Contents

xiiContents5.1.5 Stability Criterion ................................... 945.2 Exercise8:LongWavesinaShallowLake ..................... 945.2.1 Aim .............................................. 945.2.2 TaskDescription.................................... 945.2.3 SampleCodeandAnimationScript.................... 945.2.4 Snapshot Results . ................................... 955.2.5 Additional Exercise for the Reader . .................... 955.3 Exercise9:WaveRefraction.................................. 955.3.1 Aim .............................................. 955.3.2 Background . . . . . ................................... 955.3.3 TaskDescription.................................... 965.3.4 Lateral Boundary Conditions . ........................ 965.3.5 SampleCodeandAnimationScript.................... 985.3.6 Results............................................ 985.3.7 Additional Exercise for the Reader . .................... 985.4 The Wind-Forced Shallow-Water Model. . . . .................... 995.4.1 TheGoverningEquations ............................ 995.4.2 Semi-implicit Approach for Bottom Friction . . . . . . ...... 995.4.3 Finite-Difference Equations . . ........................1005.5 Exercise10:Wind-DrivenFlowinaLake ......................1015.5.1 Aim ..............................................1015.5.2 CreationofVariableBathymetry ......................1015.5.3 SampleCode.......................................1015.5.4 TaskDescription....................................1015.5.5 Tricks for Long Model Simulations ....................1025.5.6 Results............................................1025.5.7 SampleCodeandAnimationScript....................1035.5.8 Caution ...........................................1035.5.9 Additional Exercise for the Reader . ....................1045.6 Movement of Tracers. . . . . ...................................1045.6.1 Lagrangian Versus Eulerian Tracers ....................1045.6.2 A Difficul Task . ...................................1045.6.3 Eulerian Advection Schemes . . ........................1045.6.4 Stability Criterion for the Advection Equation . . . . . ......1065.7 Exercise11:EulerianAdvection ..............................1065.7.1 Aim ..............................................1065.7.2 TaskDescription....................................1075.7.3 Results............................................1075.7.4 Recommendation ...................................1095.7.5 SampleCodeandAnimationScript....................1095.8 Exercise12:Trajectories.....................................1095.8.1 Aim ..............................................1095.8.2 TaskDescription....................................1095.8.3 Results............................................1095.8.4 SampleCodeandAnimationScript....................111