Wave Breaking: A Numerical Study [Paperback]

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.- 2.8.1 The exact K equation.- 2.8.2 The exact ? equation.- 2.8.3 The exact $$\overline $$ equation.- 2.9 Turbulence models.- 2.9.1 Definition and classification.- 2.9.2 Algebraic models.- 2.9.3 The K (one-equation) model.- 2.9.4 The two-equation K-? model.- 2.9.5 Reynolds-stress transport models.- 2.9.6 The K-?-A model.- 2.9.7 Practical considerations.- 2.10 Boundary conditions for K and ?.- 2.10.1 Wall boundary conditions.- 2.10.2 Planes and axes of symmetry.- 2.10.3 Turbulent non-turbulent interfaces.- 2.10.4 Free-surface boundary conditions.- 3: Mathematical modeling of breaking shallow water waves. Proposed methodology.- 3.1 Introduction.- 3.2 Physical processes.- 3.2.1 Wave breaking criteria.- 3.2.2 Shallow water steepening vs. dispersion.- 3.2.3 Wave overturning.- 3.2.4 Breaking wave propagation and decay.- 3.2.5 Other physical effects.- 3.3 Mathematical descriptions.- 3.3.1 Wave theories. Range of validity.- 3.3.2 Shallow water equations. Characteristics and discontinuities.- 3.3.3 Boussinesq-type shallow water equations.- 3.3.4 Overturning wave models.- 3.4 Wave theories for very shallow water.- 3.4.1 Solitary waves.- 3.4.2 Hydraulic jumps. Discrete forms of the conservation laws.- 3.5 Summary of experimental investigations.- 3.5.1 Wave-wave interactions.- 3.5.2 Hydraulic jumps.- 3.5.3 Waves breaking on a slope.- 3.6 Description of the proposed methodology.- 4: MAC-type methods for incompressible free-surface flows.- 4.1 Intrls4