Wave Breaking
A Numerical Study
Published on 5. March 1992
Book
Paperback/Softback
VIII, 196 pages
978-3-540-54942-0 (ISBN)
Description
In this monograph, a finite difference algorithm for study- ing two dimensional wave breaking in the vertical plane is developed. The essential feature of this algorithm is the combination of the Volume-of-Fluid (VOF) technique for arbi- trary free surfaces and the k-E turbulence model. This me- thodology allows a self-contained study for wave transforma- tion processes in shallow water before, during and after breaking. This capability is illustrated in several calcula- tions. This book will be of interest for final year graduates, postgraduates and researchers working in the fields of tur- bulence modelling, wave hydrodynamics, coastal engineering, and oceanography of coastal regions.
More details
Series
Edition
Softcover reprint of the original 1st ed. 1992
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
College/higher education
Professional and scholarly
Research
Illustrations
VIII, 196 p.
Dimensions
Height: 24.2 cm
Width: 17 cm
Weight
366 gr
ISBN-13
978-3-540-54942-0 (9783540549420)
DOI
10.1007/978-3-642-84688-5
Schweitzer Classification
Other editions
Additional editions
Content
1: Introduction.- 1.1 Nature and scope of the work.- 1.2 Methodology.- 1.3 Innovations and conclusions.- 2: General aspects of incompressible flow. Theoretical review.- 2.1 Introduction.- 2.2 The Navier-Stokes equations for uniform, incompressible fluids.- 2.3 Initial and boundary conditions.- 2.4 The energy equation.- 2.5 The vorticity equation.- 2.6 The pressure Poisson equation for incompressible flows.- 2.7 General aspects of turbulent flows. Averaging methods and Reynolds equations.- 2.8 Turbulence transport equations.- 2.9 Turbulence models.- 2.10 Boundary conditions for K and ?.- 3: Mathematical modeling of breaking shallow water waves. Proposed methodology.- 3.1 Introduction.- 3.2 Physical processes.- 3.3 Mathematical descriptions.- 3.4 Wave theories for very shallow water.- 3.5 Summary of experimental investigations.- 3.6 Description of the proposed methodology.- 4: MAC-type methods for incompressible free-surface flows.- 4.1 Introduction.- 4.2 The choice of the mesh.- 4.3 The MAC (Marker-And-Cell) method.- 4.4 The projection method.- 4.5 The SMAC (Simplified-Marker-And-Cell) method.- 4.6 The pressure-velocity iteration method.- 4.7 Numerical treatment of free-surfaces.- 4.8 Stability considerations.- 4.9 Conclusions.- 5: Description of the numerical model.- 5.1 Introduction.- 5.2 Momentum equation approximations.- 5.3 Continuity equation approximation.- 5.4 Approximations for the K and ? equations.- 5.5 Updating the fluid configuration.- 5.6 Velocity boundary conditions.- 5.7 Boundary conditions for the K and ? equations.- 5.8 Initial conditions for the K and ? equations.- 5.9 Stability considerations.- 5.10 Programming considerations.- 5.11 Selected test problems.- 6: Numerical simulation of shallow water waves.- 6.1 Introduction.- 6.2 Propagation ofa solitary wave over a horizontal bottom.- 6.3 Collision between solitary waves.- 6.4 Simulation of undular, transitional and turbulent hydraulic jumps.- 6.5 Breaking of a solitary wave over a slope.- 6.6 Breaking of a train of solitary waves over a slope.- 7: Conclusions. Future research and development.- 7.1 Summary and conclusions.- 7.2 Future research and development.- References.