the equations of oceanic motions

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The Equations Of Oceanic Motions

Author : Peter Müller
ISBN : 9781139458368
Genre : Science
File Size : 28. 2 MB
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Modeling and prediction of oceanographic phenomena and climate is based on the integration of dynamic equations. The Equations of Oceanic Motions derives and systematically classifies the most common dynamic equations used in physical oceanography, from large-scale thermohaline circulations to those governing small scale motions and turbulence. After establishing the basic dynamical equations that describe all oceanic motions, Müller then derives approximate equations, emphasizing the assumptions made and physical processes eliminated. He distinguishes between geometric, thermodynamic and dynamic approximations and between the acoustic, gravity, vortical and temperature-salinity modes of motion. Basic concepts and formulae of equilibrium thermodynamics, vector and tensor calculus, curvilinear coordinate systems, and the kinematics of fluid motion and wave propagation are covered in appendices. Providing the basic theoretical background for graduate students and researchers of physical oceanography and climate science, this book will serve as both a comprehensive text and an essential reference.

Numerical Ocean Circulation Modeling

Author : Dale B Haidvogel
ISBN : 9781848168244
Genre : Science
File Size : 88. 32 MB
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This book offers a comprehensive overview of the models and methods employed in the rapidly advancing field of numerical ocean circulation modeling. For those new to the field, concise reviews of the equations of oceanic motion, sub-grid-scale parameterization, and numerical approximation techniques are presented and four specific numerical models, chosen to span the range of current practice, are described in detail. For more advanced users, a suite of model test problems is developed to illustrate the differences among models, and to serve as a first stage in the quantitative evaluation of future algorithms. The extensive list of references makes this book a valuable text for both graduate students and postdoctoral researchers in the marine sciences and in related fields such as meteorology, and climate and coupled biogeochemical modeling. Contents: The Continuous EquationsThe 1D Heat and Wave EquationsConsiderations in Two DimensionsThree-Dimensional Ocean ModelsSubgridscale ParameterizationProcess-Oriented Test ProblemsSimulation of the North AtlanticThe Final Frontier Readership: Oceanographers and geoscientists. Keywords:Modelling;Oceanography;2-Dimension Ocean Models;3-Dimension Ocean Models;Ocean Circulation;North Atlantic Ocean;Hydro Static Equations;Algorithms

Atmosphere Ocean Dynamics

Author : Adrian E. Gill
ISBN : 9781483281582
Genre : Science
File Size : 67. 51 MB
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Atmosphere-Ocean Dynamics deals with a systematic and unified approach to the dynamics of the ocean and atmosphere. The book reviews the relationship of the ocean-atmosphere and how this system functions. The text explains this system through radiative equilibrium models; the book also considers the greenhouse effect, the effects of convection and of horizontal gradients, and the variability in radiative driving of the earth. Equations in the book show the properties of a material element, mass conservation, the balance of scalar quantity (such as salinity), and the mathematical behavior of the ocean and atmosphere. The book also addresses how the ocean-atmosphere system tends to adjust to equilibrium, both in the absence and presence of driving forces such as gravity. The text also explains the effect of the earth's rotation on the system, as well as the application of forced motions such as that produced by wind or temperature changes. The book explains tropical dynamics and the effects of variation of the Coriolis parameter with latitude. The text will be appreciated by meteorologists, environmentalists, students studying hydrology, and people working in general earth sciences.

Atmospheric And Oceanic Fluid Dynamics

Author : Geoffrey K. Vallis
ISBN : 9781107065505
Genre : Science
File Size : 81. 61 MB
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The atmosphere and ocean are two of the most important components of the climate system, and fluid dynamics is central to our understanding of both. This book provides a unified and comprehensive treatment of the field that blends classical results with modern interpretations. It takes the reader seamlessly from the basics to the frontiers of knowledge, from the equations of motion to modern theories of the general circulation of the atmosphere and ocean. These concepts are illustrated throughout the book with observations and numerical examples. As well as updating existing chapters, this full-color second edition includes new chapters on tropical dynamics, El Nio, the stratosphere and gravity waves. Supplementary resources are provided online, including figures from the book and problem sets, making this new edition an ideal resource for students in the atmospheric, oceanic and climate sciences, as well as in applied mathematics and engineering.

