bluuebunny/crossref_metadata_2025 huggingface dataset:
A probabilistic approach to heterogeneity in space plasmas: the case of magnetic field intensity in solar wind
Authors: Consolini G. , Bavassano B. , De Michelis P.
Published: April 2010

Abstract. Since the early 90s it was shown that Probability Distribution Functions (PDFs) of small scale differences (fluctuations) of several quantities in space plasmas display significant departures from Gaussianity. The non-Gaussian shape of PDFs was ascribed to intermittency and discussed in the framework of intermittent MHD turbulence. Here, we put the attention to the PDF of magnetic field intensity instead of its differences showing how the PDF of such quantity in a quiet solar wind can be related with the occurrence of heterogeneity. In detail, we derive the shape of the PDFs by simple statistical considerations based on the concept of subordination in probability theory. An interpretation and a discussion in terms of existing coherent magnetic structures in a mechanical near-equilibrium state are also presented.
Edge effect causes apparent fractal correlation dimension of uniform spatial raindrop distribution
Authors: Uijlenhoet R. , Porrà J. M. , Sempere Torres D. , Creutin J.-D.
Published: April 2010

Abstract. Lovejoy and Schertzer (1990a) presented a statistical analysis of blotting paper observations of the (two-dimensional) spatial distribution of raindrop stains. They found empirical evidence for the fractal scaling behavior of raindrops in space, with potentially far-reaching implications for rainfall microphysics and radar meteorology. In particular, the fractal correlation dimensions determined from their blotting paper observations led them to conclude that "drops are (hierarchically) clustered" and that "inhomogeneity in rain is likely to extend down to millimeter scales". Confirming previously reported Monte Carlo simulations, we demonstrate analytically that the claims based on this analysis need to be reconsidered, as fractal correlation dimensions similar to the ones reported (i.e. smaller than the value of two expected for uniformly distributed raindrops) can result from instrumental artifacts (edge effects) in otherwise homogeneous Poissonian rainfall. Hence, the results of the blotting paper experiment are not statistically significant enough to reject the Poisson homogeneity hypothesis in favor of a fractal description of the discrete nature of rainfall. Our analysis is based on an analytical expression for the expected overlap area between a circle and a square, when the circle center is randomly (uniformly) distributed inside the square. The derived expression (πr2−8r3/3+r4/2, where r denotes the ratio between the circle radius and the side of the square) can be used as a reference curve against which to test the statistical significance of fractal correlation dimensions determined from spatial point patterns, such as those of raindrops and rainfall cells.
Investigating the multifractality of point precipitation in the Madeira archipelago
Authors: de Lima M. I. P. , de Lima J. L. M. P.
Published: April 2010

Abstract. The purpose of this work is to contribute to a better understanding of the variability of precipitation in the Madeira archipelago. This archipelago is located in the Atlantic subtropical belt under the direct influence of the Azores high pressure system. It is formed by Madeira Island (728 km2) and Porto Santo Island (42 km2) and by two other groups of very small inhabited islands. The complex topography of the islands in the Madeira archipelago and their small size play a crucial role in the local precipitation regime, which is marked by high spatial variability. This paper explores the invariance of properties manifested across scales and determines the fractal and multifractal behaviour observed in the temporal structure of precipitation using daily and 10-min time series from several locations scattered over the main islands. The period covered by the precipitation records is 34 years for the daily data and almost 4 months for the 10-min data. The results show that the temporal structure of precipitation in the Madeira Archipelago exhibits scale-invariant and multifractal properties. The empirical exponent functions describing the scaling statistical properties of the precipitation intensity were characterized using multifractal parameters; these parameters are increasing our awareness of the dynamics of this process in these islands.
The transformation of an interfacial solitary wave of elevation at a bottom step
Authors: Maderich V. , Talipova T. , Grimshaw R. , Pelinovsky E. , Choi B. H. , Brovchenko I. , Terletska K. , Kim D. C.
Published: April 2010

Abstract. In this paper we study the transformation of an internal solitary wave at a bottom step in the framework of two-layer flow, for the case when the interface lies close to the bottom, and so the solitary waves are elevation waves. The outcome is the formation of solitary waves and dispersive wave trains in both the reflected and transmitted fields. We use a two-pronged approach, based on numerical simulations of the fully nonlinear equations using a version of the Princeton Ocean Model on the one hand, and a theoretical and numerical study of the Gardner equation on the other hand. In the numerical experiments, the ratio of the initial wave amplitude to the layer thickness is varied up one-half, and nonlinear effects are then essential. In general, the characteristics of the generated solitary waves obtained in the fully nonlinear simulations are in reasonable agreement with the predictions of our theoretical model, which is based on matching linear shallow-water theory in the vicinity of a step with solutions of the Gardner equation for waves far from the step.
Variability in spatial patterns of long nonlinear waves from fast ferries in Tallinn Bay
Authors: Torsvik T. , Didenkulova I. , Soomere T. , Parnell K. E.
Published: April 2010

