor simulation, the integrated approach is combined with a Lagrangian parcel method for the liquid spray and state-of-the-art unstructured LES technology for complex geometries. Two overall fuel-to-air ratios are simulated to evaluate the ability of the model to make not only absolute predictions but also quantitative predictions of trends. The Pratt & Whitney combustor is a Rich-Quench-Lean combustor in which combustion first occurs in a fuel-rich primary zone characterized by a large recirculation zone. Dilution air is then added downstream of the recirculation zone, and combustion continues in a fuel-lean secondary zone. The simulations show that large quantities of soot are formed in the fuel-rich recirculation zone, and, furthermore, the overall fuel-to-air ratio dictates both the dominant soot growth process and the location of maximum soot volume fraction. At the higher fuel-to-air ratio, the maximum soot volume fraction is found inside the recirculation zone; at the lower fuel-to-air ratio, turbulent fluctuations in the mixture fraction promote the oxidation of soot inside the recirculation zone and suppress the accumulation of a large soot volume fraction. Downstream, soot exits the combustor in intermittent fuel-rich pockets that are not mixed during the injection of dilution air and subsequent secondary fuel-lean combustion. At the higher fuel-to-air ratio, the frequency of these fuel-rich pockets is increased, leading to higher soot emissions from the combustor. Quantitatively, the soot emissions from the combustor are overpredicted by about 50%, which is a substantial improvement over previous works utilizing RANS to predict such emissions. In addition, the ratio between the two fuel-to-air ratios predicted by LES compares very favorably with the experimental measurements. Furthermore, soot growth is dominated by an acetylene-based pathway rather than an aromatic-based pathway, which is usually the dominant mechanism in nonpremixed flames. This finding is the result of the interactions between the hydrodynamics, mixing, chemistry, and soot in the recirculation zone and the resulting residence times of soot at various mixture fractions (compositions), which are not the same in this complex recirculating flow as in nonpremixed jet flames.

Nature of laminar-turbulence intermittency in shear flows

In pipe, channel, and boundary layer flows turbulence first occurs intermittently in space and time: at moderate Reynolds numbers domains of disordered turbulent motion are separated by quiescent laminar regions. Based on direct numerical simulations of pipe flow we argue here that the spatial intermittency has its origin in a nearest neighbor interaction between turbulent regions. We further show that in this regime turbulent flows are intrinsically intermittent with a well-defined equilibrium turbulent fraction but without ever assuming a steady pattern. This transition scenario is analogous to that found in simple models such as coupled map lattices. The scaling observed implies that laminar intermissions of the turbulent flow will persist to arbitrarily large Reynolds numbers.

Evaluating geostatistical methods of blending satellite and gauge data to estimate near real-time daily rainfall for Australia

Rain gauges provide valuable information about the amount and frequency of rainfall. In Australia, the majority of rain gauges are located in populated, wet coastal regions. Approximately 2000 gauges reporting within 24 h of a target day were used to make near real-time (NRT) estimates of daily precipitation. The remaining approximate to 4000 gauges for the same target day were used to evaluate bias and estimation performance using several traditional statistics. There is considerable potential to improve the estimation of rainfall in Australia using related ancillary data, particularly in sparsely gauged areas. The Tropical Rainfall Measuring Mission (TRMM) Multisatellite Precipitation Analysis (TMPA-RT) near real-time product (3B42RT) provided images (0.25 degrees resolution) of precipitation across Australia. Daily precipitation was estimated in 2009110 approximately every 5 km across Australia. This study evaluated selected geostatistical methods for estimating daily rainfall maps across Australia. It tackled the change of support problem and spatial intermittency of daily rainfall data in blending satellite and gauge data. Dissension occurred amongst traditional global statistical measures of performance which were compounded by extremes of gauge density. Overall, our assessment is that blending the 3B42RT satellite and rain gauge data was not worthwhile. However, the blending considerably reduced the estimation variance indicating that uncertainty of the map estimates was a neglected property necessary to detect change and difference in patterns. (C) 2013 Elsevier B.V. All rights reserved.

