Implementing Spectral Methods for Partial Differential Equations

Implementing Spectral Methods for Partial Differential Equations
Author: David A. Kopriva
Publisher: Springer Science & Business Media
Total Pages: 397
Release: 2009-05-27
Genre: Mathematics
ISBN: 9048122619

This book explains how to solve partial differential equations numerically using single and multidomain spectral methods. It shows how only a few fundamental algorithms form the building blocks of any spectral code, even for problems with complex geometries.

The Ocean in Motion

The Ocean in Motion
Author: Manuel G. Velarde
Publisher: Springer
Total Pages: 610
Release: 2018-03-28
Genre: Science
ISBN: 3319719343

This book commemorates the 70th birthday of Eugene Morozov, the noted Russian observational oceanographer. It contains many contributions reflecting his fields of interest, including but not limited to tidal internal waves, ocean circulation, deep ocean currents, and Arctic oceanography. Special attention is paid to studies on internal waves and especially those on tidal internal waves in the Global Ocean. These papers describe the most important open problems concerning experimental studies of internal waves and their theoretical, numerical, and laboratory modeling. Further contributions investigate the physics of surface waves and their interaction with internal waves. Here, the focus is on describing interaction processes between internal waves and deep currents in the ocean, especially currents of Antarctic Bottom Water in abyssal fractures. They also touch on the problem of oceanic circulation and related processes in fjords, including those occurring under sea ice. Given its breadth of coverage, the book will appeal to anyone interested in a survey of ocean dynamics, ranging from historic perspectives to modern research topics.

Environmental Stratified Flows

Environmental Stratified Flows
Author: Roger Grimshaw
Publisher: Springer Science & Business Media
Total Pages: 286
Release: 2006-04-11
Genre: Science
ISBN: 0306480247

The dynamics of flows in density-stratified fluids has been and remains now an important topic for scientific enquiry. Such flows arise in many contexts, ranging from industrial settings to the oceanic and atmospheric environments. It is the latter topic which is the focus of this book. Both the ocean and atmosphere are characterised by the basic vertical density stratification, and this feature can affect the dynamics on all scales ranging from the micro-scale to the planetary scale. The aim of this book is to provide a “state-of-the-art” account of stratified flows as they are relevant to the ocean and atmosphere with a primary focus on meso-scale phenomena; that is, on phenomena whose time and space scales are such that the density stratification is a dominant effect, so that frictional and diffusive effects on the one hand and the effects of the earth’s rotation on the other hand can be regarded as of less importance. This in turn leads to an emphasis on internal waves.

Internal Gravity Waves

Internal Gravity Waves
Author: Bruce R. Sutherland
Publisher: Cambridge University Press
Total Pages: 395
Release: 2010-09-02
Genre: Science
ISBN: 1316184323

The study of internal gravity waves provides many challenges: they move along interfaces as well as in fully three-dimensional space, at relatively fast temporal and small spatial scales, making them difficult to observe and resolve in weather and climate models. Solving the equations describing their evolution poses various mathematical challenges associated with singular boundary value problems and large amplitude dynamics. This book provides the first comprehensive treatment of the theory for small and large amplitude internal gravity waves. Over 120 schematics, numerical simulations and laboratory images illustrate the theory and mathematical techniques, and 130 exercises enable the reader to apply their understanding of the theory. This is an invaluable single resource for academic researchers and graduate students studying the motion of waves within the atmosphere and ocean, and also mathematicians, physicists and engineers interested in the properties of propagating, growing and breaking waves.

Introduction to the Physics of Cohesive Sediment Dynamics in the Marine Environment

Introduction to the Physics of Cohesive Sediment Dynamics in the Marine Environment
Author: Johan C. Winterwerp
Publisher: Elsevier
Total Pages: 577
Release: 2004-08-20
Genre: Science
ISBN: 0080473733

This book is an introduction to the physical processes of cohesive sediment in the marine environment. It focuses on highly dynamic systems, such as estuaries and coastal seas. Processes on the continental shelf are also discussed and attention is given to the effects of chemistry, biology and gas.The process descriptions are based on hydrodynamic and soil mechanic principles, which integrate at the soil-water interface. This approach is substantiated through a classification scheme of sediment occurrences in which distinction is made between cohesive and granular material. Emphasis is also placed on the important interactions between turbulent flow and cohesive sediment suspensions, and on the impact of flow-induced forces on the stability of the seabed. An overview of literature on cohesive sediment dynamics is presented and a number of new developments are highlighted, in particular in relation to floc formation, settling and sedimentation, consolidation, bed failure and liquefaction and erosion of the bed. Moreover, it presents a summary on methods and techniques to measure the various sediment properties necessary to quantify the various parameters in the physical-mathematical model descriptions. A number of examples and case studies have been included.

Water Wave Mechanics For Engineers And Scientists

Water Wave Mechanics For Engineers And Scientists
Author: Robert G Dean
Publisher: World Scientific Publishing Company
Total Pages: 369
Release: 1991-01-23
Genre: Technology & Engineering
ISBN: 9814365696

This book is intended as an introduction to classical water wave theory for the college senior or first year graduate student. The material is self-contained; almost all mathematical and engineering concepts are presented or derived in the text, thus making the book accessible to practicing engineers as well.The book commences with a review of fluid mechanics and basic vector concepts. The formulation and solution of the governing boundary value problem for small amplitude waves are developed and the kinematic and pressure fields for short and long waves are explored. The transformation of waves due to variations in depth and their interactions with structures are derived. Wavemaker theories and the statistics of ocean waves are reviewed. The application of the water particle motions and pressure fields are applied to the calculation of wave forces on small and large objects. Extension of the linear theory results to several nonlinear wave properties is presented. Each chapter concludes with a set of homework problems exercising and sometimes extending the material presented in the chapter. An appendix provides a description of nine experiments which can be performed, with little additional equipment, in most wave tank facilities.

The Interaction of Ocean Waves and Wind

The Interaction of Ocean Waves and Wind
Author: Peter Janssen
Publisher: Cambridge University Press
Total Pages: 310
Release: 2004-10-28
Genre: Science
ISBN: 0521465400

This book was published in 2004. The Interaction of Ocean Waves and Wind describes in detail the two-way interaction between wind and ocean waves and shows how ocean waves affect weather forecasting on timescales of 5 to 90 days. Winds generate ocean waves, but at the same time airflow is modified due to the loss of energy and momentum to the waves; thus, momentum loss from the atmosphere to the ocean depends on the state of the waves. This volume discusses ocean wave evolution according to the energy balance equation. An extensive overview of nonlinear transfer is given, and as a by-product the role of four-wave interactions in the generation of extreme events, such as freak waves, is discussed. Effects on ocean circulation are described. Coupled ocean-wave, atmosphere modelling gives improved weather and wave forecasts. This volume will interest ocean wave modellers, physicists and applied mathematicians, and engineers interested in shipping and coastal protection.