bluuebunny/crossref_metadata_2025 huggingface dataset:
Do climate simulations from models forced by averaged sea surface temperatures represent actual dynamics?
Authors: Roebber P. J. , Tsonis A. A. , Elsner J. B.
Published: April 2010

Abstract. Recently atmospheric general circulation models (AGCMs) forced by observed sea surface temperatures (SSTs) have offered the possibility of studying climate variability over periods ranging from years to decades. Such models represent and alternative to fully coupled asynchronous atmosphere ocean models whose long term integration remains problematic. Here, the degree of the approximation represented by this approach is investigated from a conceptual point of view by comparing the dynamical properties of a low order coupled atmosphere-ocean model to those of the atmospheric component of the same model when forced with monthly values of SST derived from the fully coupled simulation. The low order modelling approach is undertaken with the expectation that it may reveal general principles concerning the dynamical behaviour of the forced versus coupled systems; it is not expected that such an approach will determine the details of these differences, for which higher order modelling studies will be required. We discover that even though attractor (global) averages may be similar, local dynamics and the resultant variability and predictability characteristics differ substantially. These results suggest that conclusions concerning regional climatic variability (in time as well as space) drawn from forced modelling approaches may be contaminated by an inherently unquantifiable error. It is therefore recommended that this possibility be carefully investigated using state-of-the-art coupled AGCMs.
Three-wave coupling in a stratified MHD plasma
Authors: Axelsson P.
Published: April 2010

Abstract. A general coupling coefficient for three wave interactions in an ideal MHD plasma is presented. Using a special stratified background atmosphere, an explicit symmetric form of the coupling coefficient is derived.
Solitary wave in a Burridge-Knopoff model with slip-dependent friction as a clue to understanding the mechanism of the self-healing slip pulse in an earthquake rupture process
Authors: Wu Z. L. , Chen Y. T.
Published: April 2010

Abstract. A one-dimensional Burridge-Knopoff spring-block model with slip-dependent friction was studied to explore the possibility of a solitary wave solution existing for the problem of earthquake faulting. The result may be used as an alternative case of the crack model (e.g., Madariaga and Cochard, 1996) and the spring-block model with velocity-dependent friction (e.g., Carlson and Langer, 1989) in the understanding of the mechanism of the self-healing slip pulse proposed by Heaton (1990). In general, the conditions for a solitary wave solution to exist are discussed by the trajectory in the phase space. By taking the first order approximation, it is demonstrated that a solitary wave solution exists in which the slip behaves as a propagating solitary wave with the propagation velocity less than that of an acoustic (seismic) wave, and the source time function at each position remains the same. As an alternative approach other than numerical calculations, the analytical solution, although simple, sheds light on some of the properties of the self-healing slip pulse. From the solution it is seen that the width of the pulse depends on its propagation velocity and the friction, consistent with experience in physics. It is pointed out that the self-healing slip pulse may exist for a broad class of frictional constitutive laws which, to some extent, explains the fact that the self-healing slip pulse may be observed for a variety of earthquakes occurring within different seismogenic environments.
Dispersive mudslide-induced tsunamis
Authors: Rubino A. , Pierini S. , Backhaus J. O.
Published: April 2010

Abstract. A nonlinear nested model for mudslide-induced tsunamis is proposed in which three phases of the life of the wave, i.e. the generation, far-field propagation and costal run-up are described by means of different mathematical models, that are coupled through appropriate matching procedures. The generation and run-up dynamics are simulated through a nonlinear shallow-water model with movable lateral boundaries: in the generation region two active layers are present, the lower one describing the slide descending on a sloping topography. For the intermediate phase, representing wave propagation far from the generation region, the hydrostatic assumption is not assumed as appropriate in general and, therefore, a nonlinear model allowing for weak phase dispersion, namely a Kadomtsev-Petviashvili equation, is used. This choice is made in order to assess the relevance of dispersive features such as solitary waves and dispersive tails. It is shown that in some realistic circumstances dispersive mudslide-induced tsunami waves can be produced over relatively short, distances. In such cases the use of a hydrostatic model throughout the whole tsunami history turns out to give erroneous results. In particular, when solitary waves are generated during the tsunami propagation in the open sea, the resulting run-up process yields peculiar wave forms leading to amplified coastal inundations with respect to a mere hydrostatic context.
Evolution of unsteady jets in the Rayleigh-Taylor instability
Authors: Shtemler Y. M. , Sivashinsky G. I. , Cherniavski V. M.
Published: April 2010

Abstract. The paper concerns the temporal evolution of the Rayleigh-Taylor instability of two superimposed fluids in a vertical channel. At large times the instability results in the formation of a wide nearly-steady bubble of the lighter fluid rising through the channel, and thin long unsteady jets of the heavier fluid flowing down the channel walls. The jet flow appears to be tractable asymptotically by the method of matched expansions. The solution has been obtained with the planar tips of jets characterized by the jump of the interface slope.
Unstable periodic orbits and attractor of the barotropic ocean model
Authors: Kazantsev E.
Published: April 2010

