The Shallow Water Wave Equations: Formulation, Analysis and Application PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download The Shallow Water Wave Equations: Formulation, Analysis and Application PDF full book. Access full book title The Shallow Water Wave Equations: Formulation, Analysis and Application by Ingemar Kinnmark. Download full books in PDF and EPUB format.
Author: Ingemar Kinnmark Publisher: Springer Science & Business Media ISBN: 3642826466 Category : Science Languages : en Pages : 212
Book Description
1. 1 AREAS OF APPLICATION FOR THE SHALLOW WATER EQUATIONS The shallow water equations describe conservation of mass and mo mentum in a fluid. They may be expressed in the primitive equation form Continuity Equation _ a, + V. (Hv) = 0 L(l;,v;h) at (1. 1) Non-Conservative Momentum Equations a M("vjt,f,g,h,A) = at(v) + (v. V)v + tv - fkxv + gV, - AIH = 0 (1. 2) 2 where is elevation above a datum (L) ~ h is bathymetry (L) H = h + C is total fluid depth (L) v is vertically averaged fluid velocity in eastward direction (x) and northward direction (y) (LIT) t is the non-linear friction coefficient (liT) f is the Coriolis parameter (liT) is acceleration due to gravity (L/T2) g A is atmospheric (wind) forcing in eastward direction (x) and northward direction (y) (L2/T2) v is the gradient operator (IlL) k is a unit vector in the vertical direction (1) x is positive eastward (L) is positive northward (L) Y t is time (T) These Non-Conservative Momentum Equations may be compared to the Conservative Momentum Equations (2. 4). The latter originate directly from a vertical integration of a momentum balance over a fluid ele ment. The former are obtained indirectly, through subtraction of the continuity equation from the latter. Equations (1. 1) and (1. 2) are valid under the following assumptions: 1. The fluid is well-mixed vertically with a hydrostatic pressure gradient. 2. The density of the fluid is constant.
Author: Ingemar Kinnmark Publisher: Springer Science & Business Media ISBN: 3642826466 Category : Science Languages : en Pages : 212
Book Description
1. 1 AREAS OF APPLICATION FOR THE SHALLOW WATER EQUATIONS The shallow water equations describe conservation of mass and mo mentum in a fluid. They may be expressed in the primitive equation form Continuity Equation _ a, + V. (Hv) = 0 L(l;,v;h) at (1. 1) Non-Conservative Momentum Equations a M("vjt,f,g,h,A) = at(v) + (v. V)v + tv - fkxv + gV, - AIH = 0 (1. 2) 2 where is elevation above a datum (L) ~ h is bathymetry (L) H = h + C is total fluid depth (L) v is vertically averaged fluid velocity in eastward direction (x) and northward direction (y) (LIT) t is the non-linear friction coefficient (liT) f is the Coriolis parameter (liT) is acceleration due to gravity (L/T2) g A is atmospheric (wind) forcing in eastward direction (x) and northward direction (y) (L2/T2) v is the gradient operator (IlL) k is a unit vector in the vertical direction (1) x is positive eastward (L) is positive northward (L) Y t is time (T) These Non-Conservative Momentum Equations may be compared to the Conservative Momentum Equations (2. 4). The latter originate directly from a vertical integration of a momentum balance over a fluid ele ment. The former are obtained indirectly, through subtraction of the continuity equation from the latter. Equations (1. 1) and (1. 2) are valid under the following assumptions: 1. The fluid is well-mixed vertically with a hydrostatic pressure gradient. 2. The density of the fluid is constant.
Author: Robert G Dean Publisher: World Scientific Publishing Company ISBN: 9814365696 Category : Technology & Engineering Languages : en Pages : 369
Book Description
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.
Author: C.B. Vreugdenhil Publisher: Springer Science & Business Media ISBN: 9401583544 Category : Science Languages : en Pages : 273
Book Description
A wide variety of problems are associated with the flow of shallow water, such as atmospheric flows, tides, storm surges, river and coastal flows, lake flows, tsunamis. Numerical simulation is an effective tool in solving them and a great variety of numerical methods are available. The first part of the book summarizes the basic physics of shallow-water flow needed to use numerical methods under various conditions. The second part gives an overview of possible numerical methods, together with their stability and accuracy properties as well as with an assessment of their performance under various conditions. This enables the reader to select a method for particular applications. Correct treatment of boundary conditions (often neglected) is emphasized. The major part of the book is about two-dimensional shallow-water equations but a discussion of the 3-D form is included. The book is intended for researchers and users of shallow-water models in oceanographic and meteorological institutes, hydraulic engineering and consulting. It also provides a major source of information for applied and numerical mathematicians.
