Nonlinear Processes in Geophysics
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Electron acoustic solitons in the Earth's magnetotail Abstract. Small amplitude electron - acoustic solitons are studied in a magnetized plasma consisting of two types of electrons, namely cold electron beam and background plasma electrons and two temperature ion plasma. The analysis predicts rarefactive solitons. The model may provide a possible explanation for the perpendicular polarization of the low-frequency component of the broadband electrostatic noise observed in the Earth's magnetotail.
Nonlinear Processes in Geophysics - Tập 11 Số 2 - Trang 215-218
Electron acoustic solitary waves with non-thermal distribution of electrons Abstract. Electron-acoustic solitary waves are studied in an unmagnetized plasma consisting of non-thermally distributed electrons, fluid cold electrons and ions. The Sagdeev pseudo-potential technique is used to carry out the analysis. The presence of non-thermal electrons modifies the parametric region where electron acoustic solitons can exist. For parameters representative of auroral zone field lines, the electron acoustic solitons do not exist when either α > 0.225 or Tc/Th > 0.142, where α is the fractional non-thermal electron density, and Tc (Th) represents the temperature of cold (hot) electrons. Further, for these parameters, the simple model predicts negatively charged potential structures. Inclusion of an electron beam in the model may provide the positive potential solitary structures.
Nonlinear Processes in Geophysics - Tập 11 Số 2 - Trang 275-279
Anomalous width variation of rarefactive ion acoustic solitary waves in the context of auroral plasmas Abstract. The presence of dynamic, large amplitude solitary waves in the auroral regions of space is well known. Since their velocities are of the order of the ion acoustic speed, they may well be considered as being generated from the nonlinear evolution of ion acoustic waves. However, they do not show the expected width-amplitude correlation for K-dV solitons. Recent POLAR observations have actually revealed that the low altitude rarefactive ion acoustic solitary waves are associated with an increase in the width with increasing amplitude. This indicates that a weakly nonlinear theory is not appropriate to describe the solitary structures in the auroral regions. In the present work, a fully nonlinear analysis based on Sagdeev pseudopotential technique has been adopted for both parallel and oblique propagation of rarefactive solitary waves in a two electron temperature multi-ion plasma. The large amplitude solutions have consistently shown an increase in the width with increasing amplitude. The width-amplitude variation profile of obliquely propagating rarefactive solitary waves in a magnetized plasma have been compared with the recent POLAR observations. The width-amplitude variation pattern is found to fit well with the analytical results. It indicates that a fully nonlinear theory of ion acoustic solitary waves may well explain the observed anomalous width variations of large amplitude structures in the auroral region.
Nonlinear Processes in Geophysics - Tập 11 Số 2 - Trang 219-228
Electron acoustic solitons in the presence of an electron beam and superthermal electrons Abstract. Arbitrary amplitude electron acoustic solitons are studied in an unmagnetized plasma having cold electrons and ions, superthermal hot electrons and an electron beam. Using the Sagdeev pseudo potential method, theoretical analysis is carried out by assuming superthermal hot electrons having kappa distribution. The results show that inclusion of an electron beam alters the minimum value of spectral index, κ, of the superthermal electron distribution and Mach number for which electron-acoustic solitons can exist and also changes their width and electric field amplitude. For the auroral region parameters, the maximum electric field amplitudes and soliton widths are found in the range ~(30–524) mV m−1 and ~(329–729) m, respectively, for fixed Mach number M = 1.1 and for electron beam speed of (660–1990) km s−1.
Nonlinear Processes in Geophysics - Tập 18 Số 5 - Trang 627-634
Nonlinear effects in 4D-Var Abstract. The ability of a data assimilation system to deal effectively
with nonlinearities arising from the prognostic model or the relationship
between the control variables and the available observations has received a
lot of attention in theoretical studies based on very simplified test models.
Less work has been done to quantify the importance of nonlinearities in
operational, state-of-the-art global data assimilation systems. In this paper
we analyse the nonlinear effects present in ECMWF 4D-Var and evaluate the
ability of the incremental formulation to solve the nonlinear assimilation
problem in a realistic NWP environment. We find that nonlinearities have
increased over the years due to a combination of increased model resolution
and the ever-growing importance of observations that are nonlinearly related
to the state. Incremental 4D-Var is well suited for dealing with these
nonlinear effects, but at the cost of increasing the number of outer loop
relinearisations. We then discuss strategies for accommodating the increasing
number of sequential outer loops in the tight schedules of operational global
NWP.
Nonlinear Processes in Geophysics - Tập 25 Số 3 - Trang 713-729
Isolation on the West Florida Shelf with implications for red tides and pollutant dispersal in the Gulf of Mexico Abstract. Analysis of year-long drifter trajectories and records of simulated surface Lagrangian Coherent Structures (LCSs) have suggested the presence of a resilient Cross-Shelf Transport Barrier (CSTB) on the West Florida Shelf (WFS). The CSTB was conjectured to provide a large degree of isolation, which is consequential for the fueling of red tides on the southern WFS by nutrients possibly released by rivers and canals directly on the region. Here this conjecture is thoroughly tested by identifying LCSs as well as performing tracer advection calculations based on seven-year-long records of surface and subsurface currents produced by a HYbrid-Coordinate Ocean Model (HYCOM) simulation of the Gulf of Mexico (GoM). The identified LCSs suggest that the CSTB extends downward in the water column. The tracer calculations suggest that, while the majority of the nutrients possibly released by rivers and canals directly on the southern WFS are retained within the region for long times, only a small fraction of the nutrients possibly released by rivers outside the WFS reach the southern WFS, mainly accompanying shoreward excursions of the CSTB. These results add importance to the role played by the CSTB in controlling red tide development on the WFS. Implications of the results for the dispersal of pollutants, such as oil, in the GoM are discussed.