Abstract. A numerical method for detection of unstable periodic orbits on attractors of nonlinear models is proposed.  The method requires similar techniques to data assimilation.  This fact facilitates its implementation for geophysical models.  This method was used to find numerically several low-period orbits for the barotropic ocean model in a square.  Some numerical particularities of application of this method are discussed. Knowledge of periodic orbits of the model helps to explain some of these features like bimodality of probability density functions (PDF) of principal parameters.  These PDFs have been reconstructed as weighted averages of periodic orbits with weights proportional to the period of the orbit and inversely proportional to the sum of positive Lyapunov exponents. The fraction of time spent in the vicinity of each periodic orbit has been compared with its instability characteristics. The relationship between these values shows the 93% correlation.  The attractor dimension of the model has also been approximated as a weighted average of local attractor dimensions in vicinities of periodic orbits.
Hamiltonian approach to the derivation of evolution equations for wave trains in weakly unstable media
Authors: Romanova N. N.
Published: April 2010

Abstract. The dynamics of weakly nonlinear wave trains in unstable media is studied. This dynamics is investigated in the framework of a broad class of dynamical systems having a Hamiltonian structure. Two different types of instability are considered. The first one is the instability in a weakly supercritical media. The simplest example of instability of this type is the Kelvin-Helmholtz instability. The second one is the instability due to a weak linear coupling of modes of different nature. The simplest example of a geophysical system where the instability of this and only of this type takes place is the three-layer model of a stratified shear flow with a continuous velocity profile. For both types of instability we obtain nonlinear evolution equations describing the dynamics of wave trains having an unstable spectral interval of wavenumbers. The transformation to appropriate canonical variables turns out to be different for each case, and equations we obtained are different for the two types of instability we considered. Also obtained are evolution equations governing the dynamics of wave trains in weakly subcritical media and in media where modes are coupled in a stable way. Presented results do not depend on a specific physical nature of a medium and refer to a broad class of dynamical systems having the Hamiltonian structure of a special form.
Error budget in systems with time-dependent forcings
Authors: Sancho P.
Published: April 2010

Abstract. The behaviour of the error growth is analyzed in several simple examples of systems with external time-dependent forcings. in some systems oscillations of the error around the saturation level can be observed. A common feature of these examples is the error growth dependence on initial time. In the examples here considered the improvement in the predictability derived from an adequate choice of the Initial time is comparable to those obtained by reducing the initial errors.
Hamiltonian formulation for the description of interfacial solitary waves
Authors: Grimshaw R. , Pudjaprasetya S. R.
Published: April 2010

Abstract. We consider solitary waves propagating on the interface between two fluids, each of constant density, for the case when the upper fluid is bounded above by a rigid horizontal plane, but the lower fluid has a variable depth. It is well-known that in this situation, the solitary waves can be described by a variable-coefficient Korteweg-de Vries equation. Here we reconsider the derivation of this equation and present a formulation which preserves the Hamiltonian structure of the underlying system. The result is a new variable-coefficient Korteweg-de Vries equation, which conserves energy to a higher order than the more conventional well-known equation. The new equation is used to describe the transformation of an interfacial solitary wave which propagates into a region of decreasing depth.
The nonlinear evolution of unstable coupled equatorial ocean-atmosphere modes
Authors: van der Vaart P. C. F. , Dijkstra H. A.
Published: April 2010

Abstract. In this paper we investigate whether observed intraseasonal variability in the equatorial Pacific can be attributed to finite amplitude waves resulting from unstable air-sea interactions. Within a Zebiak - Cane type model of the coupled equatorial ocean - atmosphere, the nonlinear equilibration of instabilities of a simple basic state is considered with periodic conditions on the ocean boundaries. Three mechanisms exist which can induce a finite amplitude equilibration on a time scale ε2t. Here t is the characteristic time scale of growth of the disturbance and ε the relative distance from the instability threshold. For each equilibration mechanism, the finite amplitude and period of the equilibrium state are computed as a function of ε and substantial amplitude can be reached for a reasonable degree of supercriticality. Thereafter the analysis is extended to include time-dependent external forcing. It is shown that interannual variability may result through the interaction of the response of a weak annual external forcing and the finite amplitude development of the intraseasonal instabilities.
Phase space structure and fractal trajectories in 1½ degree of freedom Hamiltonian systems whose time dependence is quasiperiodic
Authors: Brown M. G.
Published: April 2010

Abstract. We consider particle motion in nonautonomous 1 degree of freedom Hamiltonian systems for which H(p,q,t) depends on N periodic functions of t with incommensurable frequencies. It is shown that in near-integrable systems of this type, phase space is partitioned into nonintersecting regular and chaotic regions. In this respect there is no different between the N = 1 (periodic time dependence) and the N = 2, 3, ... (quasi-periodic time dependence) problems. An important consequence of this phase space structure is that the mechanism that leads to fractal properties of chaotic trajectories in systems with N = 1 also applies to the larger class of problems treated here. Implications of the results presented to studies of ray dynamics in two-dimensional incompressible fluid flows are discussed.
On the nonlinear dynamics of rupture
Authors: Ockendon H. , Turcotte D. L.
Published: April 2010

