DEPENDENCE OF HAMILTONIAN CHAOS ON PERTURBATION STRUCTURE

1993 ◽  
Vol 03 (04) ◽  
pp. 1013-1028 ◽  
Author(s):  
HUIJUN YANG
Keyword(s):  
Dynamical System ◽  
Atmospheric Chemistry ◽  
Large Scale ◽  
Invariant Tori ◽  
Distribution Functions ◽  
Wave Mixing ◽  
Perturbation Wave ◽  
Hamiltonian Chaos ◽  
Wave Numbers ◽  
Mixing And Transport

In this paper, we considered a Hamiltonian dynamical system consisting of a steady wave and a perturbation wave and studied the dependence of spatial patterns of chaos on the perturbation structure (i.e., the wave numbers of the perturbation wave). The system came from the passive wave mixing and transport problem. In order to investigate this dependence, we first did some simple mixing experiments with initially a small blob and calculated the correlation dimensions. Secondly we used Lyapunov exponents to identify the chaotic regions and the invariant tori and computed the histograms or PDFs (Probability Distribution Functions) to characterize the Hamiltonian chaos for different perturbation structure. We found that this dependence was very complicated and the complexity increases with the perturbation structure. This dynamical system became more chaotic with increase in the wave numbers. The fascinating patterns of the Hamiltonian chaos for various perturbation structures were presented. The spatial pattern of chaos on the isentropic surface of the atmosphere was given. Implications of the results of the chaotic wave mixing and transport in climate dynamics, atmospheric chemistry, aeronomy and large scale dynamics of geophysical fluid flows were briefly discussed.

Interferometric imaging condition for wave-equation migration

Geophysics ◽  
2008 ◽  
Vol 73 (2) ◽  
pp. S47-S61 ◽  
Author(s):  
Paul Sava ◽  
Oleg Poliannikov
Keyword(s):  
Large Scale ◽  
Wigner Distribution ◽  
Random Noise ◽  
Velocity Model ◽  
Distribution Functions ◽  
Small Scale ◽  
Interferometric Imaging ◽  
Imaging Data ◽  
Imaging Condition ◽  
Velocity Models

The fidelity of depth seismic imaging depends on the accuracy of the velocity models used for wavefield reconstruction. Models can be decomposed in two components, corresponding to large-scale and small-scale variations. In practice, the large-scale velocity model component can be estimated with high accuracy using repeated migration/tomography cycles, but the small-scale component cannot. When the earth has significant small-scale velocity components, wavefield reconstruction does not completely describe the recorded data, and migrated images are perturbed by artifacts. There are two possible ways to address this problem: (1) improve wavefield reconstruction by estimating more accurate velocity models and image using conventional techniques (e.g., wavefield crosscorrelation) or (2) reconstruct wavefields with conventional methods using the known background velocity model but improve the imaging condition to alleviate the artifacts caused by the imprecise reconstruction. Wedescribe the unknown component of the velocity model as a random function with local spatial correlations. Imaging data perturbed by such random variations is characterized by statistical instability, i.e., various wavefield components image at wrong locations that depend on the actual realization of the random model. Statistical stability can be achieved by preprocessing the reconstructed wavefields prior to the imaging condition. We use Wigner distribution functions to attenuate the random noise present in the reconstructed wavefields, parameterized as a function of image coordinates. Wavefield filtering using Wigner distribution functions and conventional imaging can be lumped together into a new form of imaging condition that we call an interferometric imaging condition because of its similarity to concepts from recent work on interferometry. The interferometric imaging condition can be formulated both for zero-offset and for multioffset data, leading to robust, efficient imaging procedures that effectively attenuate imaging artifacts caused by unknown velocity models.

scholarly journals On interpreting studies of tracer transport by deep cumulus convection and its effects on atmospheric chemistry

2008 ◽  
Vol 8 (20) ◽  
pp. 6037-6050 ◽  
Author(s):  
M. G. Lawrence ◽  
M. Salzmann
Keyword(s):  
Atmospheric Chemistry ◽  
Large Scale ◽  
Deep Convection ◽  
Convective Transport ◽  
Advective Transport ◽  
Tracer Transport ◽  
Transport Models ◽  
Mass Fluxes ◽  
Split Treatment ◽  
The Mean

Abstract. Global chemistry-transport models (CTMs) and chemistry-GCMs (CGCMs) generally simulate vertical tracer transport by deep convection separately from the advective transport by the mean winds, even though a component of the mean transport, for instance in the Hadley and Walker cells, occurs in deep convective updrafts. This split treatment of vertical transport has various implications for CTM simulations. In particular, it has led to a misinterpretation of several sensitivity simulations in previous studies in which the parameterized convective transport of one or more tracers is neglected. We describe this issue in terms of simulated fluxes and fractions of these fluxes representing various physical and non-physical processes. We then show that there is a significant overlap between the convective and large-scale mean advective vertical air mass fluxes in the CTM MATCH, and discuss the implications which this has for interpreting previous and future sensitivity simulations, as well as briefly noting other related implications such as numerical diffusion.

