Mathematical and Computational Models of Flows and Waves in Geophysics

Description

This volume proposes an integral approach to studying the geophysics of Earth. It is motivated by a variety of phenomena from nature with deep and direct impacts in our lives. Such events may evolve across a large range of spatial and time scales and may be observed in the ocean, the atmosphere, the volcanic surface as well as underground. The physical laws dictating the evolution of such phenomena lead to the unifying theme of this manuscript, that is, the mathematical and computational modeling of flows and waves. Consequently, the underlying models are given in terms of Partial Differential Equations (PDEs) whose solutions are approximated using numerical methods, thus providing simulations of the aforementioned phenomena, as well as the appropriate geophysical validation and interpretation. Preface Contents Geostrophic Turbulence and the Formation of Large Scale Structure 1 Introduction 2 Asymptotic Reduction of the Primitive Equations 2.1 Properties of the NHBGE 3 Spontaneous Formation of Large Scale Vortices 4 Validation 5 Finite Rossby Number 6 Cylindrical Domain: Robust Boundary Flow 7 Discussion References Ocean Surface Waves and Ocean-Atmosphere Interactions 1 Introduction 2 Recent Developments on Air-Sea Exchange of Momentum and Gases 2.1 On the Transfer of Momentum Between the Ocean and Atmosphere 2.2 On the Transfer of Mass and Carbon Dioxide Between Air and Water 3 Air-Sea Exchange of Carbon Dioxide and the Relevance of Ocean Surface Waves Within the Context of Climate Prediction 4 Remote Sensing Ocean Measurements and Their Relation to Upper Ocean Processes Direct Observations 5 Final Remarks References A 3D Two-Phase Conservative Level-Set Method Using an Unstructured Finite-Volume Formulation 1 Introduction 2 Conservative Level-Set Method 3 Numerical Method for the Level-Set Equation 3.1 Time Integration: θ-Method 3.2 Space Discretization: Finite-Volume Method 3.3 Interpolation: Upwind Scheme 3.4 Boundary Conditions 3.5 Linear System and Solver 4 Numerical Method for the Reinitialization Equation 5 Parallelization 6 Accuracy 6.1 2D Pure Convective Test 6.2 3D Pure Convective Test 6.3 Reinitialization Test 7 Two-Dimensional Numerical Results 7.1 Solid-Body Rotation 7.2 Zalesak's Disk 7.3 Single Vortex Deformation of a Circle 8 Three-Dimensional Numerical Results 8.1 Kawano 3D Solid-Body Translation 8.2 Zalesak's Sphere Vortex Deformation of a Sphere 9 Performance 10 Conclusions References The Physics of Granular Natural Flows in Volcanic Environments 1 Introduction 2 Pyroclastic Density Currents 3 Lahar 4 Numerical Simulations and Experiments 4.1 Numerical Simulations 4.2 Experiments 5 Monitoring 6 Numerical Model for Hazard Assessment 7 Discussion and Conclusions References Cooperative Gravity and Full Waveform Inversion: Elastic Case 1 Introduction 2 Forward Modeling of Geophysical Data 2.1 Gravimetric Forward Modeling 2.2 Gravimetric Forward Modeling 2.3 Waveform Forward Modeling 3 Inverse Theory for Geophysical Data 3.1 Gravimetric Inversion 3.2 Acoustic Full Waveform Inversion 3.3 Gradient Based Optimization 3.4 Elastic Full Waveform Inversion 3.5 Cooperative Inversion 4 Results 4.1 EFWI: Marmousi Model 4.2 EFWI: Texas-Shaped Model 4.3 Cooperative Inversion: Marmousi Model 4.4 Cooperative Inversion: Texas-Shaped Model 5 Conclusions References Modelling the 3D Electromagnetic Wave Equation: Negative Apparent Conductivities and Phase Changes 1 Introduction 2 Modeling Scheme 3 Apparent Conductivities at LIN 4 Code Validation 5 Applications 5.1 Sinkhole Model 5.2 Two Nearby Sinkholes 5.3 Layered Conductivity Model with a Wellbore 5.4 Vertical-Contact Model 6 Discussion 7 Conclusions Appendix 1 Appendix 2 References