Abstract. The rupture on a fault resulting in an earthquake is clearly a complex process. In order to better understand this process the continuum version of the slider-block model has been considered in some detail. In particular, the role of a cohesive breakaway zone is considered. Solutions of a "piston" problem and a "shock-tube" problem are obtained. For the "dirven" problem the cohesive breakaway solution is combined with a viscous resistance on the fault to obtain solutions that are reasonably realistic in terms of fault rupture.
Diffusion model of interacting gravity waves on the surface of deep fluid
Authors: Zakharov V. E. , Pushkarev A. N.
Published: April 2010

Abstract. A simple phenomenological model for nonlinear interactions of gravity waves on the surface of deep water is developed. The Snl nonlinear interaction term in the kinetic equation for wave action is replaced by the nonlinear second-order diffusion-type operator. Analytical and numerical studies show that the new model gives a reasonably good description of a real situation, consuming three order of magnitude less computer time.
Internal gravity waves: Analysis using the periodic, inverse scattering transform
Authors: Zimmerman W. B. , Haarlemmer G. W.
Published: April 2010

Abstract. The discrete periodic inverse scattering transform (DPIST) has been shown to provide the salient features of nonlinear Fourier analysis for surface shallow water waves whose dynamics are governed by the Korteweg-de Vries (KdV) equation - (1) linear superposition of components with power spectra that are invariants of the motion of nonlinear dispersive waves and (2) nonlinear filtering. As it is well known that internal gravity waves also approximately satisfy the KdV equation in shallow stratified layers, this paper investigates the degree to which DPIST provides a useful nonlinear spectral analysis of internal waves by application to simulations and wave tank experiments of internal wave propagation from localized dense disturbances. It is found that DPIST analysis is sensitive to the quantity λ = (r/6s) * (ε/μ2), where the first factor depends parametrically on the Richardson number and the background shear and density profiles and the second factor is the Ursell number-the ratio of the dimensionless wave amplitude to the dimensionless squared wavenumber. Each separate wave component of the decomposition of the initial disturbance can have a different value, and thus there is usually just one component which is an invariant of the motion found by DPIST analysis. However, as the physical applications, e.g. accidental toxic gas releases, are usually concerned with the propagation of the longest wavenumber disturbance, this is still useful information. In cases where only long, monochromatic solitary waves are triggered or selected by the waveguide, the entire DPIST spectral analysis is useful.
Localized Alfvénic solutions of nondissipative and compressible MHD
Authors: Chanteur G.
Published: April 2010

Abstract. Alfvénic solutions of nondissipative MHD are entirely determined by their magnetic configuration. With the supplementary assumption of incompressibility any solenoidal field can be used to construct an Alfvénic solution. It is demonstrated that for nondissipative and compressible MHD the energy equation constrains the magnetic field of Alfvénic solutions to have a constant strength along field lines. Some topological solitons known in nondissipative and incompressible MHD do not have this property. New localized axisymmetric Alfvénic solutions of nondissipative and compressible MHD are explicitly constructed.
Polar spacecraft observations of the turbulent outer cusp/magnetopause boundary layer of Earth
Authors: Pickett J. S. , Menietti J. D. , Dowell J. H. , Gurnett D. A. , Scudder J. D.
Published: April 2010

Abstract. The orbit of the Polar spacecraft has been ideally suited for studying the turbulent region of the cusp that is located near or just outside the magnetopause current sheet at 7-9 RE. The wave data obtained in this region show that electromagnetic turbulence is dominant in the frequency range 1-10 Hz. The waves responsible for this turbulence usually propagate perpendicular to the local magnetic field and have an index of refraction that generally falls between the estimated cold plasma theoretical values of the electromagnetic lower hybrid and whistler modes and may be composed of both modes in concert with kinetic Alfvén waves and/or fast magnetosonic waves. Fourier spectra of the higher frequency wave data also show the electromagnetic turbulence at frequencies up to and near the electron cyclotron frequency. This higher frequency electromagnetic turbulence is most likely associated with whistler mode waves. The lower hybrid drift and current gradient instabilities are suggested as possible mechanisms for producing the turbulence. The plasma and field environment of this turbulent region is examined and found to be extremely complex. Some of the wave activity is associated with processes occurring locally, such as changes in the DC magnetic field, while others are associated with solar wind and interplanetary magnetic field changes.
Mirror mode structures and ELF plasma waves in the Giacobini-Zinner magnetosheath
Authors: Tsurutani B. T. , Lakhina G. S. , Smith E. J. , Buti B. , Moses S. L. , Coroniti F. V. , Brinca A. L. , Slavin J. A. , Zwickl R. D.
Published: April 2010