Abstract. High-speed ferries are known to generate wakes with unusually long periods, and occasionally large amplitudes which may serve as a qualitatively new forcing factor in coastal regions that are not exposed to a sea swell. An intrinsic feature of such wakes is their large spatial variation. We analyze the variability of wake conditions for the coasts of Tallinn Bay, the Baltic Sea, a sea area with very intense fast ferry traffic. The modelled ship wave properties for several GPS-recorded ship tracks reasonably match the measured waves in terms of both wave heights and periods. It is shown that the spatial extent of the wake patterns is very sensitive to small variations in sailing conditions. This feature leads to large variations of ship wave loads at different coastal sections with several locations regularly receiving high ship wave energy. The runup of the largest ship wakes on the beach increases significantly with an increase in wave height whereas shorter (period <2–5 s) waves merge into longer waves in the shoaling and runup process.
Upper stratospheric ozone decrease events due to a positive feedback between ozone and the ozone dissociation rate
Authors: Sonnemann G. R. , Hartogh P.
Published: April 2010

Abstract. Ozone measurements taken with a ground based microwave instrument at Lindau (51.66° N, 10.13° E) over some years showed strong ozone decrease events within the stratopause region, particularly during the winter half-year. These events are characterized by a marked drop of the ozone mixing ratio from two to three ppmv to less than half a ppmv in extreme cases. Simultaneous water vapor measurements at the same place, also carried out by a microwave instrument, showed a strong increase of its mixing ratio and the temperature was also enhanced during these episodes. The theoretical analysis brought evidence that these events result from a positive feedback in the complex radiatively-chemical system between the ozone column density and the ozone dissociation rate.
Electrostatic solitary waves in current layers: from Cluster observations during a super-substorm to beam experiments at the LAPD
Authors: Pickett J. S. , Chen L.-J. , Santolík O. , Grimald S. , Lavraud B. , Verkhoglyadova O. P. , Tsurutani B. T. , Lefebvre B. , Fazakerley A. , Lakhina G. S. , Ghosh S. S. , Grison B. , Décréau P. M. E. , Gurnett D. A. , Torbert R. , Cornilleau-Wehrlin N. , Dandouras I. , Lucek E.
Published: April 2010

Abstract. Electrostatic Solitary Waves (ESWs) have been observed by several spacecraft in the current layers of Earth's magnetosphere since 1982. ESWs are manifested as isolated pulses (one wave period) in the high time resolution waveform data obtained on these spacecraft. They are thus nonlinear structures generated out of nonlinear instabilities and processes. We report the first observations of ESWs associated with the onset of a super-substorm that occurred on 24 August 2005 while the Cluster spacecraft were located in the magnetotail at around 18–19 RE and moving northward from the plasma sheet to the lobes. These ESWs were detected in the waveform data of the WBD plasma wave receiver on three of the Cluster spacecraft. The majority of the ESWs were detected about 5 min after the super-substorm onset during which time 1) the PEACE electron instrument detected significant field-aligned electron fluxes from a few 100 eV to 3.5 keV, 2) the EDI instrument detected bursts of field-aligned electron currents, 3) the FGM instrument detected substantial magnetic fluctuations and the presence of Alfvén waves, 4) the STAFF experiment detected broadband electric and magnetic waves, ion cyclotron waves and whistler mode waves, and 5) CIS detected nearly comparable densities of H+ and O+ ions and a large tailward H+ velocity. We compare the characteristics of the ESWs observed during this event to those created in the laboratory at the University of California-Los Angeles Plasma Device (LAPD) with an electron beam. We find that the time durations of both space and LAPD ESWs are only slightly larger than the respective local electron plasma periods, indicating that electron, and not ion, dynamics are responsible for generation of the ESWs. We have discussed possible mechanisms for generating the ESWs in space, including the beam and kinetic Buneman type instabilities and the acoustic instabilities. Future studies will examine these mechanisms in more detail using the space measurements as inputs to models, and better relate the ESW space measurements to the laboratory through PIC code models.
ENSO's non-stationary and non-Gaussian character: the role of climate shifts
Authors: Boucharel J. , Dewitte B. , Garel B. , du Penhoat Y.
Published: April 2010