Crisis, unstable dimension variability, and bifurcations in a system with high-dimensional phase space: Coupled sine circle maps

The phenomenon of crisis in systems evolving in high-dimensional phase space can show unexpected and interesting features. We study this phenomenon in the context of a system of coupled sine circle maps. We establish that the origins of this crisis lie in a tangent bifurcation in high dimensions, and identify the routes that lead to the crisis. Interestingly, multiple routes to crisis are seen depending on the initial conditions of the system, due to the high dimensionality of the space in which the system evolves. The statistical behavior seen in the phase diagram of the system is also seen to change due to the dynamical phenomenon of crisis, which leads to transitions from nonspreading to spreading behavior across an infection line in the phase diagram. Unstable dimension variability is seen in the neighborhood of the infection line. We characterize this crisis and unstable dimension variability using dynamical characterizers, such as finite-time Lyapunov exponents and their distributions. The phase diagram also contains regimes of spatiotemporal intermittency and spatial intermittency, where the statistical quantities scale as power laws. We discuss the signatures of these regimes in the dynamic characterizers, and correlate them with the statistical characterizers and bifurcation behavior. We find that it is necessary to look at both types of correlators together to build up an accurate picture of the behavior of the system.

Time-dependent analysis of aftershock events and structural impacts on intraplate crustal seismicity of the Van earthquake (Mw 7.1, 23 October 2011), E-Anatolia

AbstractThe Van earthquake (M W 7.1, 23 October 2011) in E-Anatolia is typical representative of intraplate earthquakes. Its thrust focal character and aftershock seismicity pattern indicate the most prominent type of compound earthquakes due to its multifractal dynamic complexity and uneven compressional nature, ever seen all over Turkey. Seismicity pattern of aftershocks appears to be invariably complex in its overall characteristics of aligned clustering events. The population and distribution of the aftershock events clearly exhibit spatial variability, clustering-declustering and intermittency, consistent with multifractal scaling. The sequential growth of events during time scale shows multifractal behavior of seismicity in the focal zone. The results indicate that the extensive heterogeneity and time-dependent strength are considered to generate distinct aftershock events. These factors have structural impacts on intraplate seismicity, suggesting multifractal and unstable nature of the Van event. Multifractal seismicity is controlled by complex evolution of crustal-scale faulting, mechanical heterogeneity and seismic deformation anisotropy. Overall seismicity pattern of aftershocks provides the mechanism for strain softening process to explain the principal thrusting event in the Van earthquake. Strain localization with fault weakening controls the seismic characterization of Van earthquake and contributes to explain the anomalous occurrence of aftershocks and intraplate nature of the Van earthquake.

Visualization of the structural response of a hypersonic turbulent boundary layer to convex curvature

The effects of convex curvature on the outer structure of a Mach 4.9 turbulent boundary layer (Reθ = 4.7 × 104) are investigated using condensate Rayleigh scattering and analyzed using spatial correlations, intermittency, and fractal theory. It is found that the post-expansion boundary layer structure morphology appears subtle, but certain features exhibit a more obvious response. The large-scale flow structures survive the initial expansion, appearing to maintain the same physical size. However, due to the nature of the expansion fan, a differential acceleration effect takes place across the flow structures, causing them to be reoriented, leaning farther away from the wall. The onset of intermittency moves closer towards the boundary layer edge and the region of intermittent flow decreases. It is likely that this reflects the less frequent penetration of outer irrotational fluid into the boundary layer, consistent with a boundary layer that is losing its ability to entrain freestream fluid. The fractal dimension of the turbulent/nonturbulent interface decreases with increasing favorable pressure gradient, indicating that the interface's irregularity decreases. Because fractal scale similarity does not encompass the largest scales, this suggests that the change in fractal dimension is due to the action of the smaller-scales, consistent with the idea that the small-scale flow structures are quenched during the expansion in response to bulk dilatation.