Abstract. We show evidence for mirror mode structures at comet Giacobini-Zinner. These are plasma structures with alternating high ß and low ß regions driven unstable when ß /ß > 1+ 1/. These structures are detected in a region just adjacent to the magnetic tail and have scale sizes of ≈ 12 H2O group ion cyclotron radii. Calculations are presented to show that mirror mode instability can occur due to the perpendicular pressure associated with H2O+ cometary pickup ions in the region of mirror mode observation. Adjacent regions (in the magnetic tail and further in the sheath) are found to be stable to the mirror mode. Plasma waves are detected in relation with the mirror mode structures. Low frequency 56 to 100 Hz waves are present in the high beta portions, and high frequency, 311 Hz to 10 kHz, waves are present in low beta regions. These may be electromagnetic lion roar waves and electrostatic festoon-shaped waves, respectively, in analogy to plasma waves detected in the Earth's magnetosheath.
Energetic particle cross-field diffusion: Interaction with Magnetic Decreases (MDs)
Authors: Tsurutani B. T. , Lakhina G. S. , Winterhalter D. , Arballo J. K. , Galvan C. , Sukurai R.
Published: April 2010

Abstract. Magnetic field Decreases (MDs) are detected in the heliospheric polar regions. The MDs have minimum spatial scales sizes of 25 proton thermal gyroradii, and are typically bounded by tangential or rotational discontinuities. The distribution of the magnitudes of the decreases within AIDs is a continuum, with the smallest decreases being most frequent in occurrence. The largest decreases can be 80% of the ambient field. The thickness distribution is also a continuum, and is shown to be independent of the field magnitude decrease. Charged particle interactions with the MDs lead to particle guiding center displacements and hence particle cross-held diffusion. We develop a diffusion model to apply to energetic ion interactions with MDs using the MD properties described in this paper. One specific day of data is used to illustrate that the particle cross-field diffusion will be extremely rapid due to such interactions.
Sporadic wind wave horse-shoe patterns
Authors: Annenkov S. Yu. , Shrira V. I.
Published: April 2010

Abstract. The work considers three-dimensional crescent-shaped patterns often seen on water surface in natural basins and observed in wave tank experiments. The most common of these 'horse-shoe-like' patterns appear to be sporadic, i.e., emerging and disappearing spontaneously even under steady wind conditions. The paper suggests a qualitative model of these structures aimed at explaining their sporadic nature, physical mechanisms of their selection and their specific asymmetric form. First, the phenomenon of sporadic horse-shoe patterns is studied numerically using the novel algorithm of water waves simulation recently developed by the authors (Annenkov and Shrira, 1999). The simulations show that a steep gravity wave embedded into widespectrum primordial noise and subjected to small nonconservative effects typically follows the simple evolution scenario: most of the time the system can be considered as consisting of a basic wave and a single pair of oblique satellites, although the choice of this pair tends to be different at different instants. Despite the effective low-dimensionality of the multimodal system dynamics at relatively sho ' rt time spans, the role of small satellites is important: in particular, they enlarge the maxima of the developed satellites. The presence of Benjamin-Feir satellites appears to be of no qualitative importance at the timescales under consideration. The selection mechanism has been linked to the quartic resonant interactions among the oblique satellites lying in the domain of five-wave (McLean's class II) instability of the basic wave: the satellites tend to push each other out of the resonance zone due to the frequency shifts caused by the quartic interactions. Since the instability domain is narrow (of order of cube of the basic wave steepness), eventually in a generic situation only a single pair survives and attains considerable amplitude. The specific front asymmetry is found to result from the interplay of quartic and quintet interactions and non-conservative effects: the growing and grown satellites have a specific value of phase with respect to the basic wave that corresponds to downwind orientation of the convex sides of wave fronts. As soon as the phase relation is violated, the satellite's amplitude quickly decreases down to the noise level.
On the advection of tracer by eddies on the beta-plane: A numerical study
Authors: Benilov E. S.
Published: April 2010

Abstract. The evolution of tracer "injected" into an equivalent barotropic eddy on the beta-plane is examined numerically. The eddy is governed by the standard quasigeostrophic equation, and the concentration of tracer is governed by the advection equation with diffusion. At the initial moment of time, the streamfunction and distribution of tracer are both radially or elliptically symmetric. After the first 10-30 days, a spirallike strip, where the gradient of concentration is large, develops in the tracer field, whereas the eddy remains smooth for a relatively long time. To put this conclusion in quantitative terms, a "tracer variability indicator" is introduced and shown to grow much faster than a similar characteristic of the potential vorticity field (notwithstanding the fact that the tracer concentration and PV satisfy the same governing equation). A simple explanation as to why the tracer is more affected by filamentation than PV is provided for eddies with small Burger number. It is demonstrated that the high-gradient strip develops, unless stopped by turbulent diffusion, into an inversion (non-monotonicity) of the tracer concentration field. Finally, the results of simulations are compared to the spiral patterns in the real-life eddies observed in the East Australian Current.
Nonlinear analysis of magnetospheric data Part II. Dynamical characteristics of the AE index time series and comparison with nonlinear surrogate data
Authors: Pavlos G. P. , Kugiumtzis D. , Athanasiu M. A. , Hatzigeorgiu N. , Diamantidis D. , Sarris E. T.
Published: April 2010