Abstract. El Niño Southern Oscillation (ENSO) is the dominant mode of climate variability in the Pacific, having socio-economic impacts on surrounding regions. ENSO exhibits significant modulation on decadal to inter-decadal time scales which is related to changes in its characteristics (onset, amplitude, frequency, propagation, and predictability). Some of these characteristics tend to be overlooked in ENSO studies, such as its asymmetry (the number and amplitude of warm and cold events are not equal) and the deviation of its statistics from those of the Gaussian distribution. These properties could be related to the ability of the current generation of coupled models to predict ENSO and its modulation. Here, ENSO's non-Gaussian nature and asymmetry are diagnosed from in situ data and a variety of models (from intermediate complexity models to full-physics coupled general circulation models (CGCMs)) using robust statistical tools initially designed for financial mathematics studies. In particular α-stable laws are used as theoretical background material to measure (and quantify) the non-Gaussian character of ENSO time series and to estimate the skill of ``naïve'' statistical models in producing deviation from Gaussian laws and asymmetry. The former are based on non-stationary processes dominated by abrupt changes in mean state and empirical variance. It is shown that the α-stable character of ENSO may result from the presence of climate shifts in the time series. Also, cool (warm) periods are associated with ENSO statistics having a stronger (weaker) tendency towards Gaussianity and lower (greater) asymmetry. This supports the hypothesis of ENSO being rectified by changes in mean state through nonlinear processes. The relationship between changes in mean state and nonlinearity (skewness) is further investigated both in the Zebiak and Cane (1987)'s model and the models of the Intergovernmental Panel for Climate Change (IPCC). Whereas there is a clear relationship in all models between ENSO asymmetry (as measured by skewness or nonlinear advection) and changes in mean state, they exhibit a variety of behaviour with regard to α-stability. This suggests that the dynamics associated with climate shifts and the occurrence of extreme events involve higher-order statistical moments that cannot be accounted for solely by nonlinear advection.
Return-current formation in the electron beam – plasma system
Authors: Karlický M. , Bárta M.
Published: April 2010

Abstract. Using a 3-D electromagnetic particle-in-cell model an evolution of the electron distribution function in the beam-plasma system with the return current is computed. It was found that the resulting electron distribution function depends on the magnetic field assumed along the beam-propagation direction. While for small magnetic fields the electron distribution function becomes broad in the direction perpendicular to the beam propagation due to the Weibel (filamentation) instability and the return current is formed by a shifted bulk distribution, for stronger magnetic fields the distribution, especially on the return current side, is extended in the beam-propagation direction. To understand better the instabilities influencing the mentioned processes, the dispersion diagrams are computed and discussed.
Long's equation in terrain following coordinates
Authors: Humi M.
Published: April 2010

Abstract. Long's equation describes two dimensional stratified atmospheric flow over terrain which is represented by the geometry of the domain. The solutions of this equation over simple topography were investigated analytically and numerically by many authors. In this paper we derive a new terrain following formulation of this equation which incorporates the terrain as part of the differential equation rather than the geometry of the domain. This new formulation enables us to compute analytically steady state gravity wave patterns over complex topography in some limiting cases of the parameters that appear in this equation.
Multiscaling analysis of high resolution space-time lidar-rainfall
Authors: Mandapaka P. V. , Lewandowski P. , Eichinger W. E. , Krajewski W. F.
Published: April 2010

Abstract. In this study, we report results from scaling analysis of 2.5 m spatial and 1 s temporal resolution lidar-rainfall data. The high resolution spatial and temporal data from the same observing system allows us to investigate the variability of rainfall at very small scales ranging from few meters to ~1 km in space and few seconds to ~30 min in time. The results suggest multiscaling behaviour in the lidar-rainfall with the scaling regime extending down to the resolution of the data. The results also indicate the existence of a space-time transformation of the form t~Lz at very small scales, where t is the time lag, L is the spatial averaging scale and z is the dynamic scaling exponent.
Long-term evolution of strongly nonlinear internal solitary waves in a rotating channel
Authors: Sánchez-Garrido J. C. , Vlasenko V.
Published: April 2010

Abstract. The evolution of internal solitary waves (ISWs) propagating in a rotating channel is studied numerically in the framework of a fully-nonlinear, nonhydrostatic numerical model. The aim of modelling efforts was the investigation of strongly-nonlinear effects, which are beyond the applicability of weakly nonlinear theories. Results reveal that small-amplitude waves and sufficiently strong ISWs evolve differently under the action of rotation. At the first stage of evolution an initially two-dimensional ISW transforms according to the scenario described by the rotation modified Kadomtsev-Petviashvili equation, namely, it starts to evolve into a Kelvin wave (with exponential decay of the wave amplitude across the channel) with front curved backwards. This transition is accompanied by a permanent radiation of secondary Poincaré waves attached to the leading wave. However, in a strongly-nonlinear limit not all the energy is transmitted to secondary radiated waves. Part of it returns to the leading wave as a result of nonlinear interactions with secondary Kelvin waves generated in the course of time. This leads to the formation of a slowly attenuating quasi-stationary system of leading Kelvin waves, capable of propagating for several hundreds hours as a localized wave packet.
Plankton bloom controlled by horizontal stirring
Authors: McKiver W. , Neufeld Z. , Scheuring I.
Published: April 2010