Evolution of heliospheric magnetized configurations via topological invariants

The analogy between magnetohydrodynamics (MHD) and knot theory is utilized in presenting a new method for an analysis of stability and evolution of complex magnetic heliospheric flux tubes. Planar projection of a three-dimensional magnetic configuration depicts the structure as a two-dimensional diagram with crossings, to which one may assign mathematical operations leading to robust topological invariants. These invariants enrich the topological information of magnetic configurations beyond helicity. It is conjectured that the field which emerges from the solar photosphere is structured as one of the simplest knots—unknot or prime knot—and these flux ropes are then stretched while carried by the solar wind into the interplanetary medium. Preservation of invariants for small diffusivity and large cross section of the emerging magnetic flux makes them impervious to large scale reconnection, allowing us to predict the observed structures at 1AU as elongated prime knots. Similar structures may be observed in magnetic clouds which got disconnected from their footpoints and in ion drop-out configurations from a compact flare source in solar impulsive solar events. Observation of small scale magnetic features consistent with prime knots may indicate spatial intermittency and non-Gaussian statistics in the turbulent cascade process. For flux tubes with higher resistivity, magnetic energy decay rate should decrease with increased knot complexity as the invariants are then harder to be violated. These observations could be confirmed if adjacent satellites happen to measure distinctly oriented magnetic fields with directionally varying suprathermal particle fluxes.

Dissipation and enstrophy statistics in turbulence: are the simulations and mathematics converging?

AbstractSince the advent of cluster computing over 10 years ago there has been a steady output of new and better direct numerical simulation of homogeneous, isotropic turbulence with spectra and lower-order statistics converging to experiments and many phenomenological models. The next step is to directly compare these simulations to new models and new mathematics, employing the simulated data sets in novel ways, especially when experimental results do not exist or are poorly converged. For example, many of the higher-order moments predicted by the models converge slowly in experiments. The solution with a simulation is to do what an experiment cannot. The calculation and analysis of Yeung, Donzis & Sreenivasan (J. Fluid Mech., this issue, vol. 700, 2012, pp. 5–15) represents the vanguard of new simulations and new numerical analysis that will fill this gap. Where individual higher-order moments of the vorticity squared (the enstrophy) and kinetic energy dissipation might be converging slowly, they have focused upon ratios between different moments that have better convergence properties. This allows them to more fully explore the statistical distributions that eventually must be modelled. This approach is consistent with recent mathematics that focuses upon temporal intermittency rather than spatial intermittency. The principle is that when the flow is nearly singular, during ‘bad’ phases, when global properties can go up and down by many orders of magnitude, if appropriate ratios are taken, convergence rates should improve. Furthermore, in future analysis it might be possible to use these ratios to gain new insights into the intermittency and regularity properties of the underlying equations.

Energy dissipation rate surrogates in incompressible Navier–Stokes turbulence

AbstractHigh-resolution direct numerical simulations of isotropic homogeneous turbulence are used to understand the differences between the effects of spatial intermittency on the energy dissipation rate and on surrogates for the dissipation rate that are based on measurements of a subset of the strain rate tensor. In particular, the one-dimensional longitudinal and transverse surrogates, as well as a surrogate based on the asymmetric part of the strain rate tensor, are considered. The instantaneous surrogates are studied locally, locally averaged in space and conditionally averaged to see what statistics of the dissipation rate might accurately be inferred given measurements of the surrogates. The simulations with the Reynolds numbers based on the Taylor microscale of 102–235 are highly resolved for accurate evaluation of higher-order statistics. The probability densities of the local and locally averaged surrogates are significantly different from the corresponding statistics for the dissipation rate itself. All of the surrogates are more intermittent than the dissipation rate, the transverse surrogate is more intermittent than the longitudinal and these trends are still prominent even when the fields are spatially averaged at length scales close to the integral length scale. As a consequence, the intermittency exponent computed from the moments of the locally averaged longitudinal and transverse surrogates is approximately 1.5 and 2.2 times higher, respectively, than that computed by the same method from the dissipation rate field. In addition, while different methods of computing intermittency exponent from the dissipation rate field yield the same result, different methods applied to a surrogate are inconsistent.