Abstract. In this study we have used dynamical characteristies such as Lyapunov exponents, nonlinear dynamic models and mutual information for the nonlinear analysis of the magnetospheric AE index time series. Similarly with the geometrical characteristic studied in Pavlos et al. (1999b), we have found significant differences between the original time series and its surrogate data. These results also suggest the rejection of the null hypothesis that the AE index belongs to the family of stochastic linear signals undergoing a static nonlinear distortion. Finally, we believe that these results support the hypothesis of nonlinearity and chaos for the magnetospheric dynamics.
Deterministic description of a phase transition in a medium of interacting waves
Authors: Vassalo Pereira J.
Published: April 2010

Abstract. We describe an effect of phase-locking catastrophe arising in an ensemble of a great number of oscillators interacting by means of their emitting waves. These waves can be either pulsatile, that is, soliton-like, or continuous stationary waves generated by the oscillators considered as resonators. Each one of these waves will introduce certain perturbations among the phases of the oscillators of the ensemble in such a way that it is possible to follow in time the distribution of these phases. In fact, we deduce the p.d.e's governing the evolution in time of this distribution, which displays a tendency of accumulating around certain of its values (phase-locking), and also of sudden increasing of the intensity of the physical effect (a "phase transition").
3D reconnection due to oblique modes: a simulation of Harris current sheets
Authors: Lapenta G. , Brackbill J. U.
Published: April 2010

Abstract. Simulations in three dimensions of a Harris current sheet with mass ratio, mi/me = 180, and current sheet thickness, pi/L = 0.5, suggest the existence of a linearly unstable oblique mode, which is independent from either the drift-kink or the tearing instability. The new oblique mode causes reconnection independently from the tearing mode. During the initial linear stage, the system is unstable to the tearing mode and the drift kink mode, with growth rates that are accurately described by existing linear theories. How-ever, oblique modes are also linearly unstable, but with smaller growth rates than either the tearing or the drift-kink mode. The non-linear stage is first reached by the drift-kink mode, which alters the initial equilibrium and leads to a change in the growth rates of the tearing and oblique modes. In the non-linear stage, the resulting changes in magnetic topology are incompatible with a pure tearing mode. The oblique mode is shown to introduce a helical structure into the magnetic field lines.
On a nonlinear state of the electromagnetic ion/ion cyclotron instability
Authors: Cremer M. , Scholer M.
Published: April 2010

Abstract. We have investigated the nonlinear properties of the electromagnetic ion/ion cyclotron instability (EMIIC) by means of hybrid simulations (macroparticle ions, massless electron fluid). The instability is driven by the relative (super-Alfvénic) streaming of two field-aligned ion beams in a low beta plasma (ion thermal pressure to magnetic field pressure) and may be of importance in the plasma sheet boundary layer. As shown in previously reported simulations the waves propagate obliquely to the magnetic field and heat the ions in the perpendicular direction as the relative beam velocity decreases. By running the simulation to large times it can be shown that the large temperature anisotropy leads to the ion cyclotron instability (IC) with parallel propagating Alfvén ion cyclotron waves. This is confirmed by numerically solving the electromagnetic dispersion relation. An application of this property to the plasma sheet boundary layer is discussed.
Magnetic holes in the solar wind between 0.3 AU and 17 AU
Authors: Sperveslage K. , Neubauer F. M. , Baumgärtel K. , Ness N. F.
Published: April 2010

Abstract. Magnetic holes (MHs) are depressions of the magnetic field magnitude. Turner et al. (1977) identified the first MHs in the solar wind and determined an occurrence rate of 1.5 MHs/d. Winterhalter et al. (1994) developed an automatic identification criterion to search for MHs in Ulysses data in the solar wind between 1 AU and 5.4 AU. We adopt their criterion to expand the search to the heliocentric distances down to 0.3 AU using data from Helios 1 and 2 and up to 17 AU using data from Voyager 2. We relate our observations to two theoretical approaches which describe the so-called linear MHs in which the magnetic vector varies in magnitude rather than direction. Therefore we focus on such linear MHs with a directional change less than 10º. With our observations of about 850 MHs we present the following results: Approximately 30% of all the identified MHs are linear. The maximum angle between the initial magnetic field vector and any vector inside the MH is 20º in average and shows a weak relation to the depth of the MHs. The angle between the initial magnetic field and the minimum variance direction of those structures is large and very probably close to 90º. The MHs are placed in a high β environment even though the average solar wind shows a smaller β. The widths decrease from about 50 proton inertial length in a region between 0.3 AU and 0.4 AU heliocentric distance to about 15 proton inertial length at distances larger than 10 AU. This quantity is correlated with the β of the MH environments with respect to the heliocentric distance. There is a clear preference for the occurrence of depressions instead of compressions. We discuss these results with regard to the main theories of MHs, the mirror instability and the alternative soliton approach. Although our observational results are more consistent with the soliton theory we favour a combination of both. MHs might be the remnants of initial mirror mode structures which can be described as solitons during the main part of their lifetime.
MHD effects of the solar wind flow around planets
Authors: Biernat H. K. , Erkaev N. V. , Farrugia C. J. , Vogl D. F. , Schaffenberger W.
Published: April 2010

