Download or read book Analytical Study of the Hasegawa Mima Model a Multi layer and a Continuously Stratified Geostrophic Models of Ocean Dynamics written by Aseel Farhat and published by . This book was released on 2012 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study a viscous two-layer quasi-geostrophic beta-plane model that is forced by imposition of a spatially uniform vertical shear in the eastward (zonal) component of the layer flows. We prove that the model is linearly unstable, but that non-linear solutions are bounded in time by a bound which is independent of the initial data and is determined only by the physical parameters of the model. We further prove, using arguments first presented in the study of the Kuramoto-Sivashinsky equation, the existence of an absorbing ball in appropriate function spaces, and in fact the existence of a compact finite-dimensional attractor, and provide upper bounds for the fractal and Hausdorff dimensions of the attractor. Finally, we show the existence of an inertial manifold for the dynamical system generated by the model's solution operator. Our results provide rigorous justification for observations made by Panetta based on long-time numerical integrations of the model equations. The three-dimensional inviscid Hasegawa-Mima model is one of the fundamental models that describe plasma turbulence. The model also appears as a simplified reduced Rayleigh-Benard convection model. The mathematical analysis of the Hasegawa-Mima equation is challenging due to the absence of any smoothing viscous terms, as well as to the presence of an analogue of the vortex stretching terms. Similar to the case of the three-dimensional Euler equations, we prove the short time existence and uniqueness of high regularity solutions for the three-dimensional Hasegawa-Mima equations. We introduce and study a model that is inspired by the inviscid Hasegawa-Mima model, which we call a pseudo-Hasegawa-Mima model. The introduced model is easier to investigate analytically than the original inviscid Hasegawa-Mima model, as it has a nicer mathematical structure. The resemblance between this model and the Euler equations of inviscid incompressible fluids inspired us to adapt the techniques and ideas introduced for the two-dimensional and the three-dimensional Euler equations to prove the global well-posedness of solutions for our model. This is in addition to proving and implementing a new technical logarithmic inequality, generalizing the Brezis-Gallouet and the Brezis-Wainger inequalities.
Download or read book Quasi Geostrophic Theory of Oceans and Atmosphere written by Fabio Cavallini and published by Springer Science & Business Media. This book was released on 2012-08-11 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: Large-scale winds and currents tend to balance Coriolis and pressure gradient forces. The time evolution of these winds and currents is the subject of the quasi-geostrophic theory. Chapter 1 presents concepts and equations of classical inertial fluid mechanics. Chapter 2 deals with the equations of thermodynamics that close the governing equations of the fluids. Then, the motion is reformulated in a uniformly rotating reference frame. Chapter 3 deals with the shallow-water model and the homogeneous model of wind-driven circulation. The chapter also describes a classical application of the Ekman layer to the atmosphere. Chapter 4 considers the two-layer model, as an introduction to baroclinic flows, together with the concept of available potential energy. Chapter 5 takes into account continuously stratified flows in the ocean and in the atmosphere.
Download or read book Numerical Modeling of Ocean Dynamics written by Zygmunt Kowalik and published by World Scientific. This book was released on 1993 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: While there are several excellent books dealing with numerical analysis and analytical theory, one has to practically sift through hundreds of references. This monograph is an attempt to partly rectify this situation. It aims to introduce the application of finite-difference methods to ocean dynamics as well as review other complex methods. Systematically presented, the monograph first gives a detailed account of the basics and then go on to discuss the various applications. Recognising the impossibility of covering the entire field of ocean dynamics, the writers have chosen to focus on transport equations (diffusion and advection), shallow water phenomena ? tides, storm surges and tsunamis, three-dimensional time dependent oceanic motion, natural oscillations, and steady state phenomena. The many aspects covered by this book makes it an indispensable handbook and reference source to both professionals and students of this field.
