bluuebunny/crossref_metadata_2025 huggingface dataset:
Renormalization group method for Farley-Buneman fluctuations: basic results
Authors: Hamza A. M.
Published: April 2010

Abstract. Sudan and Keskinen in [1979] derived a set of equations governing the nonlinear evolution of density fluctuations in a low-pressure weakly ionized plasma driven unstable by the E x B or gradient-drift instability. This problem is of fundamental importance in ionospheric physics. The nonlinear nature of the equations makes it very hard to write a closed form solution. In this paper we propose to use "Dynamical Renormalization Group" methods to study the long-- wavelength, long-time behaviour of density correlations generated in this ionospheric plasma stirred by a Gaussian random force characterized by a correlation function (fk fk) k. The effect of the small scales on the large scale dynamics in the limit k -> 0 and infinite "Reynolds" number, can be expressed in the form of renormalized coefficients; in our case renormalized diffusion. If one assumes the power spectra to be given by the kolmogorov argument of cascading of energy, then one can not only derive a subgrid model based on the results of RNG, and this has been done by Hamza and Sudan [1995], but one can also extract the skewness of the spectra as we do in this paper.
A new theoretical paradigm to describe hysteresis, discrete memory and nonlinear elastic wave propagation in rock
Authors: McCall K. R. , Guyer R. A.
Published: April 2010

Abstract. The velocity of sound in rock is a
strong function of pressure, indicating that wave propagation in rocks
is very nonlinear. The quasistatic elastic properties of rocks axe hysteretic, possessing discrete memory. In this paper
a new theory is developed, placing all of these properties (nonlinearity, hysteresis, and memory) on equal footing. The starting point of the new theory is closer to a
microscopic description of a rock than the starting point of the traditional five-constant theory of nonlinear elasticity. However, this starting point (the number density ρ of generic mechanical elements in an abstract space) is deliberately independent of a specific microscopic model. No
prejudice is imposed as to the mechanism causing nonlinear response
in the microscopic mechanical elements. The new theory (1)
relates suitable stress-strain measurements to the number density ρ and (2) uses the number density ρ to find
the behaviour of nonlinear elastic waves. Thus the new theory provides
for the synthesis of the full spectrum of elastic behaviours of
a rock. Early development of the new theory is sketched in this contribution.
Intermittency, non-Gaussian statistics and fractal scaling of MHD fluctuations in the solar wind
Authors: Marsch E. , Tu C.-Y.
Published: April 2010

Abstract. This paper gives a review of some recent work on intermittency, non-Gaussian statistics, and fractal scaling of solar wind magnetohydrodynamic turbulence. Model calculations and theories are discussed and put in their context with the in-situ observations of the solar wind fluctuations, essentially of the flow velocity and magnetic field. Emphasis is placed more on a comparison of the data with the theory than on a complete derivation of the model results, which are treated in a more tutorial fashion. The introduction reminds of some important observations and key aspects of the solar wind turbulence. Then structure functions are defined and observational results discussed. The probability density functions provide a direct means to analyse the statistical properties of the fluctuations. Evidence for non-Gaussian statistics is provided. Intermittency and simple scaling models are discussed, which yield algebraic expressions for the scaling exponents of the structure functions. The concept of the extended self-similarity is presented and corresponding observational evidence for its existence in the solar wind is provided. Subsequently, and extended structure function model, including the p-model scaling and a scale-dependent cascade, is discussed and compared with selected measurements. The basics of the multifractals are presented and applied to solar wind data. The multifractal scaling of the kinetic energy flux as proxy for the unknown cascading rate is established observationally, and the so-called multifractal spectrum is obtained. Finally, the scaling exponents of the associated correlation functions are derived and analysed. The paper concludes with a discussion of the empirical results and prospects for the future research in this field and in solar wind MHD turbulence in general.
Width dependent collisionless electron dynamics in the static fields of the shock ramp, 1, Single particle behavior and implications for downstream distribution
Authors: Gedalin M. , Balikhin M. A.
Published: April 2010

Abstract. We study the collisionless dynamics of electrons in the shock ramp using the numerical trajectory analysis in the model electric and magnetic fields of the shock. Even with very modest assumptions about the cross-shock potential the electron trajectories are very sensitive to the width of the ramp. The character of electron motion changes from the fully adiabatic (with conservation of v2  /B) when the ramp is wide, to the nonadiabatic one, when the ramp becomes sufficiently narrow. The downstream electron distribution also changes drastically, although this change depends on the initial electron temperature.
Approximate asymptotic integration of a higher order water-wave equation using the inverse scattering transform
Authors: Osborne A. R.
Published: April 2010