Abstract. The study of the interaction of the solar wind with magnetized and unmagnetized planets forms a central topic of space research. Focussing on planetary magnetosheaths, we review some major developments in this field. Magnetosheath structures depend crucially on the orientation of the interplanetary magnetic field, the solar wind Alfvén Mach number, the shape of the obstacle (axisymmetric/non-axisymmetric, etc.), the boundary conditions at the magnetopause (low/high magnetic shear), and the degree of thermal anisotropy of the plasma. We illustrate the cases of Earth, Jupiter and Venus. The terrestrial magnetosphere is axisymmetric and has been probed in-situ by many spacecraft. Jupiter's magnetosphere is highly non-axisymmetric. Furthermore, we study magnetohydrodynamic effects in the Venus magnetosheath.
Modelling of large-scale structures arising under developed turbulent convection in a horizontal fluid layer (with application to the problem of tropical cyclone origination)
Authors: Levina G. V. , Starkov M. V. , Startsev Se. E. , Zimin V. D. , Mioseev S. S.
Published: April 2010

Abstract. The work is concerned with the results of theoretical and laboratory modelling the processes of the large-scale structure generation under turbulent convection in the rotating-plane horizontal layer of an incompressible fluid with unstable stratification. The theoretical model describes three alternative ways of creating unstable stratification: a layer heating from below, a volumetric heating of a fluid with internal heat sources and combination of both factors. The analysis of the model equations show that under conditions of high intensity of the small-scale convection and low level of heat loss through the horizontal layer boundaries a long wave instability may arise. The condition for the existence of an instability and criterion identifying the threshold of its initiation have been determined. The principle of action of the discovered instability mechanism has been described. Theoretical predictions have been verified by a series of experiments on a laboratory model. The horizontal dimensions of the experimentally-obtained long-lived vortices are 4÷6 times larger than the thickness of the fluid layer. This work presents a description of the laboratory setup and experimental procedure. From the geophysical viewpoint the examined mechanism of the long wave instability is supposed to be adequate to allow a description of the initial step in the evolution of such large-scale vortices as tropical cyclones - a transition form the small-scale cumulus clouds to the state of the atmosphere involving cloud clusters (the stage of initial tropical perturbation).
Toward an understanding of the nonlinear nature of atmospheric photochemistry: Origin of the complicated dynamic behaviour of the mesospheric photochemical system
Authors: Konovalov I. B. , Feigin A. M.
Published: April 2010

Abstract. The methods of nonlinear dynamics are used to reveal the origin of complicated dynamic behaviour (CDB) of a dynamic model of the mesospheric photochemical system (PCS) perturbed by diurnal variations in photolysis rates. We found that CDB appearance during the multi-day evolution is unambiguously determined by two peculiarities in the model behaviour during its 24-hours evolution. These peculiarities are the presence of a stage of abrupt changes in reagent concentrations and the "humped" dependence of the end-night atomic hydrogen concentrations on those at the beginning of the night. Using a successive analysis we found that these two peculiarities are, in turn, conditioned by the specific features of the chemical processes involved in the model, namely, by the catalytic cycle whose net rate is independent of the concentration of the destroyed species (here, it is atomic oxygen). We believe that similar peculiarities inherent in other atmospheric PCSs indicate that under appropriate conditions they may also demonstrate CDB. We identified the mechanism of the CDB appearance and described it in two ways. The first one reveals a sequence of the processes causing the exponential (on the average) growth of a perturbation of the solution with time. In particular, we found that the behaviour of small perturbations of an arbitrary solution of model equations is identical to the behaviour of a linear oscillator excited parametrically. The second way shows the mechanism of CDB appearance by means of 1-dimensional mapping, which is, basically, the same as the well-known Feigenbaum mappings.
Nonlinear analysis of magnitude and interevent time interval sequences for earthquakes of the Caucasian region
Authors: Matcharashvili T. , Chelidze T. , Javakhishvili Z.
Published: April 2010