Author: James Johnston Stoker Publisher: Courier Dover Publications ISBN: 0486839923 Category : Science Languages : en Pages : 593
Book Description
First published in 1957, this is a classic monograph in the area of applied mathematics. It offers a connected account of the mathematical theory of wave motion in a liquid with a free surface and subjected to gravitational and other forces, together with applications to a wide variety of concrete physical problems. A never-surpassed text, it remains of permanent value to a wide range of scientists and engineers concerned with problems in fluid mechanics. The four-part treatment begins with a presentation of the derivation of the basic hydrodynamic theory for non-viscous incompressible fluids and a description of the two principal approximate theories that form the basis for the rest of the book. The second section centers on the approximate theory that results from small-amplitude wave motions. A consideration of problems involving waves in shallow water follows, and the text concludes with a selection of problems solved in terms of the exact theory. Despite the diversity of its topics, this text offers a unified, readable, and largely self-contained treatment.
Author: Nikolaos D. Katopodes Publisher: Butterworth-Heinemann ISBN: 0128154888 Category : Technology & Engineering Languages : en Pages : 850
Book Description
Free-Surface Flow: Shallow-Water Dynamics presents a novel approach to this phenomenon. It bridges the gap between traditional books on open-channel flow and analytical fluid mechanics. Shallow-water theory is established by formal integration of the Navier-Stokes equations, and boundary resistance is developed by a rigorous construction of turbulent flow models for channel flow. In addition, the book presents a comprehensive description of shallow-water waves by mathematical analysis. These methods form the foundation for understanding flood routing, sudden water releases, dam and levee break, sluice gate dynamics and wave-current interaction. - Bridges the gap between traditional books on open-channel flow and wave mechanics - Presents a comprehensive description of shallow-water waves by characteristic and bicharacteristic analysis - Presents techniques for wave control and active flood mitigation
Author: Richard P. Signell Publisher: MDPI ISBN: 3038423629 Category : Computers Languages : en Pages : 421
Book Description
This book is a printed edition of the Special Issue "Selected Papers from the 14th Estuarine and Coastal Modeling Conference" that was published in JMSE
Author: O. C. Zienkiewicz Publisher: Elsevier ISBN: 008045559X Category : Mathematics Languages : en Pages : 457
Book Description
Dealing with general problems in fluid mechanics, convection diffusion, compressible and incompressible laminar and turbulent flow, shallow water flows and waves, this is the leading text and reference for engineers working with fluid dynamics in fields including aerospace engineering, vehicle design, thermal engineering and many other engineering applications. The new edition is a complete fluids text and reference in its own right. Along with its companion volumes it forms part of the indispensable Finite Element Method series.New material in this edition includes sub-grid scale modelling; artificial compressibility; full new chapters on turbulent flows, free surface flows and porous medium flows; expanded shallow water flows plus long, medium and short waves; and advances in parallel computing. - A complete, stand-alone reference on fluid mechanics applications of the FEM for mechanical, aeronautical, automotive, marine, chemical and civil engineers. - Extensive new coverage of turbulent flow and free surface treatments
Author: David Lannes Publisher: American Mathematical Soc. ISBN: 0821894706 Category : Mathematics Languages : en Pages : 347
Book Description
This monograph provides a comprehensive and self-contained study on the theory of water waves equations, a research area that has been very active in recent years. The vast literature devoted to the study of water waves offers numerous asymptotic models.
Author: Ingemar Kinnmark
Author: Ingemar Kinnmark
Author: Robert G Dean
Author: C.B. Vreugdenhil
Author: James Johnston Stoker
Author: Nikolaos D. Katopodes
Author: 
Author: Richard P. Signell
Author: 
Author: O. C. Zienkiewicz
Author: David Lannes