Abstract. The complete mathematical and physical characterization of nonlinear water wave dynamics has been an important goal since the fundamental partial differential equations were discovered by Euler over 200 years ago. Here I study a subset of the full solutions by considering the irrotational, unidirectional multiscale expansion of these equations in shallow-water. I seek to integrate the first higher-order wave equation, beyond the order of the Korteweg- deVries equation, using the inverse scattering transform. While I am unable to integrate this equation directly, I am instead able to integrate an analogous equation in a closely related hierarchy. This new integrable wave equation is tested for physical validity by comparing its linear dispersion relation and solitary wave solution with those of the full water wave equations and with laboratory data. The comparison is remarkably close and thus supports the physical applicability of the new equation. These results are surprising because the inverse scattering transform, long thought to be useful for solving only very special, low-order nonlinear wave equations, can now be thought of as a useful tool for approximately integrating a wide variety of physical systems to higher order. I give a simple scenario for adapting these results to the nonlinear Fourier analysis of experimentally measured wave trains.
Particle-in-cell simulations of a lens on an f-plane
Authors: Kirwan, Jr. A. D. , Grosch C. E. , Holdzkom II. J. J.
Published: April 2010

Abstract. A particle-in-cell ansatz for solving the Euler equations in a rotating frame is described. The approach is ideally suited for "layered" models of flows with sharp density and velocity fronts. The material and Coriolis accelerations in the Euler equations are solved at each particle while the gradient accelerations are evaluated on a grid and interpolated at each time step to the particles. The height of each particle is fixed and, depending on the application may be constant for all particles or may vary from particle to particle. The approach is used here to predict the evolution of a lens in a layered model with lower layer outcropping. The integral invariant of the volume is conserved exactly and total energy and total angular momentum are conserved to within 3% throughout a 30 day simulation. Exceptional resolution of the density and velocity fronts is maintained during the simulation without imposing any numerical viscosity. the model also reproduces essential characteristics of analytic solutions to a parabolic shaped lens. This algorithm is well suited to parallel implementation; all of the calculations reported here were done on an IBM SP2. Performance speedup and execution time as a function of the number of processors is given.
Wave interactions in a shallow-water model
Authors: Wiklund K.
Published: April 2010

Abstract. By using a Hamiltonian method, non-linear three-wave interaction in a class of systems related to the shallow water model is considered and a general coupling coefficient is presented. In the special case where two inertial waves and one Rossby wave interact resonantly, it is found that even a very small shear of the background velocity can be important in the interaction process. The stability of the system is considered by using a pseudo-energy method. Some implications for the dynamics of atmospheric flows are pointed out.
Integrable unsteady motion with an application to ocean eddies
Authors: Kirwan, Jr. A. D. , Lipphardt, Jr. B. L.
Published: April 2010

Abstract. Application of the Brown-Samelson theorem, which shows that particle motion is integrable in a class of vorticity-conserving, two-dimensional incompressible flows, is extended here to a class of explicit time dependent dynamically balanced flows in multilayered systems. Particle motion for nonsteady two-dimensional flows with discontinuities in the vorticity or potential vorticity fields (modon solutions) is shown to be integrable. An example of a two-layer modon solution constrained by observations of a Gulf Stream ring system is discussed.
On the spectral distribution of kinetic energy in large-scale atmospheric flow
Authors: Wiin-Nielsen A.
Published: April 2010

Abstract. A one-dimensional form of the equation of motion with forcing and dissipation is formulated in the spectral domain and used to make long term integrations from which the spectral distribution of the kinetic energy is determined The forcing in the wave number domain is determined in advance and kept constant for the duration of the time integrations. The dissipation is proportional to the second derivative of the velocity. The applied equation is made non-dimensional by selecting a length scale from which the time scale and the velocity scale may be determined. The resulting equation contains no parameters apart from the forcing. The integrations use a large number of spectral components and no approximation is made with respect to the non-linear interaction among the spectral components. Starting from an initial state in which all the velocity components are set to zero the equation is integrated for a long time to see if it reaches a steady state. The spectral distribution of the kinetic energy is determined in the steady state, and it is found that the distribution, in agreement with observational studies, may be approximated by a power law of the form n-3 within certain wave number regions. The wave numbers for which the -3 power law applies is found between the region of maximum forcing and the dissipation range. The intensity of the maximum forcing is varied to see how the resulting steady state varies. In addition, the maximum number of spectral components is varied. However, the available computing power sets an upper limit to the number of components.
Advection of pollutants by internal solitary waves in oceanic and atmospheric stable stratifications
Authors: Haarlemmer G. W. , Zimmerman W. B.
Published: April 2010

Abstract. When a pollutant is released into the ocean or atmosphere under turbulent conditions, even a steady release is captured by large eddies resulting in localized patches of high concentration of the pollutant. If such a cloud of pollutant subsequently enters a stable stratification-either a pycnocline or thermocline-then internal waves are excited. Since large solitary internal waves have a recirculating core, pollutants may be trapped in the sclitary wave, and advected large distances through the waveguide provided by the stratification. This paper addresses the mechanisms, through computer and physical simulation, by which a localized release of a dense pollutant results in solitary waves that trap the pollutant or disperse the pollutant faster than in the absence of the waves.
On the Hamiltonian approach: Applications to geophysical flows
Authors: Goncharov V. , Pavlov V.
Published: April 2010