Hydrodynamics Of Oceans And Atmospheres

Author : Carl Eckart
ISBN : 9781483149561
Genre : Technology & Engineering
File Size : 89. 22 MB
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Hydrodynamics of Oceans and Atmospheres is a systematic account of the hydrodynamics of oceans and atmospheres. Topics covered range from the thermodynamic functions of an ideal gas and the thermodynamic coefficients for water to steady motions, the isothermal atmosphere, the thermocline, and the thermosphere. Perturbation equations, field equations, residual equations, and a general theory of rays are also presented. This book is comprised of 17 chapters and begins with an introduction to the basic equations and their solutions, with the aim of illustrating the laws of dynamics. The nonlinear equations of thermodynamics and hydrodynamics are analyzed using the methods of perturbation theory, with emphasis on the zero-order solution; zero-order states of an ideal gas; the first-order equations; the additive barotropic terms; and boundary conditions. The following chapters focus on the steady component of atmospheric pressure; free steady motion with or without rotation; field equations and general theorems relating to such equations; and the stratification of the Earth's atmosphere, oceans, and lakes. The next two chapters present calculations concerning the isothermal atmosphere, with particular reference to plane level surfaces with or without rotation. The final chapter looks at spherical level surfaces with rotation. This monograph will be of interest to physicists, oceanographers, atmospheric scientists, and meteorologists.

Introduction To Pdes And Waves For The Atmosphere And Ocean

Author : Andrew Majda
ISBN : 0821883496
Genre : Mathematics
File Size : 45. 56 MB
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Written by a leading specialist in the area of atmosphere/ocean science (AOS), the book presents an excellent introduction to this important topic. The goals of these lecture notes, based on courses presented by the author at the Courant Institute of Mathematical Sciences, are to introduce mathematicians to the fascinating and important area of atmosphere/ocean science (AOS) and, conversely, to develop a mathematical viewpoint on basic topics in AOS of interest to the disciplinary AOS community, ranging from graduate students to researchers. The lecture notes emphasize the serendipitous connections between applied mathematics and geophysical flows in the style of modern applied mathematics, where rigorous mathematical analysis as well as asymptotic, qualitative, and numerical modeling all interact to ease the understanding of physical phenomena. Reading these lecture notes does not require a previous course in fluid dynamics, although a serious reader should supplement these notes with material such The book is intended for graduate students and researchers working in interdisciplinary areas between mathematics and AOS. It is excellent for supplementary course reading or independent study.

Ocean Dynamics

Author : Dirk Olbers
ISBN : 9783642234507
Genre : Science
File Size : 63. 45 MB
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Ocean Dynamics’ is a concise introduction to the fundamentals of fluid mechanics, non-equilibrium thermodynamics and the common approximations for geophysical fluid dynamics, presenting a comprehensive approach to large-scale ocean circulation theory. The book is written on the physical and mathematical level of graduate students in theoretical courses of physical oceanography, meteorology and environmental physics. An extensive bibliography and index, extensive side notes and recommendations for further reading, and a comparison with the specific atmospheric physics where applicable, makes this volume also a useful reading for researchers. Each of the four parts of the book – fundamental laws, common approximations, ocean waves, oceanic turbulence and eddies, and selected aspects of ocean dynamics – starts with elementary considerations, blending then classical topics with more advanced developments of fluid mechanics and theoretical oceanography. The last part covers the theory of the global wind-driven circulation in homogeneous and stratified regimes, the circulation and overturning in the Southern Ocean, and the global meridional overturning and thermohaline-driven circulation. Emphasis is placed on simple physical models rather than access to extensive numerical results, enabling students to understand and reproduce the complex theory mostly by analytical means. All equations and models are derived in detail and illustrated by numerous figures. The appendix provides short excursions into the mathematical background, such as vector analysis, statistics, and differential equations

