Numerical modeling of waves for a tsunami early warning system

Contents
1 Introduction 3
1.1 Tsunami . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.1 Tsunamis generated by landslides . . . . . . . . . . . . 4
1.2 Aims and structure of the present work . . . . . . . . . . . . . 7
2 Tsunami wave modelling 11
2.1 Irrotational water waves theories . . . . . . . . . . . . . . . . 11
2.2 Tsunami waves modeling. Literature review . . . . . . . . . . 17
3 Description of the numerical model 23
3.1 Model equations derivation . . . . . . . . . . . . . . . . . . . . 24
3.1.1 Field equation . . . . . . . . . . . . . . . . . . . . . . . 24
3.1.2 Boundary conditions . . . . . . . . . . . . . . . . . . . 28
3.1.3 Waves generation . . . . . . . . . . . . . . . . . . . . . 30
3.2 Model applications . . . . . . . . . . . . . . . . . . . . . . . . 32
3.3 Application of the parabolic approximation of the MSE . . . . 35
3.3.1 Derivation of the parabolic MSE . . . . . . . . . . . . . 36
4 Model validation 39
4.1 The Scott–Russel’s wave generator . . . . . . . . . . . . . . . 40
4.2 Axial-symmetric landslide generated waves . . . . . . . . . . . 47
4.3 Inclusion of waves generation term - Numerical experiments . 51
4.3.1 Constant depth experiments . . . . . . . . . . . . . . . 54
4.3.2 Experiments on a plane slope . . . . . . . . . . . . . . 60
4.4 Landslide generated waves along a straigth beach . . . . . . . 63
4.5 Landslide generated waves around a conical island . . . . . . . 67
4.5.1 Waves generation with the ‘indirect’ procedure . . . . . 73
4.5.2 Waves generation with the ‘direct’ procedure . . . . . . 82
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