Note: Intro -- Preface -- Contents -- List of Contributors -- CENS, CMA and the CENS-CMA Project -- CENS 1999-2009 -- CMA -- The CENS-CMA Project -- Part I Waves in Solids -- Overview -- Deformation Waves in Solids -- Introduction -- General ideas -- Notes from history -- Description of what follows -- Basic theory -- Advanced theories -- General ideas -- Separation of macro- and microstructure -- Balance of pseudomomentum -- Internal variables -- Model governing equations -- Basic linear theory -- Wave hierarchy -- Nonlinearities -- One-wave models -- Final remarks -- References -- The Perturbation Technique for Wave Interaction in Prestressed Material -- Introduction -- Prelude -- Basic relations in continuum mechanics -- Coordinate systems -- Conservation laws -- The constitutive equation -- Initial and boundary conditions -- Compatibility conditions -- Governing equations -- The perturbation technique -- The prestressed state -- Counterpropagating waves -- Harmonic waves -- Nondestructive characterization of plane strain -- Conclusions -- References -- Waves in Inhomogeneous Solids -- Introduction -- Governing equations -- The wave-propagation algorithm -- Averaged quantities -- Numerical fluxes -- Second-order corrections -- The conservative wave propagation algorithm -- Excess quantities and numerical fluxes -- Excess quantities at the boundaries between cells -- One-dimensional waves in periodic media -- One-dimensional weakly nonlinear waves in periodic media -- One-dimensional linear waves in laminates -- Nonlinear elastic waves in laminates under impact loading -- Comparison with experimental data -- Waves in functionally graded materials -- Concluding remarks -- References -- Part II Mesoscopic Theory -- Overview -- References -- Dynamics of Internal Variables from the Mesoscopic Background for the Example of Liquid Crystals and Ferrofluids. , Introduction to liquid crystals -- Some properties of liquid crystals -- Mesoscopic theory of complex materials -- Complex materials -- Examples of internal structure -- The mesoscopic concept -- Mesoscopic balance equations -- Mesoscopic theory of uniaxial liquid crystals -- Mesoscopic balance equations -- Macroscopic balance equations -- Macroscopic constitutive quantities -- Order parameters -- Differential equation for the distribution function and for the alignment tensors -- Example of a closed differential equation for the second order alignment tensor -- Landau theory of phase transitions as a special case -- A remark on constitutive theory and the Second Law of Thermodynamics -- A set of differential equations for the moments and a second order differential equation for the alignment tensor -- Application of the mesoscopic theory to dipolar media -- Orientation distribution function and alignment tensors -- Exploitation of the balance of spin -- Equation of motion for the magnetization -- Summary -- Summary of the mesoscopic theory -- References -- Towards a Description of Twist Waves in Mesoscopic Continuum Physics -- Introduction -- Mesoscopic Continuum Physics -- Generalization of vector fields to the mesoscopic space -- Mesoscopic balances and a transport theorem -- Orientation waves -- Twist waves in classical macroscopic theory -- Twist waves in mesoscopic theory -- Comparison -- Mesoscopic mass density, orientation distribution function and macroscopic director -- Macroscopic balance equations -- Conclusions and outlook -- References -- Part III Exploiting the Dissipation Inequality -- Overview -- References -- Weakly Nonlocal Non-equilibrium Thermodynamics -- Variational Principles and Second Law -- Introduction -- Second law and weakly nonlocal constitutive spaces -- Thermodynamic evolution of internal variables. , First order nonlocality -- relaxation -- Second order nonlocality -- the Ginzburg-Landau equation -- Dual internal variables -- Hamiltonian structure -- Classical Irreversible Thermodynamics -- One component fluids -- second order nonlocal in the density -- Fluid mechanics in general -- Schrödinger-Madelung fluid -- Summary and outlook -- Appendix -- Farkas's lemma and some of its consequences -- Affine Farkas's lemma -- Liu's theorem -- References -- Part IV Waves in Fluids -- Overview -- Surface waves at the cutting edge of research and applications -- References -- Long Ship Waves in Shallow Water Bodies -- Introduction -- Linear ship wakes -- Kelvin wedge -- Navigational speeds -- Distribution of wave heights and periods -- Patterns of wakes from fast ferries -- Changes in the ship wave pattern -- Realistic spatial patterns of ship waves -- Ship waves at a fixed point -- Contribution of ship wakes to local hydrodynamics -- Parameters of wind