Abstract. It is well known that lithospheric seismic processes are characterized by self-similarity or scale invariance in terms of earthquake-size, time, space and space-time distributions, although precise details of underlying dynamics are not clear. In this study we apply nonlinear dynamics theory tools, such as a correlation dimension, "surrogate" data analysis and positive Lyapunov exponent calculation, to investigate dynamical characteristics of seismicity in the Caucasian region. Interevent time intervals and magnitude sequences are considered for different area and magnitude windows. We find significant evidence of a low dimensional nonlinear structure of earthquake time distribution, obtained by consideration of time interval sequences between all events encountered, above some threshold magnitude, in the original catalogue. However nonlinear structure is absent in artificially generated sequences of time intervals between independent events as well as time intervals between aftershocks. It seems that this kind of filtration of the original catalogue destroys the existing temporal structure of considered lithospheric processes. Unlike artificial inter-aftershock time interval sequences, obtained by removing independent events from the original series, the time interval sequence between the Racha earthquake aftershocks reveals clear evidence of nonlinear structure. Earthquake magnitude dynamics. for all considered regions and magnitude windows, reveal high dimensional nonlinearity.
Evolution of magnetic helicity in the course of kinetic magnetic reconnection
Authors: Wiegelmann T. , Büchner J.
Published: April 2010

Abstract. We investigate the evolution of magnetic helicity density in the course of 2D and 3D kinetic magnetic reconnection through thin current sheets. In 2D, the helicity density near a reconnection X-line becomes purely quadrupolar structured, while in 3D, an additional dipolar structure occurs. This dipolar structure is related to kinetic current instabilities and becomes dominant for spontaneous 3D reconnection, in accordance with the dominating current instabilities. The 2D simulations have been carried out with a newly developed Vlasov-code and the 3D simulations with the particle-in-cell code GISMO.
An example of resonances, coherent structures and topological phase transitions - the origin of the low frequency broadband spectrum in the auroral zone
Authors: Chang T.
Published: April 2010

Abstract. We consider the phenomena of intermittent turbulence in magnetized space plasmas from the point of view of topological phase transitions involving the merging and interactions of anisotropic coherent structures. The stochastic behaviour of these coherent plasma structures can undergo complex changes as the dynamic system evolves, similar to those commonly observed in (first and second order) equilibrium phase transitions. When conditions are favourable, such topological entities can evolve into a state of forced and/or self-organized criticality (FSOC). As an example, we apply these ideas to the understanding of the origin of the commonly observed broadband power-law low frequency electric field spectral densities and the characteristic filamentary current structures in the auroral zone. The broadband turbulence can provide efficient resonant energization of the ionospheric oxygen ions.
Hilbert problems for the geosciences in the 21st century
Authors: Ghil M.
Published: April 2010

Abstract. The scientific problems posed by the Earth's fluid envelope, and its atmosphere, oceans, and the land surface that interacts with them are central to major socio-economic and political concerns as we move into the 21st century. It is natural, therefore, that a certain impatience should prevail in attempting to solve these problems. The point of this review paper is that one should proceed with all diligence, but not excessive haste: "festina lente," as the Romans said two thousand years ago, i.e. "hurry in a measured way." The paper traces the necessary progress through the solutions to the ten problems: 1. What is the coarse-grained structure of low-frequency atmospheric variability, and what is the connection between its episodic and oscillatory description? 2. What can we predict beyond one week, for how long, and by what methods? 3. What are the respective roles of intrinsic ocean variability, coupled ocean-atmosphere modes, and atmospheric forcing in seasonal-to-interannual variability? 4. What are the implications of the answer to the previous problem for climate prediction on this time scale? 5. How does the oceans' thermohaline circulation change on interdecadal and longer time scales, and what is the role of the atmosphere and sea ice in such changes? 6. What is the role of chemical cycles and biological changes in affecting climate on slow time scales, and how are they affected, in turn, by climate variations? 7. Does the answer to the question above give us some trigger points for climate control? 8. What can we learn about these problems from the atmospheres and oceans of other planets and their satellites? 9. Given the answer to the questions so far, what is the role of humans in modifying the climate? 10. Can we achieve enlightened climate control of our planet by the end of the century? A unified framework is proposed to deal with these problems in succession, from the shortest to the longest timescale, i.e. from weeks to centuries and millennia. The framework is that of dynamical systems theory, with an emphasis on successive bifurcations and the ergodic theory of nonlinear systems. The main ideas and methods are outlined and the concept of a modelling hierarchy is introduced. The methodology is applied across the modelling hierarchy to Problem 5, which concerns the thermohaline circulation and its variability. Key words. Climate dynamics, nonlinear systems, numerical bifurcations, mathematical geophysics
Diffusive draining and growth of eddies
Authors: Balasuriya S. , Jones C. K. R. T.
Published: April 2010

Abstract. The diffusive effect on barotropic models of mesoscale eddies is addressed, using the Melnikov method from dynamical systems. Simple geometric criteria are obtained, which identify whether a given eddy grows or drains out, under a diffusive (and forcing) perturbation on a potential vorticity conserving flow. Qualitatively, the following are shown to be features conducive to eddy growth (and, thereby, stability in a specific sense): (i) large radius of curvature of the eddy boundary, (ii) potential vorticity contours more tightly packed within the eddy than outside, (iii) acute eddy pinch-angle, (iv) small potential vorticity gradient across the eddy boundary, and (v) meridional wind forcing, which increases in the northward direction. The Melnikov approach also suggests how tendrils (filaments) could be formed through the breaking of the eddy boundary, as a diffusion-driven advective process.
A theory of the Earth's magnetic field and of sunspots, based on a self-excited dynamo incorporating the Hall effect
Authors: de Paor A.
Published: April 2010