Fluctuations in the direction of propagation of intermittent low‐frequency ionospheric waves

Low‐frequency (8–28 Hz), long‐wavelength electrostatic waves in the ionospheric E region over northern Scandinavia are studied by using data obtained from an instrumented rocket having four probes mounted on two perpendicular booms. Two data sets are available, one for upleg and one for downleg conditions with somewhat different ionospheric parameters. The ionospheric plasma is unstable with respect to the electrostatic Farley‐Buneman instability in both cases, but the DC electric field is somewhat enhanced during the downleg part of the flight. We find that the direction of wave propagation as given by the local normalized fluctuating electrostatic field vector varies randomly within an interval of aspect angles. The distribution of the directional change per time unit is determined. The waves propagate predominantly in the electrojet direction, but significant variations in directions can be found, both with respect to the magnetic field (the aspect angle) and with respect to the electrojet direction. Some of our results are in variance with related radar observations in the electrojet near the equator. Indications of significant spatial intermittency of the signal is demonstrated. Large‐amplitude electrostatic fluctuations are confined to spatially localized regions and have a narrower aspect angle distribution with reduced directional fluctuations. We introduce an intermittency measure based on average excess time statistics for the record for the absolute value of the detected time‐varying electric fields. We thus determine the average of time intervals spent above a prescribed amplitude threshold level. The results are compared with an analytical expression obtained for a reference nonintermittent Gaussian signal. The general analysis requires the joint probability density of signal amplitude and its time derivative to be known. The analytical models for quantifying the intermittency effects were tested by synthetic time series allowing study of the transition from non‐Gaussian to Gaussian random signals.

LES model for sooting turbulent nonpremixed flames

In this work, an integrated Large Eddy Simulation (LES) model is developed for sooting turbulent nonpremixed flames and validated in a laboratory scale flame. The integrated approach leverages state-of-the-art developments in both soot modeling and turbulent combustion modeling and gives special consideration to the small-scale interactions between turbulence, soot, and chemistry. The oxidation of the fuel and the formation of gas-phase soot precursors is described by the Flamelet/Progress Variable model, which has been previously extended to account for radiation losses. However, previous DNS studies have shown that Polycyclic Aromatic Hydrocarbons (PAH), the immediate precursors of soot particles, exhibit significant unsteady effects due to relatively slow chemistry. To model these unsteady effects, a transport equation is solved for a lumped PAH species. In addition, due to the removal of PAH from the gas-phase, alternative definitions of the mixture fraction, progress variable, and enthalpy are proposed. The evolution of the soot population is modeled with the Hybrid Method of Moments (HMOM), an efficient statistical model requiring the solution of only a few transport equations describing statistics of the soot population. The filtered source terms in these equations that describe the various formation, growth, and destruction processes are closed with a recently developed presumed subfilter PDF approach that accounts for the high spatial intermittency of soot. The integrated LES model is validated in a piloted natural gas turbulent jet diffusion flame and is shown to predict the magnitude of the maximum soot volume fraction in the flame relatively accurately, although the maximum soot volume fraction is shown to be rather sensitive to the subfilter scalar dissipation rate model.