Numerical Models Of Ocean Circulation

Author :
ISBN : NAP:00227
Genre : Ocean circulation
File Size : 43. 42 MB
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Waves In Oceanic And Coastal Waters

Author : Leo H. Holthuijsen
ISBN : 9781139462525
Genre : Science
File Size : 28. 60 MB
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Waves in Oceanic and Coastal Waters describes the observation, analysis and prediction of wind-generated waves in the open ocean, in shelf seas, and in coastal regions with islands, channels, tidal flats and inlets, estuaries, fjords and lagoons. Most of this richly illustrated book is devoted to the physical aspects of waves. After introducing observation techniques for waves, both at sea and from space, the book defines the parameters that characterise waves. Using basic statistical and physical concepts, the author discusses the prediction of waves in oceanic and coastal waters, first in terms of generalised observations, and then in terms of the more theoretical framework of the spectral energy balance. He gives the results of established theories and also the direction in which research is developing. The book ends with a description of SWAN (Simulating Waves Nearshore), the preferred computer model of the engineering community for predicting waves in coastal waters.

Numerical Modeling Of Ocean Dynamics

Author : Zygmunt Kowalik
ISBN : 9789814365666
Genre : Technology & Engineering
File Size : 26. 42 MB
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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. Contents:Formulation of the General Equations:Equations of Motion, Continuity and DiffusionTwo-Dimensional EquationsApplication of the Stream FunctionViscosity in the Turbulent FlowTransport Equations:Mathematical RudimentsBoundary and Initial ConditionsBasic Numerical PropertiesExplicit Versus Implicit Numerical SchemesCentered Numerical SchemesComputational Errors: Diffusion and DispersionComputational and Physical Modes of the Numerical SolutionDiffusive ProcessesApplication of the Higher Order Computational Schemes to the Advective EquationTwo-Dimensional Numerical Models:Basic ProblemsNumerical Solution of the System of EquationsStep by Step Approach to the Construction and Analysis of Simple Numerical SchemesTwo-Dimensional ModelsNumerical FilteringGrid RefinementSimulation of Long Wave Run-UpFinite-Differencing of the Time DerivativeFinite-Differencing of the Space DerivativeTreatment of Open BoundariesTreatment of the Nonlinear Advective TermsMoving Boundary Models and Inclusion of Tidal FlatsNested Grids and Multiple GridsStretched Coordinates and Transformed Grid SystemsThree-Dimensional Time-Dependent Motion:IntroductionNumerical Modeling of the Fjord CirculationThree-Dimensional Motion in the Shallow SeasThree Dimensional Modeling Utilizing the Mode Splitting and Sigma CoordinateGeneral Circulation Model — Rigid Lid ConditionA Three-Dimensional Semi-Implicit ModelA Two-Layer ModelMode Splitting and Reduced Gravity ModelQuasi-Geostrophic ModelsStreamfunction ModelsThe Bidston ModelsHaidvogel et al.'s ModelNormal Modes:IntroductionSeichesThe Normal Mode ApproachSolutions for Lakes and Bays with Uniform and Variable DepthSystems with BranchesResonance Calculation for Irregular-Shaped BasinsSecondary UndulationsHelmholtz ModeOpen Boundary ConditionsNumerical Models for Resonance CalculationsKelvin Waves, Sverdrup Waves and Poincaré WavesInfluence of Ice Cover on Normal ModesSteady State Processes:Oceanographic ExamplesNumerical ApproximationBoundary ConditionsNumerical MethodsDirect MethodsHigher Order Accuracy Schemes for Convection-Dominated FlowAppendix 1ReferencesSubject Index Readership: Oceanographers, coastal engineers and environment scientists. keywords:

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