Abstract. Here we show a simple mechanism in which changes in the rate of horizontal stirring by mesoscale ocean eddies can trigger or suppress plankton blooms and can lead to an abrupt change in the average plankton density. We consider a single species phytoplankton model with logistic growth, grazing and a spatially non-uniform carrying capacity. The local dynamics have multiple steady states for some values of the carrying capacity that can lead to localized blooms as fluid moves across the regions with different properties. We show that for this model even small changes in the ratio of biological timescales relative to the flow timescales can greatly enhance or reduce the global plankton productivity. Thus, this may be a possible mechanism in which changes in horizontal mixing can trigger plankton blooms or cause regime shifts in some oceanic regions. Comparison between the spatially distributed model and Lagrangian simulations considering temporal fluctuations along fluid trajectories, demonstrates that small scale transport processes also play an important role in the development of plankton blooms with a significant influence on global biomass.
What determines size distributions of heavy drops in a synthetic turbulent flow?
Authors: Zahnow J. C. , Feudel U.
Published: April 2010

Abstract. We present results from an individual particle based model for the collision, coagulation and fragmentation of heavy drops moving in a turbulent flow. Such a model framework can help to bridge the gap between the full hydrodynamic simulation of two phase flows, which can usually only study few particles and mean field based approaches for coagulation and fragmentation relying heavily on parameterization and are for example unable to fully capture particle inertia. We study the steady state that results from a balance between coagulation and fragmentation and the impact of particle properties and flow properties on this steady state. We compare two different fragmentation mechanisms, size-limiting fragmentation where particles fragment when exceeding a maximum size and shear fragmentation, where particles break up when local shear forces in the flow exceed the binding force of the particle. For size-limiting fragmentation the steady state is mainly influenced by the maximum stable particle size, while particle and flow properties only influence the approach to the steady state. For shear fragmentation both the approach to the steady state and the steady state itself depend on the particle and flow parameters. There we find scaling relationships between the steady state and the particle and flow parameters that are determined by the stability condition for fragmentation.
Variability of magnetic field spectra in the Earth's magnetotail
Authors: Petrukovich A. A. , Malakhov D. V.
Published: April 2010

Abstract. We investigate the variability of magnetic fluctuation spectra below 1 Hz in the Earth's plasma sheet using specially selected long observation intervals by Geotail spacecraft. The spectra can be generally described by a negative power law with two kinks. The range between kinks ~0.02–0.2 Hz has the most stable power law index ~2.4–2.6. Indices at the lower and the higher frequencies are more variable and generally increase with power of fluctuations. In the sub-second range fluctuations are strongly localized and indices are closer to 3. At the lower-frequency end indices are about 1.5. The lower kink is usually well defined on average spectra and its frequency tends to increase with activity. Combination of spectrum index α and fractal dimension δ is expected to follow the Berry relation α+2δ=5, but actually is ~5.5.
Accurate estimation of third-order moments from turbulence measurements
Authors: Podesta J. J. , Forman M. A. , Smith C. W. , Elton D. C. , Malécot Y. , Gagne Y.
Published: April 2010

Abstract. Politano and Pouquet's law, a generalization of Kolmogorov's four-fifths law to incompressible MHD, makes it possible to measure the energy cascade rate in incompressible MHD turbulence by means of third-order moments. In hydrodynamics, accurate measurement of third-order moments requires large amounts of data because the probability distributions of velocity-differences are nearly symmetric and the third-order moments are relatively small. Measurements of the energy cascade rate in solar wind turbulence have recently been performed for the first time, but without careful consideration of the accuracy or statistical uncertainty of the required third-order moments. This paper investigates the statistical convergence of third-order moments as a function of the sample size N. It is shown that the accuracy of the third-moment <(δ v||)3> depends on the number of correlation lengths spanned by the data set and a method of estimating the statistical uncertainty of the third-moment is developed. The technique is illustrated using both wind tunnel data and solar wind data.
Another look at climate sensitivity
Authors: Zaliapin I. , Ghil M.
Published: April 2010

Abstract. We revisit a recent claim that the Earth's climate system is characterized by sensitive dependence to parameters; in particular, that the system exhibits an asymmetric, large-amplitude response to normally distributed feedback forcing. Such a response would imply irreducible uncertainty in climate change predictions and thus have notable implications for climate science and climate-related policy making. We show that equilibrium climate sensitivity in all generality does not support such an intrinsic indeterminacy; the latter appears only in essentially linear systems. The main flaw in the analysis that led to this claim is inappropriate linearization of an intrinsically nonlinear model; there is no room for physical interpretations or policy conclusions based on this mathematical error. Sensitive dependence nonetheless does exist in the climate system, as well as in climate models – albeit in a very different sense from the one claimed in the linear work under scrutiny – and we illustrate it using a classical energy balance model (EBM) with nonlinear feedbacks. EBMs exhibit two saddle-node bifurcations, more recently called "tipping points," which give rise to three distinct steady-state climates, two of which are stable. Such bistable behavior is, furthermore, supported by results from more realistic, nonequilibrium climate models. In a truly nonlinear setting, indeterminacy in the size of the response is observed only in the vicinity of tipping points. We show, in fact, that small disturbances cannot result in a large-amplitude response, unless the system is at or near such a point. We discuss briefly how the distance to the bifurcation may be related to the strength of Earth's ice-albedo feedback.
A delay differential model of ENSO variability – Part 2: Phase locking, multiple solutions and dynamics of extrema
Authors: Zaliapin I. , Ghil M.
Published: April 2010