scholarly journals Probabilistic downscaling of precipitation data in a subtropical mountain area: a two-step approach

2011 ◽  
Vol 18 (2) ◽  
pp. 223-234 ◽  
Author(s):  
R. Haas ◽  
K. Born
Keyword(s):  
Complex Terrain ◽  
Large Scale ◽  
Distribution Functions ◽  
Data Availability ◽  
Cumulative Distribution ◽  
Second Step ◽  
Mountain Area ◽  
Investigation Area ◽  
Distribution Parameters ◽  
Mountain Environment

Abstract. In this study, a two-step probabilistic downscaling approach is introduced and evaluated. The method is exemplarily applied on precipitation observations in the subtropical mountain environment of the High Atlas in Morocco. The challenge is to deal with a complex terrain, heavily skewed precipitation distributions and a sparse amount of data, both spatial and temporal. In the first step of the approach, a transfer function between distributions of large-scale predictors and of local observations is derived. The aim is to forecast cumulative distribution functions with parameters from known data. In order to interpolate between sites, the second step applies multiple linear regression on distribution parameters of observed data using local topographic information. By combining both steps, a prediction at every point of the investigation area is achieved. Both steps and their combination are assessed by cross-validation and by splitting the available dataset into a trainings- and a validation-subset. Due to the estimated quantiles and probabilities of zero daily precipitation, this approach is found to be adequate for application even in areas with difficult topographic circumstances and low data availability.

TREATMENT OF THE ERROR DUE TO UNRESOLVED SCALES IN SEQUENTIAL DATA ASSIMILATION

2011 ◽  
Vol 21 (12) ◽  
pp. 3619-3626 ◽  
Author(s):  
ALBERTO CARRASSI ◽  
STÉPHANE VANNITSEM
Keyword(s):  
Dynamical System ◽  
Kalman Filter ◽  
Data Assimilation ◽  
Large Scale ◽  
Model Error ◽  
Environmental Modeling ◽  
Sequential Data ◽  
Chaotic Dynamical System ◽  
Error Covariance ◽  
Sequential Data Assimilation

In this paper, a method to account for model error due to unresolved scales in sequential data assimilation, is proposed. An equation for the model error covariance required in the extended Kalman filter update is derived along with an approximation suitable for application with large scale dynamics typical in environmental modeling. This approach is tested in the context of a low order chaotic dynamical system. The results show that the filter skill is significantly improved by implementing the proposed scheme for the treatment of the unresolved scales.

New Finite Element Modeling Strategy for Large-Scale Industrial Problems in Structural Acoustics

2000 ◽  
Author(s):  
Saikat Dey ◽  
Luise S. Couchman
Keyword(s):  
Finite Element ◽  
Finite Element Modeling ◽  
Large Scale ◽  
Structural Acoustics ◽  
Simple Scheme ◽  
Numerical Examples ◽  
High Wave ◽  
Wave Numbers ◽  
Complex Structural ◽  
Modeling Strategy

Abstract A simple scheme to model and mesh stiffened shell-like structures is presented. Combined with a high-order finite/infinite element based infrastructure, it enables the solution of complex structural acoustics problems at high wave numbers. Numerical examples are presented to show the applicability of the method at high wave-numbers.

scholarly journals The evolution of biogeochemistry: revisited

2020 ◽  
Author(s):  
Thomas S. Bianchi
Keyword(s):  
20Th Century ◽  
Atmospheric Chemistry ◽  
Large Scale ◽  
Agricultural Soils ◽  
Human Impacts ◽  
Organic Geochemistry ◽  
Evolutionary Genetics ◽  
Satellite Monitoring ◽  
Analytical Approaches