Nonlinear Processes in Geophysics - Tập 17 Số 6 - Trang 685-696
Cross wavelet analysis: significance testing and pitfalls Abstract. In this paper, we present a detailed evaluation of cross wavelet analysis of bivariate time series. We develop a statistical test for zero wavelet coherency based on Monte Carlo simulations. If at least one of the two processes considered is Gaussian white noise, an approximative formula for the critical value can be utilized. In a second part, typical pitfalls of wavelet cross spectra and wavelet coherency are discussed. The wavelet cross spectrum appears to be not suitable for significance testing the interrelation between two processes. Instead, one should rather apply wavelet coherency. Furthermore we investigate problems due to multiple testing. Based on these results, we show that coherency between ENSO and NAO is an artefact for most of the time from 1900 to 1995. However, during a distinct period from around 1920 to 1940, significant coherency between the two phenomena occurs.
Nonlinear Processes in Geophysics - Tập 11 Số 4 - Trang 505-514
Nonequilibrium plankton community structures in an ecohydrodynamic model system Abstract. Due to the local and global impacts of algae blooms and patchiness on water quality, carbon cycling and climate, models of plankton dynamics are of current interest. In this paper, the temporal and spatial patterns in natural plankton communities are interpreted as transient and stationary nonequilibrium solutions of dynamical nonlinear interaction-diffusion-advection systems. A simple model of phytoplankton-zooplankton dynamics (Scheffer, 1991) is presented in space and time. After summarizing the local properties as multiple stability and oscillations, the emergence of spatial and spatio- temporal patterns is considered, accounting also for diffusion and weak advection. In order to study the emergence and stability of these structures under hydrodynamic forcing, the interaction- diffusion-advection model is coupled to the hydrodynamic equations. It is shown, that the formation of nonequilibrium spatio-temporal density patterns due to the interplay of the deterministic nonlinear biological interactions and physical processes is a rare occurrence in rapidly flowing waters. The two-timing perturbation technique is applied to problems with very rapid single-directed steady flows. A channel under tidal forcing serves as and example for a system with a relatively high detention time of matter. Generally, due to the different time and length scales of planktic interactions, diffusion and transport, initial nonequilibrium plankton patches are simply moved through the system unless the strong hydrodynamic forces do not destroy them before.
Nonlinear Processes in Geophysics - Tập 1 Số 1 - Trang 3-11
Multifractal intermittency of Eulerian and Lagrangian turbulence of ocean temperature and plankton fields Abstract. In this paper, we present evidence that intermittency of Eulerian and Lagrangian turbulence of ocean temperature and plankton fields is multifractal and furthermore can be analysed with the help of universal multifractals. We analyse time series of temperature and in vivo fluorescence taken from a drifter in the mixed coastal waters of the eastern English Channel. Two analysis techniques are used to compute the fundamental universal multifiractal parameters, which describe all the statistics of the turbulent fluctuations: the analysis of the scale invariant structure function exponent ζ(q) and the Double Trace Moment technique. At small scales, we do not detect any significant difference between the universal multifiractal behavior of temperature and fluorescence in an Eulerian framework. This supports the hypothesis that the latter is passively advected with the flow as the former. On the one hand, we show that large scale measurements are Lagrangian and indeed we obtain for temperature fluctuations a ω2 power spectrum corresponding to the theoretical scaling of a Lagrangian passive scalar. Furthermore, we show that Lagrangian temperature fluctuations are multiscaling and intermittent. On the other hand, the flatter slope at large scales of the fluorescence power spectrum points out that the plankton is at these scales a "biologically active" scalar.
Nonlinear Processes in Geophysics - Tập 3 Số 4 - Trang 236-246
Chaotic dynamics and the role of covariance inflation for reduced rank Kalman filters with model error Abstract. The ensemble Kalman filter and its variants have shown to be robust for data assimilation in high dimensional geophysical models, with localization, using ensembles of extremely small size relative to the model dimension. However, a reduced rank representation of the estimated covariance leaves a large dimensional complementary subspace unfiltered. Utilizing the dynamical properties of the filtration for the backward Lyapunov vectors, this paper explores a previously unexplained mechanism, providing a novel theoretical interpretation for the role of covariance inflation in ensemble-based Kalman filters. Our derivation of the forecast error evolution describes the dynamic upwelling of the unfiltered error from outside of the span of the anomalies into the filtered subspace. Analytical results for linear systems explicitly describe the mechanism for the upwelling, and the associated recursive Riccati equation for the forecast error, while nonlinear approximations are explored numerically.
Nonlinear Processes in Geophysics - Tập 25 Số 3 - Trang 633-648
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