Abstract. We consider a highly idealized model for El Niño/Southern Oscillation (ENSO) variability, as introduced in an earlier paper. The model is governed by a delay differential equation for sea-surface temperature T in the Tropical Pacific, and it combines two key mechanisms that participate in ENSO dynamics: delayed negative feedback and seasonal forcing. We perform a theoretical and numerical study of the model in the three-dimensional space of its physically relevant parameters: propagation period τ of oceanic waves across the Tropical Pacific, atmosphere-ocean coupling κ, and strength of seasonal forcing b. Phase locking of model solutions to the periodic forcing is prevalent: the local maxima and minima of the solutions tend to occur at the same position within the seasonal cycle. Such phase locking is a key feature of the observed El Niño (warm) and La Niña (cold) events. The phasing of the extrema within the seasonal cycle depends sensitively on model parameters when forcing is weak. We also study co-existence of multiple solutions for fixed model parameters and describe the basins of attraction of the stable solutions in a one-dimensional space of constant initial model histories.
Size-frequency relation of earthquakes in load-transfer models of fracture
Authors: Gómez J. B. , Iñiguez D. , Pacheco A. F.
Published: April 2010

Abstract. Using Monte Carlo simulations of the process of breaking in arrays of elements with load-transfer rules, we have obtained the size- frequency relation of the avalanches occurring in 1- and 2-dimensional stochastic fracture models. The resulting power-law behaviour resembles the Gutenberg-Richter law for the relation between the size (liberated energy) of earthquakes and their number frequency. The value of the power law exponent is calculated as a function of the degree of stress dissipation present in the model. The degree of dissipation is implemented in a straightforward and simple way by assuming that only a fraction of the stress is transferred in each breaking event. The models are robust with respect to the degree of dissipation and we observe a consistent power-law behaviour for a broad range of dissipation values, both in ID and 2D. The value of the power-law exponent is similar to the phenomenological b- value (0.8 < b < 1.1) for intermediate magnitude earthquakes.
What can asymptotic expansions tell us about large-scale quasi-geostrophic anticyclonic vortices?
Authors: Stegner A. , Zeitlin V.
Published: April 2010

Abstract. The problem of the large-scale quasi-geostrophic anticyclonic vortices is studied in the framework of the baratropic rotating shallow- water equations on the β-plane. A systematic approach based on the multiplescale asymptotic expansions is used leading to a hierarchy of governing equations for the large-scale vortices depending on their characteristic size, velocity and a free surface elevation. Among them are the Charney-Obukhov equation, the intermediate geostrophic model equation, the frontal dynamics equation and some new nonlinear quasi-geostrophic equation. We are looking for steady-drifting axisymmetric anticyclonic solutions and find them in a consistent way only in this last equation. These solutions are soliton-like in the sense that the effects of weak non-linearity and dispersion balance each other. The same regimes on the paraboloidal β-plane are studied, all giving a negative result in what concerns the axisymmetric steady solutions, except for a strong elevation case where any circular profile is found to be steadily propagating within the accuracy of the approximation.
Non-equilibrium effects of core-cooling and time-dependent internal heating on mantle flush events
Authors: Yuen D. A. , Balachandar S. , Steinbach V. C. , Honda S. , Reuteler D. M. , Smedsmo J. J. , Lauer G. S.
Published: April 2010

Abstract. We have examined the non-equilibrium effects of core-cooling and time-dependent internal-heating on the thermal evolution of the Earth's mantle and on mantle flush events caused by the two major phase transitions. Both two- and three-dimensional models have been employed. The mantle viscosity responds to the secular cooling through changes in the averaged temperature field. A viscosity which decreases algebraically with the average temperature has been considered. The time-dependent internal-heating is prescribed to decrease exponentially with a single decay time. We have studied the thermal histories with initial Rayleigh numbers between 2 x 107 and 108 . Flush events, driven by the non-equilibrium forcings, are much more dramatic than those produced by the equilibrium boundary conditions and constant internal heating. Multiple flush events are found under non-equilibrium conditions in which there is very little internal heating or very fast decay rates of internal-heating. Otherwise, the flush events take place in a relatively continuous fashion. Prior to massive flush events small-scale percolative structures appear in the 3D temperature fields. Time-dependent signatures, such as the surface heat flux, also exhibits high frequency oscillatory patterns prior to massive flush events. These two observations suggest that the flush event may be a self-organized critical phenomenon. The Nusselt number as a function of the time-varying Ra does not follow the Nusselt vs. Rayleigh number power-law relationship based on equilibrium (constant temperature) boundary conditions. Instead Nu(t) may vary non-monotonically with time because of the mantle flush events. Convective processes in the mantle operate quite differently under non-equilibrium conditions from its behaviour under the usual equilibrium situations.
Identifying sets of acceptable solutions to non-linear, geophysical inverse problems which have complicated misfit functions
Authors: Lomax A. , Snieder R.
Published: April 2010