Experimental investigation of geodesic acoustic mode spatial structure, intermittency, and interaction with turbulence in the DIII-D tokamak

Geodesic acoustic modes (GAMs) and zonal flows are nonlinearly driven, axisymmetric (m=0andn=0) E×B flows, which are thought to play an important role in establishing the saturated level of turbulence in tokamaks. Results are presented showing the GAM’s observed spatial scales, temporal scales, and nonlinear interaction characteristics, which may have implications for the assumptions underpinning turbulence models towards the tokamak edge (r/a>rsim0.75). Measurements in the DIII-D tokamak [Luxon, Nucl. Fusion 42, 614 (2002)] have been made with multichannel Doppler backscattering systems at toroidal locations separated by 180∘; analysis reveals that the GAM is highly coherent between the toroidally separated systems (γ>0.8) and that measurements are consistent with the expected m=0andn=0 structure. Observations show that the GAM in L-mode plasmas with ~2.5-4.5 MW auxiliary heating occurs as a radially coherent eigenmode, rather than as a continuum of frequencies as occurs in lower temperature discharges; this is consistent with theoretical expectations when finite ion Larmor radius effects are included. The intermittency of the GAM has been quantified, revealing that its autocorrelation time is fairly short, ranging from about 4 to about 15 GAM periods in cases examined, a difference that is accompanied by a modification to the probability distribution function of the E×B velocity at the GAM frequency. Conditionally-averaged bispectral analysis shows the strength of the nonlinear interaction of the GAM with broadband turbulence can vary with the magnitude of the GAM. Data also indicate a wavenumber dependence to the GAM’s interaction with turbulence.

Large eddy simulation subfilter modeling of soot-turbulence interactions

The small-scale interactions between turbulence, chemistry, and soot have a profound effect on the soot formation, growth, and destruction processes in turbulent reacting flows. In this work, the small-scale subfilter interactions between turbulence and soot are modeled using a presumed subfilter PDF for the statistical moments of the soot number density function. Due to a very large (infinite) Schmidt number, soot is confined to very thin structures. In addition, soot is formed initially from Polycyclic Aromatic Hydrocarbons, which exhibit a strong sensitivity to the local scalar dissipation rate in the flow field. These interactions of soot with the gas-phase chemistry, molecular transport, and turbulence result in very high spatial and temporal intermittency. Therefore, the soot subfilter PDF is presumed to be a pair of delta distributions with a sooting mode and a non-sooting mode. In addition to the mean values of the scalars, one additional parameter is needed to specify this distribution. The presumed soot subfilter PDF approach is evaluated a priori using a recent two-dimensional direct numerical simulation (DNS) database of soot evolution in a nonpremixed flame. The analysis shows that predictions of the soot intermittency as well as the soot source terms are improved with this presumed soot subfilter PDF approach compared to simply using the mean values of the soot scalars. Several choices for specifying the additional parameter of the PDF are also evaluated with the database. The results show that the parameter is best specified using the second moment of the soot number density. In addition, the transport equation for the second moment of the number density is briefly discussed. A model for the lone unclosed term is proposed and evaluated with the DNS data.

DIRECTIONAL ALIGNMENT AND NON-GAUSSIAN STATISTICS IN SOLAR WIND TURBULENCE

The magnetic and velocity field fluctuations in magnetohydrodynamic turbulence can be characterized by their directional alignment and induced electric field. These manifest as coherent spatial correlations which are measures of Alfvenicity and turbulence cascade strength, respectively. Solar wind observations and direct numerical simulations find that these distinctive correlations, caused by rapid relaxation processes that act to suppress nonlinearity, occur in localized spatial patches. This cellularization of magnetofluid turbulence is inconsistent with a superposition of Gaussian fields and could be related to spatial intermittency or other non-Gaussian statistics.

Fractal systems of central places based on intermittency of space-filling

The central place models are fundamentally important in theoretical geography and city planning theory. The texture and structure of central place networks have been demonstrated to be self-similar in both theoretical and empirical studies. However, the underlying rationale of central place fractals in the real world has not yet been revealed so far. This paper is devoted to illustrating the mechanisms by which the fractal patterns can be generated from central place systems. The structural dimension of the traditional central place models is d = 2 indicating no intermittency in the spatial distribution of human settlements. This dimension value is inconsistent with empirical observations. Substituting the complete space filling with the incomplete space filling, we can obtain central place models with fractional dimension D < d = 2 indicative of spatial intermittency. Thus the conventional central place models are converted into fractal central place models. If we further integrate the chance factors into the improved central place fractals, the theory will be able to explain the real patterns of urban places very well. As empirical analyses, the US cities and towns are employed to verify the fractal-based models of central places.

