Mathematical Models

Jean-Michel Tanguy, Ministry of Sustainable Development, France.

• Introduction xixJean-Michel TANGUYChapter 1. Reminders on the Mechanical Properties of Fluids 1Jacques GEORGE1.1. Laws of conservation, principles and general theorems 11.2. Enthalpy, rotation, mixing, saturation 131.3. Thermodynamic relations, relations of state and laws of behavior 201.4. Turbulent flow 261.5. Dynamics of geophysical fluids 30Chapter 2. 3D Navier-Stokes Equations 35Véronique DUCROCQ2.1. The continuity hypothesis 352.2. Lagrangian description/Eulerian description 362.3. The continuity equation 372.4. The movement quantity assessment equation 382.5. The energy balance equation 412.6. The equation of state 412.7. Navier-Stokes equations for a fluid in rotation 41Chapter 3. Models of the Atmosphere 43Jean COIFFIER3.1. Introduction 433.2. The various simplifications and corresponding models 443.3. The equations with various systems of coordinates 563.4. Some typical conformal projections 613.5. The operational models 673.6. Bibliography 69Chapter 4. Hydrogeologic Models 71Dominique THIÉRY4.1. Equation of fluid mechanics 714.2. Continuity equation in porous media 724.3. Navier-Stokes’ equations 744.4. Darcy’s law 764.5. Calculating mass storage from the equations of state 804.6. General equation of hydrodynamics in porous media 824.7. Flows in unsaturated media 844.8. Bibliography 91Chapter 5. Fluvial and Maritime Currentology Models 93Jean-Michel TANGUY5.1. 3D hydrostatic model 995.2. 2D horizontal model for shallow water 1075.3. 1D models of fluvial flows 1195.4. Putting 1D models into real time 1315.5. Bibliography 151Chapter 6. Urban Hydrology Models 155Bernard CHOCAT6.1. Global models and detailed models used in surface flows 1566.2. Rainfall representation and rainfall-flow transformation 1616.3. Modeling of the losses into the ground 1646.4. Transfer function 1696.5. Modeling of the hydraulic operating conditions of the networks 1776.6. Production and transport of polluting agents 1896.7. Conclusion 2056.8. Bibliography 206Chapter 7. Tidal Model and Tide Streams 213Bernard SIMON7.1. Tidal coefficient 2147.2. Non-harmonic methods 2157.3. Compatibilities 2167.4. Tidal coefficient 2227.5. Modeling 2237.6. Tidal currents 226Chapter 8. Wave Generation and Coastal Current Models 235Jean-Michel TANGUY, Jean-Michel LEFÈVRE and Philippe SERGENT8.1. Types of swell models 2358.2. Spectral approach in high waters 2428.3. Wave generation models 2468.4. Wave propagation models 2608.5. Agitating models within the harbors 2668.6. Non-linear wave model: Boussinesq model 2988.7. Coastal current models influenced or created by the swell 3208.8. Bibliography 325Chapter 9. Solid Transport Models and Evolution of the Seabed 335Benoît LE GUENNEC and Jean-Michel TANGUY9.1. Transport due to the overthrust effect 3389.2. Total load 3449.3. Bed forms and roughness 3449.4. Suspension transport 3469.5. Evolution model of movable beds 3579.6. Conclusion 3649.7. Bibliography 364Chapter 10. Oil Spill Models 371Pierre DANIEL10.1. Behavior of hydrocarbons in marine environment 37110.2. Oil spill drift models 37210.3. Example: the MOTHY model 37510.4. Calculation algorithm of the path of polluting particles 37810.5. Example of a drift prediction map 37910.6. Bibliography 379Chapter 11. Conceptual, Empirical and Other Models 381Christelle ALOT and Florence HABETS11.1. Evapotranspiration 38211.2. Bibliography 394Chapter 12. Reservoir Models in Hydrology 397Patrick FOURMIGUÉ and Patrick ARNAUD12.1. Background 39712.2. Main principles 39912.3. Mathematical tools 40112.4. Forecasting 40312.5. Integration of the spatial information 40512.6. Modeling limits 40612.7. Bibliography 406Chapter 13. Reservoir Models in Hydrogeology 409Dominique THIÉRY13.1. Principles and objectives 40913.2. Catchment basin 41013.3. Setting the model up 41113.4. Data and parameters 41213.5. Application domains 412Chapter 14. Artificial Neural Network Models 419Anne JOHANNET14.1. Neural networks: a rapidly changing domain 42014.2. Neuron and architecture models 42214.3. How to take into account the non-linearity 42914.4. Case study: identification of the rainfall-runoff relation of a karst 43414.5. Acknowledgments 44114.6. Bibliography 441Chapter 15. Model Coupling 445Rachid ABABOU, Denis DARTUS and Jean-Michel TANGUY15.1. Model coupling 44615.2. Bibliography 488Chapter 16. A Set of Hydrological Models 493Charles PERRIN, Claude MICHEL and Vasken ANDRÉASSIAN16.1. Introduction 49316.2. Description of the annual GR1A rainfall-runoff model 49516.3. Description of the monthly GR2M rainfall-runoff model 49616.4. Description of the daily GR4J rainfall-runoff model 50016.5. Applications of the models 50516.6. Conclusions and future work 50616.7. Bibliography 507List of Authors 511Index 515General Index of Authors 517Summary of the Other Volumes in the Series 519

"An inventory of ground measurement instruments, which provide necessary input data for the various modeling tools described in the book, is drawn up, and mathematical models describing each field within the overall subject area are detailed by a series of system equations. These are then solved by the use of numerical methods adapted to the particular characteristics of the application in question." (Environmental Expert, 19 April 2011)