Abstract. A goal of geophysical inversion is to identify all models which give an acceptable misfit between predicted and observed data. However, because of the complexity of Earth structure, the non-linearity of physical processes in the Earth, and the insufficiency of geophysical data, many geophysical inverse problems may have a large number of distinct, acceptable solutions. These problems may be characterized by a complicated surface for the misfit function in the solution parameter space. For exploring such a surface, direct inversion and simple random search methods are often inadequate. However, directed search methods such as the genetic algorithm can be configured to balance convergent and random processes to find large sets of solutions that span the acceptable regions of complicated misfit surfaces.
3D nonlinear inversion by entropy of image contrast optimization
Authors: Ryzhikov G. , Biryulina M. , Hanyga A.
Published: April 2010

Abstract. An approach to solve 3D inverse problem associated with inverting seismic reflection data is presented. It exploits the a priori assumption that the reflection data, reduced properly, can be interpreted as a perturbation of a dynamical response of a certain 'reference background'. It is supposed that the corresponding perturbation of medium parameters can be treated in terms of the 'Ray + Born'- or 'Rytov + Born'- set of medium functions. This for the reflection data means that 'kinematical' part does not generate reflections, while proper reflections are caused by single-scattering perturbations. Moreover, it is guessed that the latters are cooperated in a vicinity of a certain unknown 2D smooth surface ('Interfaces'). When this a I ' information is adequate, the approach allows to recover both the low-frequency features of the medium (the background) and its discontinuities. The approach involves a new optimization criterion, called the Entropy of Image Contrast (EnIC), and a new global optimization algorithm, called Regularized Global Approximation algorithm (RGA-algorithm). It allows to choose such a background that the linerized inversion provides the most focused image of interfaces. In other words, it yields the maximum-contrast, or minimum-entropy, interface image. The method takes into account the large amounts of data that have to be processed in 3D inversion and the sparseness of input data. It is also robust with respect to the noise in the data.
A centre manifold approach to solitary waves in a sheared, stably stratified fluid layer
Authors: Zimmerman W. B. , Velarde M. G.
Published: April 2010

Abstract. The centre manifold approach is used to derive an approximate equation for nonlinear waves propagating in a sheared, stably stratified fluid layer. The evolution equation matches limiting forms derived by other methods, including the inviscid, long wave approximation leading to the Korteweg- deVries equation. The model given here allows large modulations of the height of the waveguide. This permits the crude modelling of shear layer instabilities at the upper material surface of the waveguide which excite solitary internal waves in the waveguide. An energy argument is used to support the existence of these waves.
Nonlinear wave energy modelling in the surf zone
Authors: Karambas Th. V.
Published: April 2010

Abstract. Breaking wave energy in the surf zone is modelled through the incorporation of the time dependent energy balance equation in a non linear dispersive wave propagation model. The energy equations solved simultaneously with the momentum and continuity equation. Turbulence effects and the non uniform horizontal velocity distribution due to breaking is introduced in both the energy and momentum equations. The dissipation term is a function of the velocity defect derived from a turbulent analysis. The resulting system predicts both wave characteristics (surface elevation and velocity) and the energy distribution inside surf zone. The model is validated against experimental data and analytical expressions.
Low-order models of wave interactions in the transition to baroclinic chaos
Authors: Früh W.-G.
Published: April 2010

Abstract. A hierarchy of low-order models, based on the quasi-geostrophic two-layer model, is used to investigate complex multi-mode flows. The different models were used to study distinct types of nonlinear interactions, namely wave- wave interactions through resonant triads, and zonal flow-wave interactions. The coupling strength of individual triads is estimated using a phase locking probability density function. The flow of primary interest is a strongly modulated amplitude vacillation, whose modulation is coupled to intermittent bursts of weaker wave modes. This flow was found to emerge in a discontinuous bifurcation directly from a steady wave solution. Two mechanism were found to result in this flow, one involving resonant triads, and the other involving zonal flow-wave interactions together with a strong β-effect. The results will be compared with recent laboratory experiments of multi-mode baroclinic waves in a rotating annulus of fluid subjected to a horizontal temperature gradient.
Two dimensional estimates from ocean SAR images
Authors: Le Caillec J. M. , Garello R. , Chapron B.
Published: April 2010