Download or read book Numerical Models of Oceans and Oceanic Processes written by Lakshmi H. Kantha and published by Academic Press. This book was released on 2000-08-04 with total page 750 pages. Available in PDF, EPUB and Kindle. Book excerpt: Oceans play a pivotal role in our weather and climate. Ocean-borne commerce is vital to our increasingly close-knit global community. Yet we do not fully understand the intricate details of how they function, how they interact with the atmosphere, and what the limits are to their biological productivity and their tolerance to wastes. While satellites are helping us to fill in the gaps, numerical ocean models are playing an important role in increasing our ability to comprehend oceanic processes, monitor the current state of the oceans, and to a limited extent, even predict their future state. Numerical Models of Oceans and Oceanic Processes is a survey of the current state of knowledge in this field. It brings together a discussion of salient oceanic dynamics and processes, numerical solution methods, and ocean models to provide a comprehensive treatment of the topic. Starting with elementary concepts in ocean dynamics, it deals with equatorial, mid-latitude, high latitude, and coastal dynamics from the perspective of a modeler. A comprehensive and up-to-date chapter on tides is also included. This is followed by a discussion of different kinds of numerical ocean models and the pre- and post-processing requirements and techniques. Air-sea and ice-ocean coupled models are described, as well as data assimilation and nowcast/forecasts. Comprehensive appendices on wavelet transforms and empirical orthogonal functions are also included. This comprehensive and up-to-date survey of the field should be of interest to oceanographers, atmospheric scientists, and climatologists. While some prior knowledge of oceans and numerical modeling is helpful, the book includes an overview of enough elementary material so that along with its companion volume, Small Scale Processes in Geophysical Flows, it should be useful to both students new to the field and practicing professionals. * Comprehensive and up-to-date review * Useful for a two-semester (or one-semester on selected topics) graduate level course * Valuable reference on the topic * Essential for a better understanding of weather and climate
Download or read book Ocean Modeling and Parameterization written by Eric P. Chassignet and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: The realism of large scale numerical ocean models has improved dra matically in recent years, in part because modern computers permit a more faithful representation of the differential equations by their algebraic analogs. Equally significant, if not more so, has been the improved under standing of physical processes on space and time scales smaller than those that can be represented in such models. Today, some of the most challeng ing issues remaining in ocean modeling are associated with parameterizing the effects of these high-frequency, small-space scale processes. Accurate parameterizations are especially needed in long term integrations of coarse resolution ocean models that are designed to understand the ocean vari ability within the climate system on seasonal to decadal time scales. Traditionally, parameterizations of subgrid-scale, high-frequency mo tions in ocean modeling have been based on simple formulations, such as the Reynolds decomposition with constant diffusivity values. Until recently, modelers were concerned with first order issues such as a correct represen tation of the basic features of the ocean circulation. As the numerical simu lations become better and less dependent on the discretization choices, the focus is turning to the physics of the needed parameterizations and their numerical implementation. At the present time, the success of any large scale numerical simulation is directly dependent upon the choices that are made for the parameterization of various subgrid processes.
Download or read book Inverse Modeling of the Ocean and Atmosphere written by Andrew F. Bennett and published by Cambridge University Press. This book was released on 2005-10-20 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse Modeling of the Ocean and Atmosphere is a graduate-level book for students of oceanography and meteorology, and anyone interested in combining computer models and observations of the hydrosphere or solid earth. A step-by-step development of maximally efficient inversion algorithms, using ideal models, is complemented by computer codes and comprehensive details for realistic models. Variational tools and statistical concepts are concisely introduced, and applications to contemporary research models, together with elaborate observing systems, are examined in detail. The book offers a review of the various alternative approaches, and further advanced research topics are discussed. Derived from the author's lecture notes, this book constitutes an ideal course companion for graduate students, as well as being a valuable reference source for researchers and managers in theoretical earth science, civil engineering and applied mathematics.
