| Description |
1 online resource (324 p.) |
| Series |
Mathematics of Planet Earth ; v.9 |
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Mathematics of planet Earth ; v. 9.
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| Contents |
Basic Equations of Marine Flows / Knut Klingbeil Eric Deleersnijder Oliver Fringer Lars Umlau -- Water Waves in Isotropic and Anisotropic Media: A comparison / Leo R. M. Maas -- A Review of Nonlinear Boussinesq-Type Models for Coastal Ocean Modeling / Clint Dawson Ali Samii -- Tides in Coastal Seas. Influence of Topography and Bottom Friction / Pieter C. Roos Huib E. de Swart -- Variational Water-Wave Modeling: From Deep Water to Beaches / Onno Bokhove -- Quasi-2D Turbulence in Shallow Fluid Layers / Herman J. H. Clercx -- Turbulent Dispersion / Benoit Cushman-Roisin -- Spreading and Mixing in Near-Field River Plumes / Robert D. Hetland -- Lagrangian Modelling of Transport Phenomena Using Stochastic Differential Equations / Arnold Heemink Eric Deleersnijder Syed Hyder Ali Muttaqi Shah Ulf Gräwe -- Morphodynamic Modelling in Marine Environments: Model Formulation and Solution Techniques / H. M. Schuttelaars T. J. Zitman -- Wetting and Drying Procedures for Shallow Water Simulations / Sigrun Ortleb Jonathan Lambrechts Tuomas Kärnä |
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Intro -- Preface -- Contents -- Contributors -- 1 Basic Equations of Marine Flows -- 1.1 Mathematical Description of Fluids -- 1.1.1 Fluids as Continuous Media -- 1.1.2 Integral and Differential Formulations -- 1.1.3 Averaging of Turbulent Flows -- 1.2 Governing Equations -- 1.2.1 Volume Conservation -- 1.2.2 Salt Conservation -- 1.2.3 Heat Balance -- 1.2.4 Momentum Balance -- 1.2.5 Common Formulations and Closures -- 1.3 Summary -- References -- 2 Water Waves in Isotropic and Anisotropic Media: A comparison -- 2.1 Introduction -- 2.2 Gravity Waves |
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2.2.1 Surface Gravity Waves in Homogeneous Fluids -- 2.2.2 Gravity Waves in Heterogeneous Media -- 2.3 Inertial Waves -- 2.3.1 Waves in Shear Flows -- 2.3.2 Waves in Rotating Basins -- 2.3.3 Three-dimensional Effects -- 2.4 Discussion -- 2.4.1 The Linear Shear Flow as ̀Problematic' Equilibrium -- 2.4.2 Waves in Anisotropic Media -- 2.4.3 Mixing Due to Wave Focusing and Mean Flows -- 2.5 Conclusion -- References -- 3 A Review of Nonlinear Boussinesq-Type Models for Coastal Ocean Modeling -- 3.1 Introduction -- 3.2 The Water Wave Problem -- 3.2.1 Dispersive Properties of the Linear Waves |
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3.2.2 Scaling of Variables and Operators -- 3.2.3 Nondimensionalization of Equations -- 3.2.4 Green-Naghdi Equation -- 3.3 A Finite Element Discretization of the Green-Naghdi Equation -- 3.3.1 Notation -- 3.3.2 Functional Setting -- 3.3.3 Variational Formulation and Solution Procedure -- 3.4 Numerical Results -- 3.5 Conclusions -- References -- 4 Tides in Coastal Seas. Influence of Topography and Bottom Friction -- 4.1 Introduction -- 4.2 Model Formulation -- 4.3 Fundamental Wave Solutions -- 4.3.1 Derivation with Klein-Gordon Equation -- 4.3.2 Kelvin Wave -- 4.3.3 Poincaré Waves |
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4.3.4 Wave Solutions with a Transverse Topographic Step -- 4.4 Amphidromic Patterns in Semi-enclosed Basins -- 4.4.1 Superposition of Two Kelvin Waves -- 4.4.2 Solution to Extended Taylor Problem -- 4.4.3 Application to Basins Around the World -- 4.5 Discussion -- 4.6 Conclusions -- References -- 5 Variational Water-Wave Modeling: From Deep Water to Beaches -- 5.1 Introduction -- 5.2 Derivation of Luke's Variational Principle -- 5.3 Transformed Luke's/Miles' Variational Principles with Wavemaker -- 5.3.1 FEM and Mesh Motion -- 5.3.2 Numerical Results: Comparison with Wave-Tank Experiments |
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5.4 Coupling Water Waves to Shallow-Water Beach Hydraulics -- 5.4.1 Numerical Results: Damping of Waves on the Beach -- 5.5 Summary and Conclusions -- References -- 6 Quasi-2D Turbulence in Shallow Fluid Layers -- 6.1 Introduction -- 6.2 Two-Dimensional Turbulence -- 6.2.1 Inertial Ranges in 2D Turbulence -- 6.2.2 2D Turbulence: The Early Years -- 6.2.3 Coherent Structures and 2D Turbulence -- 6.3 2D Turbulence in Square, Rectangular and Circular Domains -- 6.3.1 Simulations of 2D Turbulence in Domains with No-Slip Walls -- 6.3.2 Quasi-Steady Final States: Laboratory Experiments |
| Summary |
Over the past few decades, numerical simulation has become instrumental in understanding the dynamics of seas, coastal regions and estuaries. The decision makers rely more and more frequently on model results for the management of these regions. Some modellers are insufficiently aware of the theoretical underpinning of the simulation tools they are using. On the other hand, a number of applied mathematicians tend to view marine sciences as a domain in which they would like to use the tools they have a good command of. Bridging the gap between model users and applied mathematicians is the main objective of the present book. In this respect a vast number of issues in which mathematics plays a crucial role will be addressed |
| Notes |
6.3.3 Forced 2D Turbulence on Confined Domains |
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Includes index |
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Online resource; title from PDF title page (SpringerLink, viewed December 13, 2022) |
| Subject |
Oceanography -- Mathematical models
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Oceanography -- Mathematical models
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Oceanografia.
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Models matem��tics.
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Teoria de l'aproximaci��
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An��lisi matem��tica.
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| Genre/Form |
Llibres electr��nics.
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| Form |
Electronic book
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| Author |
Schuttelaars, Henk
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Heemink, A. W.
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Deleersnijder, Eric
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| ISBN |
9783031095597 |
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3031095596 |
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9788303109552 |
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8303109553 |
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