Contents vii
5.2.2 Unsteady-state open channel flow 90
5.2.2.1 Governing equations 90
5.2.2.2 Numerical solution algorithm 93
5.3 Two-dimensional horizontal free surface flows 104
5.3.1 Governing equations 106
5.3.2 Initial and boundary conditions 107
5.3.3 Radiation stresses 108
5.3.4 Numerical solution scheme 109
5.4 Stratified flows in geophysical domains 126
5.4.1 Governing equations for horizontal
two-dimensional stratified flows 127
5.4.2 One-dimensional stratified system 128
6 Surface gravity water waves
135
6.1 Basic concepts of water waves 135
6.2 One-dimensional gravity long waves 137
6.2.1 Linearization of the governing equations 139
6.2.2 Discretization of the wave equation 140
6.3 Two-dimensional linear gravity long waves 152
6.4 Harbour basin resonance 161
7 Flow in porous media
169
7.1 General groundwater flow equations 169
7.1.1 Darcy equation 169
7.1.2 General form of the continuity equation 170
7.1.3 Flow in confined aquifers 171
7.1.4 Flow in unconfined aquifers 172
7.1.5 Boundary conditions in groundwater
flow domains 174
7.2 Numerical solutions of groundwater flow applications 175
7.2.1 Steady-state vertical two-dimensional
groundwater flows 175
7.2.2 Horizontal two-dimensional groundwater flows 182
7.2.3 Saltwater intrusion in coastal aquifers 189
7.2.3.1 One-dimensional equations
for saltwater intrusion 190
7.2.3.2 Computational scheme
of the governing equations 191