Abstract. This paper presents developments of the Harniltonian Approach to problems of fluid dynamics, and also considers some specific applications of the general method to hydrodynamical models. Nonlinear gauge transformations are found to result in a reduction to a minimum number of degrees of freedom, i.e. the number of pairs of canonically conjugated variables used in a given hydrodynamical system. It is shown that any conservative hydrodynamic model with additional fields which are in involution may be always reduced to the canonical Hamiltonian system with three degrees of freedom only. These gauge transformations are associated with the law of helicity conservation. Constraints imposed on the corresponding Clebsch representation are determined for some particular cases, such as, for example. when fluid motions develop in the absence of helicity. For a long time the process of the introduction of canonical variables into hydrodynamics has remained more of an intuitive foresight than a logical finding. The special attention is allocated to the problem of the elaboration of the corresponding regular procedure. The Harniltonian Approach is applied to geophysical models including incompressible (3D and 2D) fluid motion models in curvilinear and lagrangian coordinates. The problems of the canonical description of the Rossby waves on a rotating sphere and of the evolution of a system consisting of N singular vortices are investigated.
The run-up of weakly-two-dimensional solitary pulses
Authors: Brocchini M.
Published: April 2010

Abstract. The run-up of solitary-type pulses propagating at a small angle with respect to the shore normal is analysed by means of a weakly-two-dimensional extension of a solution of the nonlinear shallow water equations for a non-breaking, solitary pulse incident and reflecting on an inclined plane beach similar to that of Synolakis (1987). A simple analytic expression for the longshore velocity of the solitarytype pulse is given along with examples of computations. The proposed solution can be employed in modelling run-up flow properties of solitary-type pulses (e.g. tsunamis, primary waves of wave groups propagating in shallow waters, ...). The hodograph transformation that is used and the flow properties are illustrated in terms of contour plots. A limiting pulse amplitude is defined such that breakdown of the solution occurs. A solution for the run-up of multiplesolitary-pulses in shallow waters is also described. Some of the salient characteristics are illustrated and discussed. Breakdown conditions are analytically defined also for the multiple-solitary-pulses solution. A strong condition is given which couples information on both pulses amplitudes and distances. An easier (but weaker) version of the criterion is given in terms of a pair of decoupled formulae one for the Pulses amplitudes and the second for their initial positions. Very large run-up is achieved because of the merging of two or more solitary pulses which are smaller than the limiting Pulse. The role of pulse separation within a group of solitary Pulses is also analysed in terms of both a 'nonlinearity parameter' N and a 'groupiness parameter' G. It is found that a critical distance exists between two pulses which minimizes the back-wash velocity and, as a consequence, the nonlinearity parameter N.
The nonlinear dustgrain-charging on large amplitude electrostatic waves in a dusty plasma with trapped ions
Authors: Nejoh Y.-N.
Published: April 2010

Abstract. The nonlinear dustgrain-charging and the influence of the ion density and temperature on electrostatic waves in a dusty plasma having trapped ions are investigated by numerical calculation. This work is the first approach to the effect of trapped ions in dusty plasmas. The nonlinear variation of the dust-charge is examined, and it is shown that the characteristics of the dustcharge number sensitively depend on the plasma potential, Mach number, dust mass-to-charge ratio, trapped ion density and temperature. The fast and slow wave modes are shown in this system. An increase of the ion temperature decreases the dust-charging rate and the propagation speed of ion waves. It is found that the existence of electrostatic ion waves sensitively depends on the ion to electron density ratio. New findings of the variable-charge dust grain particles, ion density and temperature in a dusty plasma with trapped ions are predicted.
Bounded lognormal cascades as quasi-multiaffine random processes
Authors: Menabde M.
Published: April 2010

Abstract. A new model for simulating non-negative random processes is developed. The model is based on a bounded random multiplicative cascade with a lognormal generator with the scale parameter dependent on the number of steps in the cascade. It is shown, both analytically and numerically, that the simulated field has multiaffine properties within some restricted range of scales. This type of random processes is defined here as quasi-multiaffine. A procedure for retrieving the modelling parameters from real data is also discussed.
Chaos in Magnetoplasmas
Authors: Buti B.
Published: April 2010

Abstract. A nonlinear wave, in general, is equivalent to a nonlinear dynamical system, which exhibits the phenomena of chaos. By means of techniques of nonlinear dynamical systems, we have investigated the conditions under which nonlinear Alfvén waves and lower-hybrid waves can become chaotic. The role of heavy ions, in controlling the chaos in magnetoplasmas, is examined. Chaotic routes to Alfvénic turbulence, with k-1 spectra, are observed in case of externally driven nonlinear Alfvén waves. Anomalous heating and particle acceleration resulting from chaotic fields, generated by lower-hybrid waves, are briefly outlined.
Characteristics of electrostatic solitary waves observed in the plasma sheet boundary: Statistical analyses
Authors: Kojima H. , Omura Y. , Matsumoto H. , Miyaguti K. , Mukai T.
Published: April 2010