Abstract. A new viewpoint on the generation and maintenance of the Earth's magnetic field is put forward, which integrates self-exciting dynamo theory with the possibility of energy coupling along orthogonal axes provided by the Hall effect. A nonlinear third-order system is derived, with a fourth equation serving as an observer of unspecified geophysical processes which could result in field reversal. Lyapunov analysis proves that chaos is not intrinsic to this system. Relative constancy of one of the variables produces pseudo equilibrium in a second order subsystem and allows for self-excitation of the geomagnetic field. Electromagnetic analysis yields expressions for key parameters. Models for secular variations recorded at London, Palermo and at the Cape of Good Hope over the past four hundred years are offered. Offset of the Earth's magnetic axis from the geographic axis is central to time-varying declination, but its causes have not yet been established. Applicability of the model to the explanation of sunspot activity is outlined. A corroborating experiment published by Peter Barlow in 1831 is appended.
Cyclostrophic vortices in polar regions of rotating planets
Authors: Goncharov V. , Pavlov V.
Published: April 2010

Abstract. Multi-petal, rotating vortices can form in two-dimensional flows consisting of an inviscid incompressible fluid under certain conditions. Such vortices are principally nonlinear thermo-hydrodynamical structures. The proper rotation of these structures which leads to time-dependent variations of the associated temperature field can be enregistred by a stationary observer. The problem is analyzed in the framework of the contour dynamics method (CDM). An analytical solution of the reduced equation for a contour curvature is found. We give a classification of the solutions and compare the obtained results with observational data.
Adjoints and low-rank covariance representation
Authors: Tippett M. K. , Cohn S. E.
Published: April 2010

Abstract. Quantitative measures of the uncertainty of Earth system estimates can be as important as the estimates themselves. Direct calculation of second moments of estimation errors, as described by the covariance matrix, is impractical when the number of degrees of freedom of the system state is large and the sources of uncertainty are not completely known. Theoretical analysis of covariance equations can help guide the formulation of low-rank covariance approximations, such as those used in ensemble and reduced-state approaches for prediction and data assimilation. We use the singular value decomposition and recently developed positive map techniques to analyze a family of covariance equations that includes stochastically forced linear systems. We obtain covariance estimates given imperfect knowledge of the sources of uncertainty and we obtain necessary conditions for low-rank approximations to be appropriate. The results are illustrated in a stochastically forced system with time-invariant linear dynamics.
Model error in weather forecasting
Authors: Orrell D. , Smith L. , Barkmeijer J. , Palmer T. N.
Published: April 2010

Abstract. Operational forecasting is hampered both by the rapid divergence of nearby initial conditions and by error in the underlying model. Interest in chaos has fuelled much work on the first of these two issues; this paper focuses on the second. A new approach to quantifying state-dependent model error, the local model drift, is derived and deployed both in examples and in operational numerical weather prediction models. A simple law is derived to relate model error to likely shadowing performance (how long the model can stay close to the observations). Imperfect model experiments are used to contrast the performance of truncated models relative to a high resolution run, and the operational model relative to the analysis. In both cases the component of forecast error due to state-dependent model error tends to grow as the square-root of forecast time, and provides a major source of error out to three days. These initial results suggest that model error plays a major role and calls for further research in quantifying both the local model drift and expected shadowing times.
Performance of the ARPA-SMR limited-area ensemble prediction system: two flood cases
Authors: Montani A. , Marsigli C. , Nerozzi F. , Paccagnella T. , Buizza R.
Published: April 2010

Abstract. The performance of the ARPA-SMR Limited-area Ensemble Prediction System (LEPS), generated by nesting a limited-area model on selected members of the ECMWF targeted ensemble, is evaluated for two flood events that occurred during September 1992. The predictability of the events is studied for forecast times ranging from 2 to 4 days. The extent to which floods localised in time and space can be forecast at high resolution in probabilistic terms was investigated. Rainfall probability maps generated by both LEPS and ECMWF targeted ensembles are compared for different precipitation thresholds in order to assess the impact of enhanced resolution. At all considered forecast ranges, LEPS performs better, providing a more accurate description of the event with respect to the spatio-temporal location, as well as its intensity. In both flood cases, LEPS probability maps turn out to be a very valuable tool to assist forecasters to issue flood alerts at different forecast ranges. It is also shown that at the shortest forecast range, the deterministic prediction provided by the limited area model, when run in a higher-resolution configuration, provides a very accurate rainfall pattern and a good quantitative estimate of the total rainfall deployed in the flooded regions.