AbstractThe evolution of biogeochemistry, retraces the important historical steps in part, covered by Gorham (Biogeochemistry 13:199–239, 1991) in the 18–19th centuries—with new emergent linkages and trends in 20–21st centuries. In the post-phlogiston period, key synthetic connections are made between weathering, atmospheric chemistry, carbon cycling, and climate change. Early work in the 19th century, focused on weathering and the importance of organisms in the exchange of carbon dioxide between the rocks and the atmosphere, provided foundations for new analytical approaches. The role microbes in connecting abiotic and biotic processes begins to emerge, based largely on the existing knowledge of stoichiometry in agricultural soils and plants. This in part, leads to the founding of ecology and its linkages with evolution and biogeography. Verandsky boldly emerges in the 20th century, with his concepts of a biosphere and a noosphere, as concerns begin to arise about human impacts on nature. The development of organic geochemistry as a discipline, allowed for new roots to develop in the evolution of biogeochemistry through linkages between short and long-term carbon cycles. In the 20th century, a new interesting stoichiometry emerges in biogeochemistry—as related to the Green Revolution, human population growth, and eutrophication problems. The advent of long-term and large-scale experiments help to constrain the complexity of non-linearity and regional differences in fluxes and rates in biogeochemical work. A new age begins in the 21st century whereby molecular approaches (e.g. omics) combined with large-scale satellite, monitoring, survey, observatory approaches are combined in the development of Earth System models. These new connections with ecological/evolutionary genetics are one of the more dramatic and important aspects of biogeochemistry in modern times.

Study of a dynamical system with a strange attractor and invariant tori

2019 ◽  
Vol 383 (13) ◽  
pp. 1441-1449 ◽  
Author(s):  
Antonio Algaba ◽  
Manuel Merino ◽  
Bo-Wei Qin ◽  
Alejandro J. Rodríguez-Luis
Keyword(s):  
Dynamical System ◽  
Strange Attractor ◽  
Invariant Tori

scholarly journals Examination of large-scale structures in a turbulent plane mixing layer. Part 2. Dynamical systems model

2001 ◽  
Vol 441 ◽  
pp. 67-108 ◽  
Author(s):  
L. UKEILEY ◽  
L. CORDIER ◽  
R. MANCEAU ◽  
J. DELVILLE ◽  
M. GLAUSER ◽  
...  
Keyword(s):  
Dynamical System ◽  
Velocity Field ◽  
Large Scale ◽  
Stokes Equations ◽  
Temporal Dynamics ◽  
Mixing Layer ◽  
Basis Set ◽  
Large Scale Structures ◽  
Scale Structures ◽  
Low Order

The temporal dynamics of large-scale structures in a plane turbulent mixing layer are studied through the development of a low-order dynamical system of ordinary differential equations (ODEs). This model is derived by projecting Navier–Stokes equations onto an empirical basis set from the proper orthogonal decomposition (POD) using a Galerkin method. To obtain this low-dimensional set of equations, a truncation is performed that only includes the first POD mode for selected streamwise/spanwise (k1/k3) modes. The initial truncations are for k3 = 0; however, once these truncations are evaluated, non-zero spanwise wavenumbers are added. These truncated systems of equations are then examined in the pseudo-Fourier space in which they are solved and by reconstructing the velocity field. Two different methods for closing the mean streamwise velocity are evaluated that show the importance of introducing, into the low-order dynamical system, a term allowing feedback between the turbulent and mean flows. The results of the numerical simulations show a strongly periodic flow indicative of the spanwise vorticity. The simulated flow had the correct energy distributions in the cross-stream direction. These models also indicated that the events associated with the centre of the mixing layer lead the temporal dynamics. For truncations involving both spanwise and streamwise wavenumbers, the reconstructed velocity field exhibits the main spanwise and streamwise vortical structures known to exist in this flow. The streamwise aligned vorticity is shown to connect spanwise vortex tubes.

scholarly journals Neutral Hydrogen in the Magellanic Clouds

1999 ◽  
Vol 190 ◽  
pp. 37-44
Author(s):  
L. Staveley-Smith ◽  
S. Kim ◽  
S. Stanimirović
Keyword(s):  
Atomic Hydrogen ◽  
Large Scale ◽  
Milky Way ◽  
Velocity Dispersion ◽  
Neutral Hydrogen ◽  
Distribution Functions ◽  
Magellanic Clouds ◽  
Self Gravity ◽  
Rotational Shear ◽  
Compact Array

We review observations of neutral atomic hydrogen (HI) in the Magellanic Clouds (MCs). Being the nearest gas-rich neighbours of the Milky Way the MCs give us an excellent opportunity to study in detail the structure and evolution of the interstellar medium (ISM) and the effect of interactions between galaxies. HI in emission provides a probe of the structure and velocity field of the Clouds, allowing the study of their velocity dispersion, 3-D structure, and large-scale total-mass distribution. Recent data from Australia Telescope Compact Array surveys reveal a morphology (for both Clouds) which is heavily dominated by the effects of local star-formation, rotational shear, fragmentation, self-gravity and turbulence. The new data, which has a spatial resolution down to 10 pc, also allows the study of the distribution functions in velocity and mass for HI clouds. We discuss the morphology, dynamics and giant shell population of the LMC and SMC.

Sign in / Sign up

Export Citation Format

Share Document