Abstract. Synthetic Aperture Radar (SAR) images of the ocean yield a lot of information on the sea-state surface providing that the mapping process between the surface and the image is clearly defined. However it is well known that SAR images exhibit non-gaussian statistics and that the motion of the scatterers on the surface, while the image is being formed, may yield to nonlinearities. The detection and quantification of these nonlinearities are made possible by using Higher Order Spectra (HOS) methods and more specifically, bispectrum estimation. The development of the latter method allowed us to find phase relations between different parts of the image and to recognise their level of coupling, i.e. if and how waves of different wavelengths interacted nonlinearly. This information is quite important as the usual models assume strong nonlinearities when the waves are propagating in the azimuthal direction (i.e. along the satellite track) and almost no nonlinearities when propagating in the range direction. In this paper, the mapping of the ocean surface to the SAR image is reinterpreted and a specific model (i.e. a Second Order Volterra Model) is introduced. The nonlinearities are thus explained as either produced by a nonlinear system or due to waves propagating into selected directions (azimuth or range) and interacting during image formation. It is shown that quadratic nonlinearities occur for waves propagating near the range direction while for those travelling in the azimuthal direction the nonlinearities, when present, are mostly due to wave interactions but are almost completely removed by the filtering effect coming from the surface motion itself (azimuth cut-off). An inherent quadratic interaction filtering (azimuth high pass filter) is also present. But some other effects, apparently nonlinear, are not detected with the methods described here, meaning that either the usual relation developed for the Ocean-to-SAR transform is somewhat incomplete, although the mechanisms leading to its formulation seem to be correct, or that these nonlinearities cannot be detected in the classical bispectrum theory.
A spectral model for turbulence and microphysics dynamics in an ice cloud
Authors: Palmer A. J.
Published: April 2010

Abstract. A one-dimensional, nine-mode spectral model for temperature, velocity, and the mixing ratios of suspended and precipitating ice-particle components is shown to be consistent with ice-cloud observations. The observations include Doppler radar time-series measurements of a single winter ice cloud and direct measurements of mean particle size vs. icewater content for a set of ice clouds. Fitting of the model to the Doppler vertical-velocity measurements allows a prediction to be made of the vertical scale and turbulent Prandtl number active in the ice-cloud vertical motions. The model is then used to explore the question of how turbulence and gravity-wave motions affect the microphysical properties of an ice cloud. The model predicts interesting dynamical effects on the mixing ratios due to these motions, but no significant effects on the time-averaged microphysical quantities.
Statistical properties of galaxy distributions
Authors: Sylos Labini F. , Pietronero L.
Published: April 2010

Abstract. The recent availability of complete three dimensional samples of galaxies and clusters permits a direct study of their spatial properties. We present a brief review of galaxy correlations based on the methods modern statistical Physics. These methods which able to identify self-similar and non-analytical prop ties, allow us to test the usual homogeneity assumption of luminous matter distribution. We conclude that both the three dimensional prop ties, and the angular log N - log S relation, point out the fact that the distribution of galaxies and clusters fractal with D ≈ 2 up to the deepest scale probed luminous matter (≈≥ 1000h-1 Mpc). This result has important implications for the theoretical framework that should be adopted.
On the influence of a large scale coherent vortex on the turbulent cascade
Authors: Chillà F. , Pinton J.-F. , Labbé R.
Published: April 2010

Abstract. We investigate the flow between coaxial rotating disks in the situation where a strong axial vortex is present over a turbulent background. This is nonstationary and inhomogeneous as is common in most turbulent geophysical flows. We describe the s scale statistics using tools recently introduced for homogeneous turbulent flows. It seems that the cascade cess is preserved although modified by the large coherent structure.
A note on chaotic vs. stochastic behavior of the high-latitude ionospheric plasma density fluctuations
Authors: Wernik A. W. , Yeh K. C.
Published: April 2010

Abstract. Four data sets of density fluctuations measured in-situ by the Dynamics Explorer (DE 2) were analyzed in an attempt to study chaotic nature of the high-latitude turbulence and, in this way to complement the conventional spectral analysis. It has been found that the probability distribution function of density differences is far from Gaussian and similar to that observed in the intermittent fluid or MBD turbulence. This indicates that ionospheric density fluctuations are not stochastic but coherent to some extent. Wayland's and surrogate data tests for determinism in a time series of density data allowed us to differentiate between regions of intense shear and moderate shear. We observe that in the region of strong field aligned currents (FAC) and intense shear, or along the convection in the collisional regime, ionospheric turbulence behaves like a random noise with non-Gaussian statistics implying that the underlying physical process is nondeterministic. On the other hand, when FACs are weak, and shear is moderate or observations made in the inertial regime the turbulence is chaotic. The attractor dimension is lowest (1.9) for "old" convected irregularities. The dimension 3.2 is found for turbulence in the inertial regime and considerably smaller (2.4) in the collisional regime. It is suggested that a high dimension in the inertial regime may be caused by a complicated velocity structure in the shear instability region.
Cosmic ray momentum diffusion in the presence of nonlinear Alfvén waves
Authors: Michałek G. , Ostrowsky M.
Published: April 2010