Download or read book Fundamentals of Ocean Climate Models written by Stephen Griffies and published by Princeton University Press. This book was released on 2018-06-05 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book sets forth the physical, mathematical, and numerical foundations of computer models used to understand and predict the global ocean climate system. Aimed at students and researchers of ocean and climate science who seek to understand the physical content of ocean model equations and numerical methods for their solution, it is largely general in formulation and employs modern mathematical techniques. It also highlights certain areas of cutting-edge research. Stephen Griffies presents material that spans a broad spectrum of issues critical for modern ocean climate models. Topics are organized into parts consisting of related chapters, with each part largely self-contained. Early chapters focus on the basic equations arising from classical mechanics and thermodynamics used to rationalize ocean fluid dynamics. These equations are then cast into a form appropriate for numerical models of finite grid resolution. Basic discretization methods are described for commonly used classes of ocean climate models. The book proceeds to focus on the parameterization of phenomena occurring at scales unresolved by the ocean model, which represents a large part of modern oceanographic research. The final part provides a tutorial on the tensor methods that are used throughout the book, in a general and elegant fashion, to formulate the equations.
Download or read book The Finiteness of Determining Degrees of Freedom for the Quasi geostrophic Multi layer Ocean Model written by C. Bernier-Kazantsev and published by . This book was released on 1996 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Atmosphere ocean Modeling Coupling And Couplers written by Carlos Roberto Mechoso and published by World Scientific. This book was released on 2021-07-27 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: Coupled atmosphere-ocean models are at the core of numerical climate models. There is an extraordinarily broad class of coupled atmosphere-ocean models ranging from sets of equations that can be solved analytically to highly detailed representations of Nature requiring the most advanced computers for execution. The models are applied to subjects including the conceptual understanding of Earth's climate, predictions that support human activities in a variable climate, and projections aimed to prepare society for climate change. The present book fills a void in the current literature by presenting a basic and yet rigorous treatment of how the models of the atmosphere and the ocean are put together into a coupled system. The text of the book is divided into chapters organized according to complexity of the components that are coupled. Two full chapters are dedicated to current efforts on the development of generalist couplers and coupling methodologies all over the world.
Download or read book Numerical Modeling of Synoptic Scale Ocean Dynamics written by and published by . This book was released on 1994 with total page 2 pages. Available in PDF, EPUB and Kindle. Book excerpt: Research continued on theory and practice of data assimilation. Results of a study of the application of optimal interpolation (0I), the data assimilation method most commonly used in numerical weather prediction, to a regional data set were published. In that study, hydrographic data from the California Current were assimilated into the Harvard quasigeostrophic open ocean model. Good results were obtained. A study of the application of advanced data assimilation methods to simple highly nonlinear systems which exhibit strongly nonlinear behavior such as bimodality and chaos was completed. Most data assimilation methods were derived under assumptions of linearity, and therefore could be expected to fail when applied to systems which exhibit multiple equilibria or chaos. A finite element quasigeostrophic model of the Kuroshio near the coast of Japan was implemented and tested, and found to exhibit multiple stable equilibria in parameter ranges of physical interest. These multiple equilibria correspond to the observed formation and decay of the large meander inshore of the main current off the coast of Honshu. We plan to apply our newly-developed data assimilation methods for nonlinear systems to this model. Theoretical results pertaining to application of adjoint data assimilation methods to regional and large-scale models were obtained. Appearance of high-wavenumber noise which had been noted in a number of published data assimilation studies was found to be the result of omission of necessary constraints in the original formulation of the methods. (AN).
Download or read book Modelling Ocean Climate Variability written by Artem S. Sarkisyan and published by Springer Science & Business Media. This book was released on 2009-05-13 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this wide-ranging and comprehensive review of the historical development and current status of ocean circulation models, the analysis extends from simple analytical approaches to the latest high-resolution numerical models with data assimilation. The authors, both of whom are pioneer scientists in ocean and shelf sea modelling, look back at the evolution of Western and Eastern modelling methodologies during the second half of the last century. They also present the very latest information on ocean climate modelling and offer examples for a number of oceans and shelf seas. The book includes a critical analysis of literature on ocean climate variability modelling, as well as assessing the strengths and weaknesses of the best-known modelling techniques. It also anticipates future developments in the field, focusing on models based on a synthesis of numerical simulation and field observation, and on nonlinear thermodynamic model data synthesis.