Abstract. We present the characteristics of the Electrostatic Solitary Waves (ESW) observed by the Geotail spacecraft in the plasma sheet boundary layer based on the statistical analyses. We also discuss the results referring to a model of ESW generation due to electron beams, which is proposed by computer simulations. In this generation model, the nonlinear evolution of Langmuir waves excited by electron bump-on-tail instabilities leads to formation of isolated electrostatic potential structures corresponding to "electron hole" in the phase space. The statistical analyses of the Geotail data, which we conducted under the assumption that polarity of ESW potentials is positive, show that most of ESW propagate in the same direction of electron beams, which are observed by the plasma instrument, simultaneously. Further, we also find that the ESW potential energy is much smaller than the background electron thermal energy and that the ESW potential widths are typically shorter than 60 times of local electron Debye length when we assume that the ESW potentials travel in the same velocity of electron beams. These results are very consistent with the ESW generation model that the nonlinear evolution of electron bump-on-tail instability leads to the formation of electron holes in the phase space.
Nonlinear analysis of magnetospheric data Part I. Geometric characteristics of the AE index time series and comparison with nonlinear surrogate data
Authors: Pavlos G. P. , Athanasiu M. A. , Kugiumtzis D. , Hatzigeorgiu N. , Rigas A. G. , Sarris E. T.
Published: April 2010

Abstract. A long AE index time series is used as a crucial magnetospheric quantity in order to study the underlying dynainics. For this purpose we utilize methods of nonlinear and chaotic analysis of time series. Two basic components of this analysis are the reconstruction of the experimental tiine series state space trajectory of the underlying process and the statistical testing of an null hypothesis. The null hypothesis against which the experimental time series are tested is that the observed AE index signal is generated by a linear stochastic signal possibly perturbed by a static nonlinear distortion. As dis ' ' ating statistics we use geometrical characteristics of the reconstructed state space (Part I, which is the work of this paper) and dynamical characteristics (Part II, which is the work a separate paper), and "nonlinear" surrogate data, generated by two different techniques which can mimic the original (AE index) signal. lie null hypothesis is tested for geometrical characteristics which are the dimension of the reconstructed trajectory and some new geometrical parameters introduced in this work for the efficient discrimination between the nonlinear stochastic surrogate data and the AE index. Finally, the estimated geometric characteristics of the magnetospheric AE index present new evidence about the nonlinear and low dimensional character of the underlying magnetospheric dynamics for the AE index.
Nonlinear viscoelastic compaction in sedimentary basins
Authors: Yang X.-S.
Published: April 2010

Abstract. In the mathematical modelling of sediment compaction and porous media flow, the rheological behaviour of sediments is typically modelled in terms of a nonlinear relationship between effective pressure pe and porosity Φ, that is pe = pe (Φ). The compaction law is essentially a poroelastic one. However, viscous compaction due to pressure solution becomes important at larger depths and causes this relationship to become more akin to a viscous rheology. A generalised viscoelastic compaction model of Maxwell type is formulated, and different styles of nonlinear behaviour are asymptotically analysed and compared in this paper.
Wavelet filtering of chaotic data
Authors: Grzesiak M.
Published: April 2010

Abstract. Satisfactory method of removing noise from experimental chaotic data is still an open problem. Normally it is necessary to assume certain properties of the noise and dynamics, which one wants to extract, from time series. The wavelet based method of denoising of time series originating from low-dimensional dynamical systems and polluted by the Gaussian white noise is considered. Its efficiency is investigated by comparing the correlation dimension of clean and noisy data generated for some well-known dynamical systems. The wavelet method is contrasted with the singular value decomposition (SVD) and finite impulse response (FIR) filter methods.
Thin and superthin ion current sheets. Quasi-adiabatic and nonadiabatic models
Authors: Zelenyi L. M. , Sitnov M. I. , Malova H. V. , Sharma A. S.
Published: April 2010