Abstract. The relation between the spatial diffusion coefficient along the magnetic field, kII, and the momentum diffusion coefficient, Dp, for relativistic cosmic ray particles is modelled using Monte Carlo simulations. Wave fields with vanishing wave helicity and cross-helicity, constructed by superposing 'Alfvén-like' waves are considered. As the result, particle trajectories in high amplitude wave fields and then - by averaging over these trajectories - the values of transport coefficients are derived. The modelling is performed at various wave amplitudes, from δ B/B0 = 0.15 to 2.0, and for a number of wave field types. At our small amplitudes approximately the quasi-linear theory (QLT) estimates for kII and Dp are reproduced. However, with growing wave amplitude the simulated results show a small divergence from the QLT ones, with kII decreasing slower than theoretical prediction and the opposite being true for Dp. The wave field form gives only a slight influence on the wave-particle interactions at large wave amplitudes δ B/B0 ~ 1. The parameter characterizing the relative efficiency of the second-order to the first-order acceleration at shock waves, Dp κII is given in the QLT approximation by the Skilling formula V2A p2 / 9. In simulations together with increasing δ B it increases above this scale in all the cases under our study. Consequences of the present results for the second-order Fermi acceleration at shock waves are briefly addressed.
Manifestation of nonlinear elasticity in rock: convincing evidence over large frequency and strain intervals from laboratory studies
Authors: Johnson P. A. , Rasolofosaon P. N. J.
Published: April 2010

Abstract. Nonlinear elastic response in rock is established as a robust and representative characteristic rock rather than a curiosity. We show measurements of this behaviour from a variety of experiments on rock taken over many orders of magnitude in strain and frequency. The evidence leads to a pattern of unifying behaviour in rock: (1) Nonlinear response in rock is ubiquitous. (2) The response takes place over a large frequency interval (dc to 105 kHz at least). (3) The response not only occurs, as is commonly appreciated, large strains but also at small strains where this behaviour and the manifestations of this behaviour are commonly disregarded.
A reexamination of methods for evaluating the predictability of the atmosphere
Authors: Anderson J. L. , Hubeny V.
Published: April 2010

Abstract. Pioneering work by Lorenz (1965, 1968, 1969) developed a number of methods for exploring the limits of predictability of the atmosphere. One method uses an integration of a realistic numerical model as a surrogate for the atmosphere. The evolution of small perturbations to the integration are used to estimate how quickly errors resulting from a given observational error distribution would grow in this perfect model context. In reality, an additional constraint must be applied to this predictability problem. In the real atmosphere, only states that belong to the atmosphere's climate occur and one is only interested in how such realizable states diverge in time. Similarly, in a perfect model study, only states on the model's attractor occur. However, a prescribed observational error distribution may project on states that are off the attractor, resulting in unrepresentative error growth. The 'correct' error growth problem examines growth for the projection of the observational error distribution onto the model's attractor. Simple dynamical systems are used to demonstrate that this additional constraint is vital in order to correctly assess the rate of error growth. A naive approach in which this information about the model's 'climate' is not used can lead to significant errors. Depending on the dynamical system, error doubling times may be either underestimated or overestimated although the latter seems more likely for more realistic models. While the magnitude of these errors is not large in the simple dynamical systems examined, the impact could be much larger in more realistic forecast models.
The global characteristics of the three-dimensional thermal convection inside a spherical shell
Authors: Arkani-Hamed J.
Published: April 2010

Abstract. The Rayleigh number-Nusselt number, and the Rayleigh number-thermal boundary layer thickness relationships are determined for the three-dimensional convection in a spherical shell of constant physical parameters. Several models are considered with Rayleigh numbers ranging from 1.1 x 102 to 2.1 x 105 times the critical Rayleigh number. At lower Rayleigh numbers the Nusselt number of the three-dimensional convection is greater than that predicted from the boundary layer theory of a horizontal layer but agrees well with the results of an axisymmetric convection in a spherical shell. At high Rayleigh numbers of about 105 times the critical value, which are the characteristics of the mantle convection in terrestrial planets, the Nusselt number of the three-dimensional convection is in good agreement with that of the boundary layer theory. At even higher Rayleigh numbers, the Nusselt number of the three-dimensional convection becomes less than those obtained from the boundary layer theory. The thicknesses of the thermal boundary layers of the spherical shell are not identical, unlike those of the horizontal layer. The inner thermal boundary is thinner than the outer one, by about 30- 40%. Also, the temperature drop across the inner boundary layer is greater than that across the outer boundary layer.
Eddy growth and mixing in mesoscale oceanographic flows
Authors: Haller G. , Poje A. C.
Published: April 2010

Abstract. We study the relation between changes in the Eulerian topology of a two dimensional flow and the mixing of fluid particles between qualitatively different regions of the flow. In general time dependent flows, streamlines and particle paths are unrelated. However, for many mesoscale oceanographic features such as detaching rings and meandering jets, the rate at which the Euierian structures evolve is considerably slower than typical advection speeds of Lagrangian tracers. In this note we show that for two-dimensional, adiabatic fluid flows there is a direct relationship between observable changes in the topology of the Eulerian field and the rate of transport of fluid particles. We show that a certain class of flows is amenable to adiabatic or near adiabatic analysis, and, as an example, we use our results to study the chaotic mixing in the Dutkiewicz and Paldor (1994) kinematic model of the interaction of a meandering barotropic jet with a strong eddy.