In this monograph, a finite difference algorithm for studying 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 arbitrary free surfaces and the K-epsilon turbulence model. This methodology allows a self-contained study for wave transformation processes in shallow water before, during and after breaking. This capability is illustrated in several calculations. The text should be of benefit to final year graduates, postgraduates and researchers working in the fields of turbulence modelling, wave hydrodynamics, coastal engineering and the oceanography of coastal regions.
By:
Carlos M. Lemos
Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Country of Publication: Germany
Edition: Softcover reprint of the original 1st ed. 1992
Volume: 71
Dimensions:
Height: 242mm,
Width: 170mm,
Spine: 11mm
Weight: 366g
ISBN: 9783540549420
ISBN 10: 3540549420
Series: Lecture Notes in Engineering
Pages: 196
Publication Date: 05 March 1992
Audience:
College/higher education
,
Professional and scholarly
,
Further / Higher Education
,
Undergraduate
Format: Paperback
Publisher's Status: Active
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.