Abstract. Thin anisotropic current sheets (CSs) are phenomena of the general occurrence in the magnetospheric tail. We develop an analytical theory of the self-consistent thin CSs. General solitions of the Grad-Shafranov equation are obtained in a quasi-adiabatic approximation which neglects the jumps of the sheet adiabatic invariant Iz This is possible if the anisotropy of the initial distribution function is not too strong. The resulting structure of the thin CSs is interpreted as a sum of negative dia- and positive paramagnetic currents flowing near the neutral plane. In the immediate vicinity of the magnetic field reversal region the paramagnetic current arising from the meandering motion of the ions on Speiser orbits dominates. The maximum CS thick-ness is achieved in the case of weak plasma anisotropy and is of the order of the thermal ion gyroradius outside the sheet. A unified picture of thin CS scalings includes both the quasi-adiabatic regimes of weak and strong anisotropies and the nonadiabatic limit of super-strong anisotropy of the source ion distribution. The later limit corresponds to the case of almost field-aligned initial distribution, when the ratio of the drift velocity outside the CS to the thermal ion velocity exceeds the ratio of the magnetic field outside the CS to its value in-side the CS (vD/vT> B0/Bn). In this regime the jumps of Iz, become essential, and the current sheet thickness is approaching to some small but finite value, which depends upon the parameter Bn /B0. Convective electric field increases the effective anisotropy of the source distribution and might produce the essential CS thinning which could have important implications for the sub-storm dynamics.
Kinetic simulations of the coupling between current instabilities and reconnection in thin current sheets
Authors: Wiegelmann T. , Büchner J.
Published: April 2010

Abstract. We investigate the coupling between current and tearing instability modes of a thin current sheet using the particle code GISMO. We identify pure tearing modes (kx≠ 0), instabilities in the current flow direction (ky≠ 0) and general 3D reconnection modes (kx≠ 0 and ky≠ 0). Our results give evidence that the coupling between tearing modes and current instabilities plays an important role for spontaneous magnetic reconnection. These modes give a substantial contribution to magnetic reconnection, additional to the well known 2D tearing mode. When allowing reconnection to occur in three spatial dimensions, a configuration, which was initially invariant in the current How direction, develops into a configuration with no invariant direction.
Three-dimensional simulation of the electromagnetic ion/ion beam instability: cross field diffusion
Authors: Kucharek H. , Scholder M. , Matthews A. P.
Published: April 2010

Abstract. In a system with at least one ignorable spatial dimension charged particles moving in fluctuating fields are tied to the magnetic field lines. Thus, in one-and two-dimensional simulations cross-field diffusion is inhibited and important physics may be lost. We have investigated cross-field diffusion in self-consistent 3-D magnetic turbulence by fully 3-dimensional hybrid simulation (macro-particle ions, massless electron fluid). The turbulence is generated by the electromagnetic ion/ion beam instability. A cold, low density, ion beam with a high velocity stream relative to the background plasma excites the right-hand resonant instability. Such ion beams may be important in the region of the Earth's foreshock. The field turbulence scatters the beam ions parallel as well as perpendicular to the magnetic field. We have determined the parallel and perpendicular diffusion coefficient for the beam ions in the turbulent wave field. The result compares favourably well (within a factor 2) with hard-sphere scattering theory for the cross-field diffusion coefficient. The cross-field diffusion coefficient is larger than that obtained in a static field with a Kolmogorov type spectrum and similar total fluctuation power. This is attributed to the resonant behaviour of the particles in the fluctuating field.
Nonlinear wave-particle interaction upstream from the Earth's bow shock
Authors: Mazelle C. , Le Quéau D. , Meziane K.
Published: April 2010

Abstract. Well-defined ring-like backstreaming ion distributions have been recently reported from observations made by the 3DP/PESA-High analyzer onboard the WIND spacecraft in the Earth's foreshock at large distances from the bow shock, which suggests a local production mechanism. The maximum phase space density for these distributions remains localized at a nearly constant pitch-angle value for a large number of gyroperiods while the shape of the distribution remains very steady. These distributions are also observed in association with quasi-monochromatic low frequency (~ 50 mHz) waves with substantial amplitude (δB/B>0.2). The analysis of the magnetic field data has shown that the waves are propagating parallel to the background field in the right-hand mode. Parallel ion beams are also often observed in the same region before the observation of both the ring-like distributions and the waves. The waves appear in cyclotron resonance with the ion parallel beams. We investigate first the possibility that the ion beams could provide the free energy source for driving an ion/ion instability responsible for the ULF wave occurrence. For that, we solve the wave dispersion relation with the observed parameters. Second, we show that the ring-like distributions could then be produced by a coherent nonlinear wave-particle interaction. It tends to trap the ions into narrow cells in velocity space centered on a well-defined pitch-angle, directly related to the saturation wave amplitude in the analytical theory. The theoretical predictions are in good quantitative agreement with the observations
On wave turbulence in MHD
Authors: Galtier S. , Nazarenko S. V. , Newell A. C.
Published: April 2010

Abstract. We describe the fundamental differences between weak (wave) turbulence in incompressible and weakly compressible MHD at the level of three-wave interactions. The main difference is in the structure of the resonant manifolds and the mechanisms of redistribution of spectral densities along the applied magnetic field B0. Similar to pure acoustic waves, a three-wave resonance between collinear wave vectors is observed but, in addition, we also have a resonance through tilted planes and spheres. The properties of resonances and their consequences for the asymptotics are also discussed.
Nonlinear evolution of the parametric instability: numerical predictions versus observations in the heliosphere
Authors: Malara F. , Primavera L. , Veltri P.
Published: April 2010