Download or read book Large scale Atmosphere ocean Dynamics Analytical methods and numerical models written by John Norbury and published by . This book was released on 2002 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The complex flows in the atmosphere and oceans are believed to be accurately modelled by the Navier-Stokes equations of fluid mechanics together with classical thermodynamics. However, due to the enormous complexity of these equations, meteorologists and oceanographers have constructed approximate models of the dominant, large-scale flows that control the evolution of weather systems. The simplifications often result in models that are amenable to solution both analytically and numerically. This volume and its companion explain why such simplifications to Newton's second law produce accurate, useful models and, just as the meteorologist seeks patterns in the weather, mathematicians seek structure in the governing equations. They show how geometry and analysis facilitate solution strategies. -- Amazon.
Download or read book Large Scale Atmosphere Ocean Dynamics Volume 1 written by John Norbury and published by Cambridge University Press. This book was released on 2002-08-15 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: The complex flows in the atmosphere and oceans are believed to be accurately modelled by the Navier-Stokes equations of fluid mechanics together with classical thermodynamics. However, due to the enormous complexity of these equations, meteorologists and oceanographers have constructed approximate models of the dominant, large-scale flows that control the evolution of weather systems. The simplifications often result in models that are amenable to solution both analytically and numerically. This volume and its companion explain why such simplifications to Newton's second law produce accurate, useful models and, just as the meteorologist seeks patterns in the weather, mathematicians seek structure in the governing equations. They show how geometry and analysis facilitate solution strategies.
Download or read book Dynamical Evaluation of Ocean Models Using the Gulf Stream as an Example written by and published by . This book was released on 2010 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ocean models run with atmospheric forcing but without ocean data assimilation are useful in studies of ocean model dynamics and simulation skill. Models that give realistic simulations with accurate dynamics, when run without data assimilation, are essential for eddy-resolving ocean prediction because of the multiple roles that ocean models must play in ocean nowcasting and forecasting, including dynamical interpolation during data assimilation, representing sparsely observed subsurface ocean features from the mixed layer depth to abyssal currents, converting atmospheric forcing into ocean responses, imposing topographic and geometric constraints, performing ocean forecasts, and providing boundary and initial conditions to nested regional and coastal models. A wide range of ocean dynamics contribute to these different roles. Here we focus on evaluating the dynamics of mid-latitude ocean currents simulated by state-of-the- art, eddy-resolving ocean general circulation models (OGCMs) with high vertical resolution, using the Gulf Stream as an example.
Download or read book A Review of Ocean Models written by Walter J. Grabowski and published by . This book was released on 1981 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This report is a review of current trends and approaches to modeling various ocean phenomena. We begin with a brief discussion of large scale circulation models. This leads to a summary of models of large (i.e., tens of kilometers) fronts and attempts to model them. The next section is a detailed discussion of upper ocean dynamics and the models used for simulations. The final section discusses Garrett-Munk type internal wave models and models of the effects of finestructure. (Author).
Download or read book Instability of Density Fronts in Layer and Continuously Stratified Models written by Yasushi Fukamachi and published by . This book was released on 1992 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Energy Transfers for Multilayer Hydrodynamic Ocean Models General Formulation and Specific Examples written by Donna W. Blake and published by . This book was released on 1987 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two dynamic models, useful in studying ocean circulations, are treated: the inviscid multilayer hydrodynamic model and the inviscid multilayer reduced-gravy hydrodynamic model or, for brevity, the finite depth model and the reduced-gravity model. The two models are identical except that the velocity is required to be zero in the bottom layer of the reduced-gravity model. The latter model retains most of the physical properties of the finite depth model but has considerably fewer computational requirements. Two different formulations of the energetics are obtained: layer-layer and layer-interface. In both, the kinetic energy per unit area of a layer is specified. Both formulations are valid mathematically and physically so the selection of one depends on what types of energy transfers the user wishes to examine. The energetics, or energy analysis, is presented for a general multilayer case for both models and both formulations. The energetics in both formulations are considered for specific cases: the one-, two-, and three-layer cases for the finite depth model and the one and two active layer cases for the reduced-gravity model.