Getting ahead: context-dependent responses to odorant filaments drive along-stream progress during odor tracking in blue crabs

The chemosensory signal structure governing the upstream progress of blue crabs to an odorant source was examined. We used a three-dimensional laser-induced fluorescence system to collect chemical concentration data simultaneously with behavior observations of actively tracking blue crabs (Callinectes sapidus) in a variety of plume types. This allowed us to directly link chemical signal properties at the antennules and legs to subsequent upstream motion while altering the spatial and temporal intermittency characteristics of the sensory field. Our results suggest that odorant stimuli elicit responses in a binary fashion by causing upstream motion, provided the concentration at the antennules exceeds a specific threshold. In particular, we observed a significant association between crab velocity changes and odorant spike encounters defined using a threshold that is scaled to the mean of the instantaneous maximum concentration. Thresholds were different for each crab, indicating a context-sensitive response to signal dynamics. Our data also indicate that high frequency of odorant spike encounters terminate upstream movement. Further, the data provide evidence that the previous state of the crab and prior stimulus history influence the behavioral response (i.e. the response is context dependent). Two examples are: (1) crabs receiving prior odorant spikes attained elevated velocity more quickly in response to subsequent spikes; and (2) prior acceleration or deceleration of the crab influenced the response time period to a particular odorant spike. Finally, information from both leg and antennule chemosensors interact, suggesting parallel processing of odorant spike properties during navigation.

Spatial downscaling of precipitation from GCMs for climate change projections using random cascades: A case study in Italy

We present a Stochastic Space Random Cascade (SSRC) approach to downscale precipitation from a General Circulation Models (GCMs), developed for the assessment of water resources under climate change scenarios for the Oglio river (1440 km2), in the Italian Alps. The snow‐fed Oglio river displays complex physiography and high environmental gradient and statistical downscaling methods are required for climate change assessment. First, a back cast analysis is carried out to evaluate the most representative within a set of four available GCMs (R30, ECHAM4, PCM, HadCM3). Monthly precipitation for the window 1990–2000 from 270 gauging stations (one every 25 km2) in northern Italy is used and scores from objective indicators are calculated. The SSRC model is then tuned upon the Oglio river catchment for spatial downscaling (2 km2) of daily precipitation from the NCAR Parallel Climate Model, giving the comparatively best results for the area. Scale Recursive Estimation coupled with the Expectation Maximization algorithm is used for model estimation. The seasonal parameters of the multiplicative cascade are accommodated by statistical distributions conditioned upon the climatic forcing, based on a regression analysis. The SSRC approach reproduces well the spatial clustering, intermittency, self‐similarity, and spatial correlation structure of precipitation fields, with relatively low computational burden. Downscaling of future precipitation scenarios (A2 scenario from the Parallel Climate Model) is then carried out and some preliminary conclusions are drawn.

Spatial Intermittency of Surface Layer Wind Fluctuations at Mesoscale Range

We study various hourly surface layer wind series recorded at different sites in the Netherlands by the "Royal Netherlands Meteorological Institute." By reporting all velocity magnitude correlation coefficients, associated with the available couples of locations, as a function of their spatial distance, we find that they fall on a single curve. This curve turns out to be remarkably well described by a logarithmic shape, characteristic of continuous cascades with an intermittency coefficient λ2 ≃ 0.04 and an integral scale L ≃ 600 km. Along the same line, we study the scaling properties of spatial velocity increment structure functions. This allows one to estimate the ζ(q) spectrum and to confirm an intermittent nature of mesoscale fluctuations similar to the one observed in fully developed turbulence.