Abstract. Low-frequency turbulence in the solar wind is characterized by a high degree of Alfvénicity close to the Sun. Cross-helicity, which is a measure of Alfvénic correlation, tends to decrease with increasing distance from the Sun at high latitudes as well as in slow-speed streams at low latitudes. In the latter case, large scale inhomogeneities (velocity shears, the heliospheric current sheet) are present, which are sources of decorrelation; yet at high latitudes, the wind is much more homogeneous, and a possible evolution mechanism is represented by the parametric instability. The parametric decay of an circularly polarized broadband Alfvén wave is then investigated, as a source of decorrelation. The time evolution is followed by numerically integrating the full set of nonlinear MHD equations, up to instability saturation. We find that, for   ~ 1, the final cross-helicity is ~ 0.5, corresponding to a partial depletion of the initial correlation. Compressive fluctuations at a moderate level are also present. Most of the spectrum is dominated by forward propagating Alfvénic fluctuations, while backscattered fluctuations dominate large scales. With increasing time, the spectra of Elsässer variables tend to approach each other. Some results concerning quantities measured in the high-latitude wind are reviewed, and a qualitative agreement with the results of the numerical model is found.
Climate model attractors: chaos, quasi-regularity and sensitivity to small perturbations of external forcing
Authors: Dymnikov V. P. , Gritsoun A. S.
Published: April 2010

Abstract. In this paper we discuss some theoretical results obtained for climate models (theorems for the existence of global attractors and inertial manifolds, estimates of attractor dimension and Lyapunov exponents, symmetry property of Lyapunov spectrum). We define the conditions for "quasi-regular behaviour" of a climate system. Under these conditions, the system behaviour is subject to the Kraichnan fluctuation-dissipation relation. This fact allows us to solve the problem of determining a system's sensitivity to small perturbations to an external forcing. The applicability of the above approach to the analysis of the climate system sensitivity is verified numerically with the example of the two-layer quasi-geostrophic atmospheric model.
Bifurcations and instabilities in rotating two-layer fluids: I.f-plane
Authors: Lovegrove A. F. , Moroz I. M. , Read P. L.
Published: April 2010

Abstract. In this paper, we show that the behaviour of weakly nonlinear waves in a 2-layer model of baroclinic instability on an f-plane with varying viscosity is determined by a single, degenerate codimension three bifurcation. In the process, we show how previous studies, using the method of multiple scales to derive evolution equations for the slowly varying amplitude of the growing wave, arise as special limits of the general evolution description. A companion study will extend the results to a β-plane.
The role of soil states in medium-range weather predictability
Authors: Fukutome S. , Prim C. , Schär C.
Published: April 2010

Abstract. Current day operational ensemble weather prediction systems generally rely upon perturbed atmospheric initial states, thereby neglecting the eventual effect on the atmospheric evolution that uncertainties in initial soil temperature and moisture fields could bring about during the summer months. The purpose of this study is to examine the role of the soil states in medium-range weather predictability. A limited area weather prediction model is used with the atmosphere/ land-surface system in coupled or uncoupled mode. It covers Europe and part of the north Atlantic, and is driven by prescribed sea-surface temperatures over the sea, and by atmospheric reanalyses at its lateral boundaries. A series of  3 member ensembles of summer simulations are used to assess the predictability of a reference simulation assumed to be perfect. In a first step, two ensembles are simulated: the first with the atmosphere coupled to the land-surface model, the second in the uncoupled mode with perfect soil conditions prescribed every 6 hours. Subsequent experiments are combinations thereof, in which the uncoupled and coupled modes alternate in the course of a simulation. The results show that there are "stable" and "unstable" periods in the weather evolution under consideration. During the stable periods, the predictability (measured in terms of ensemble spread at 500 hPa) of the coupled and uncoupled dynamical systems is almost identical; prescribing the perfect soil conditions has a negligible impact upon the atmospheric predictability. In contrast, the predictability during an unstable phase is found to be remarkably improved in the uncoupled ensembles. This effect results from guiding the atmospheric phase-space trajectory along its perfect evolution. It persists even when switching back from the uncoupled to the coupled mode prior to the onset of the unstable phase, a result that underlines the importance of soil moisture and temperature in data assimilation systems.
Lyapunov, Floquet, and singular vectors for baroclinic waves
Authors: Samelson R. M.
Published: April 2010

Abstract. The dynamics of the growth of linear disturbances to a chaotic basic state is analyzed in an asymptotic model of weakly nonlinear, baroclinic wave-mean interaction. In this model, an ordinary differential equation for the wave amplitude is coupled to a partial differential equation for the zonal flow correction. The leading Lyapunov vector is nearly parallel to the leading Floquet vector f1 of the lowest-order unstable periodic orbit over most of the attractor. Departures of the Lyapunov vector from this orientation are primarily rotations of the vector in an approximate tangent plane to the large-scale attractor structure. Exponential growth and decay rates of the Lyapunov vector during individual Poincaré section returns are an order of magnitude larger than the Lyapunov exponent l ≈ 0.016. Relatively large deviations of the Lyapunov vector from parallel to f1 are generally associated with relatively large transient decays. The transient growth and decay of the Lyapunov vector is well described by the transient growth and decay of the leading Floquet vectors of the set of unstable periodic orbits associated with the attractor. Each of these vectors is also nearly parallel to f1. The dynamical splitting of the complete sets of Floquet vectors for the higher-order cycles follows the previous results on the lowest-order cycle, with the vectors divided into wave-dynamical and decaying zonal flow modes. Singular vectors and singular values also generally follow this split. The primary difference between the leading Lyapunov and singular vectors is the contribution of decaying, inviscidly-damped wave-dynamical structures to the singular vectors.
Numerical simulations of a three-wave coupling occurring in the ionospheric plasma
Authors: Usui H. , Matsumoto H. , Gendrin R.
Published: April 2010

Abstract. We studied a three-wave coupling process occurring in an active experiment of microwave power transmission (MPT) in the ionospheric plasma by performing one-dimensional electromagnetic PIC (Particle-In-Cell) simulations. In order to examine the spatial variation of the coupling process, we continuously emitted intense electromagnetic waves from an antenna located at a simulation boundary. In the three-wave coupling, a low-frequency electrostatic wave is excited as the result of a nonlinear interaction between the forward propagating pump wave and backscattered wave. In the simulations, low-frequency electrostatic bursts are discontinuously observed in space. The discontinuity of the electrostatic bursts is accounted for by the local electron heating due to the bursts and the associated modification of the wave dispersion relation. In a case where the pump wave propagates along the geomagnetic field Bext , several bursts of Langmuir waves are observed. Since the first burst consumes a part of the pump wave energy, the pump wave is weakened and cannot trigger the three-wave coupling beyond the region where the burst occurs. Since the dispersion relation of the Langmuir wave is variable, due to the local electron heating by the burst, the coupling condition eventually becomes unsatisfied and the first interaction becomes weak. Another burst of Langmuir waves is observed at a different region beyond the location of the first burst. In the case of perpendicular propagation, the upper hybrid wave, one of the mode branches of the electron cyclotron harmonic waves, is excited. Since the dispersion relation of the upper hybrid wave is less sensitive to the electron temperature, the coupling condition is not easily violated by the temperature increase. As a result, the three-wave coupling periodically takes place in time and eventually, the transmission ratio of the microwaves becomes approximately 20%, while almost no attenuation of the pump waves is observed after the first electrostatic burst in the parallel case. We also examined the dependency of the temporal growth rate for the electrostatic waves on the amplitude of the pump wave.
Impulse exchange at the surface of the ocean and the fractal dimension of drifter trajectories
Authors: Summers D. M.
Published: April 2010

Abstract. An impulse-based model is developed to represent a coupling between turbulent flow in the atmosphere and turbulent flow in the ocean. In particular, it is argued that the atmosphere flowing horizontally over the ocean surface generates a velocity fluctuation field in the latter's near-surface flow. The mechanism for this can be understood kinematically in terms of an exchange of tangentially-oriented fluid impulse at the air-sea interface. We represent this exchange numerically through the creation of Lagrangian elements of impulse density. An indication of the efficacy of such a model would lie in its ability to predict the observed fractal dimension of lateral trajectories of submerged floats set adrift in the ocean. To this end, we examine the geometry of lateral tracer-paths determined from the present model.
Scaling and singularity characteristics of solar wind and magnetospheric fluctuations
Authors: Vörös Z. , Jankovičová D. , Kovács P.
Published: April 2010

Abstract. Preliminary results are presented which suggest that scaling and singularity characteristics of solar wind and ground-based magnetic fluctuations appear to be a significant component in the solar wind-magnetosphere interaction processes. Of key importance is the intermittence of the "magnetic turbulence" as seen in ground-based and solar wind magnetic data. The methods used in this paper (estimation of flatness and multifractal spectra) are commonly used in the studies of fluid or MHD turbulence. The results show that single observatory characteristics of magnetic fluctuations are different from those of the multi-observatory AE-index. In both data sets, however, the influence of the solar wind fluctuations is recognizable. The correlation between the scaling/singularity features of solar wind magnetic fluctuations and the corresponding geomagnetic response is demonstrated in a number of cases. The results are also discussed in terms of patchy reconnection processes in the magnetopause and forced and/or self-organized criticality (F/SOC) of internal magnetosphere dynamics.
On the mean-field theory of the Karlsruhe Dynamo Experiment
Authors: Rädler K.-H. , Rheinhardt M. , Apstein E. , Fuchs H.
Published: April 2010

Abstract. In the Forschungszentrum Karlsruhe an experiment has been constructed which demonstrates a homogeneous dynamo as is expected to exist in the Earth's interior. This experiment is discussed within the framework of mean-field dynamo theory. The main predictions of this theory are explained and compared with the experimental results. Key words. Dynamo, geodynamo, dynamo experiment, mean-field dynamo theory, a-effect
Granular flow in equilibrium with the bottom: experimental analysis and theoretical prediction
Authors: Zanuttigh B. , Lamberti A.
Published: April 2010

Abstract. The paper presents measurements performed on the granular flow that develops in a drum partially filled with sand grains and rotating at various speeds. The aims of the paper are: to provide experimental evidence and measurements on grain flow in a drum; to compare theoretical and experimental velocity profiles; to point out discrepancies among theory and experiments. Velocity and "temperature" profiles were obtained with a Laser Doppler Anemometer (LDA) in the mid-section of the stream, where the flow is usually uniform; image analysis and visual observations of the flow were also carried out to evaluate the local slope, the depths of the characteristic flow regions and the concentration of the granular material. A semi-empirical relation that fits the experimental velocity profiles is presented and compared with Takahashi's velocity distributions for rigid and erodible bed. As proven by the distributions of free surface elevation, velocity, volumetric concentration and grain size across the drum, the three-dimensional nature of the flow field is not negligible. By increasing the drum rotation speed, in correspondence with critical and supercritical flows, changes in the flow regime are observed with formation of quasi-stationary surface waves. Wave development is described by analysing the extension and form of the experimental and theoretical velocity profiles. Wave effects on measurements are quantified and checked comparing the free-surface velocity-discharge relation obtained from experiments and from Takahashi's model for erodible bed.
Higher-order Korteweg-de Vries models for internal solitary waves in a stratified shear flow with a free surface
Authors: Grimshaw R. , Pelinovsky E. , Poloukhina O.
Published: April 2010

Abstract. A higher-order extension of the familiar Korteweg-de Vries equation is derived for internal solitary waves in a density- and current-stratified shear flow with a free surface. All coefficients of this extended Korteweg-de Vries equation are expressed in terms of integrals of the modal function for the linear long-wave theory. An illustrative example of a two-layer shear flow is considered, for which we discuss the parameter dependence of the coefficients in the extended Korteweg-de Vries equation.
Controlling thermal chaos in the mantle by positive feedback from radiative thermal conductivity
Authors: Dubuffet F. , Yuen D. A. , Rainey E. S. G.
Published: April 2010

Abstract. The thermal conductivity of mantle materials has two components, the lattice component klat from phonons and the radiative component krad due to photons. These two contributions of variable thermal conductivity have a nonlinear dependence in the temperature, thus endowing the temperature equation in mantle convection with a strongly nonlinear character. The temperature derivatives of these two mechanisms have different signs, with ∂klat /∂T negative and dkrad /dT positive. This offers the possibility for the radiative conductivity to control the chaotic boundary layer instabilities developed in the deep mantle. We have parameterized the weight factor between krad and klat with a dimensionless parameter f , where f = 1 corresponds to the reference conductivity model. We have carried out two-dimensional, time-dependent calculations for variable thermal conductivity but constant viscosity in an aspect-ratio 6 box for surface Rayleigh numbers between 106 and 5 × 106. The averaged Péclet < Pe > numbers of these flows lie between 200 and 2000. Along the boundary in f separating the chaotic and steady-state solutions, the < Pe > number decreases and the Nusselt number increases with internal heating, illustrating the feedback between internal heating and radiative thermal conductivity. For purely basal heating situation, the time-dependent chaotic flows become stabilized for values of f of between 1.5 and 2. The bottom thermal boundary layer thickens and the surface heat flow increases with larger amounts of radiative conductivity. For magnitudes of internal heating characteristic of a chondritic mantle, much larger values of f , exceeding 10, are required to quench the bottom boundary layer instabilities. By isolating the individual conductive mechanisms, we have ascertained that the lattice conductivity is partly responsible for inducing boundary layer instabilities, while the radiative conductivity and purely depth-dependent conductivity exert a stabilizing influence and help to control thermal chaos developed in the deep mantle. These results have been verified to exist also in three-dimensional geometry and would argue for the need to consider the potentially important role played by radiative thermal conductivity in controlling chaotic flows in time-dependent mantle convection, the mantle heat transfer, the number of hotspots and the attendant mixing of geochemical anomalies.
Cross recurrence plot based synchronization of time series
Authors: Marwan N. , Thiel M. , Nowaczyk N. R.
Published: April 2010

Abstract. The method of recurrence plots is extended to the cross recurrence plots (CRP) which, among others, enables the study of synchronization or time differences in two time series. This is emphasized in a distorted main diagonal in the cross recurrence plot, the line of synchronization (LOS). A non-parametrical fit of this LOS can be used to rescale the time axis of the two data series (whereby one of them is compressed or stretched) so that they are synchronized. An application of this method to geophysical sediment core data illustrates its suitability for real data. The rock magnetic data of two different sediment cores from the Makarov Basin can be adjusted to each other by using this method, so that they are comparable.