waves in semi-enclosed seas -- Ship wakes versus wind waves -- Ship wakes and the coast -- Excessive near-bottom velocities and impulse loads -- Conclusions -- References -- Modelling of Ship Waves from High-speed Vessels -- Waves generated by ships -- Governing equations and results from linear wave theory -- Steady ship wakes and ship wave parameters -- Wave making resistance to steady ship motion -- Ship wake patterns in deep and shallow water -- Why is wake wash from high-speed vessels a problem? -- Properties of long wave model equations -- Approximations for shallow water flow -- Comparison between different model equations -- Numerical modelling of ship waves -- Numerical models based on Boussinesq-type equations -- Ship representation by a moving pressure disturbance -- The influence of the dispersive and nonlinear components -- Concluding Remarks -- References. , New Trends in the Analytical Theory of Long Sea Wave Runup -- Introduction -- Basic equations and parameters -- Method of solution: hodograph transformation -- Linear approximation of nonlinear long wave runup -- The relation between linear and nonlinear runup properties -- Runup of solitary waves -- Runup of periodic waves -- Conclusion -- References -- Part V Mathematical Methods -- Overview -- The Pseudospectral Method and Discrete Spectral Analysis -- Introduction -- The model equations -- The pseudospectral method -- Approximation of space derivatives -- The discrete Fourier transform -- The essence of the pseudospectral method -- The pseudospectral method and different equation types -- Filtering and other practical tips -- Discrete spectral analysis -- Spectral amplitudes and spectral densities -- Cumulative spectrum and time averaged normalised spectral densities -- Applications -- Conclusions -- References -- Foundations of Finite Element Methods for Wave Equations of Maxwell Type -- Introduction -- Analysis of the finite element method for waves -- Linear wave equations -- Convergence theory for linear equations -- Consistency -- Eigenvalue approximation -- Construction of finite element spaces -- Algebra -- Differential geometry -- Finite elements on cellular complexes -- Conclusion -- References -- An Introduction to the Theory of Scalar Conservation Laws with Spatially Discontinuous Flux Functions -- Introduction -- The Riemann problem -- Existence of a solution -- Vanishing viscosity and smoothing -- The Cauchy problem -- A model equation -- Uniqueness of entropy solutions -- References -- Index.

Note: Intro -- Preventive Methods for Coastal Protection -- Foreword -- References -- Preface -- The BalticWay Project -- PROJECT PARTNERS -- Project coordinator: -- Oleg Andrejev (1941-2012) -- Contents -- Chapter 1: Towards Mitigation of Environmental Risks -- 1.1 Introduction -- 1.2 The Notion of Risk, Probability and Consequences -- 1.3 Changing Paradigms of Local and Remote Risks -- 1.4 Managing Propagation of Contaminants and Oil Spills -- 1.5 Ship Routing Systems -- 1.6 Environmental Management of Ship Routes -- 1.7 Minimizing the Remote Impact of Ship Traf c -- 1.8 Site-Speci c Cost of the Consequences -- 1.9 Separation of the Impact of Wind, Waves and Currents -- 1.10 Dynamical and Statistical Forecast -- 1.11 Favourable Patterns of Currents and Current-Induced Transport -- 1.12 Quanti cation of Offshore Domains -- 1.13 A Preventive Technology of Environmental Management -- 1.14 From Classical Physical Oceanography to Environmental Management -- 1.15 Concluding Remarks -- References -- Part I: Modelling the Underlying Dynamics -- Chapter 2: Topography, Hydrography, Circulation and Modelling of the Baltic Sea -- 2.1 Introduction to the Baltic Sea Geometry and Topography -- 2.2 Basic Hydrography -- 2.2.1 Salinity -- 2.2.2 Temperature -- 2.3 Circulation Dynamics -- 2.3.1 Basic Principles -- 2.3.2 Barotropic and Baroclinic Flows and Rossby Radii -- 2.3.3 Dynamics of Surface Currents -- 2.3.4 Inertial Oscillations -- 2.3.5 Ekman Drift -- 2.3.6 Geostrophic Flow -- 2.3.7 Surface Circulation of the Baltic Sea and the Gulf of Finland -- 2.3.8 Three-Dimensional Water Circulation -- 2.4 Numerical Modelling of the Baltic Sea -- 2.5 Summary: How the Baltic Sea Can Be Replicated by Numerical Models of Today -- References -- Chapter 3: Introduction to Computational Fluid Dynamics and Ocean Modelling -- 3.1 Introduction -- 3.2 Numerical Models. , 3.2.1 Methods Used in CFD Modelling -- 3.2.2 The Finite Difference Method -- 3.3 Numerical Ocean Modelling -- 3.3.1 Physical Characteristics of Ocean Dynamics -- 3.3.1.1 Time Scales and Space Scales for Ocean Dynamics -- 3.3.2 Model Equations on a Rotating Frame of Reference -- 3.3.2.1 The Boussinesq Approximation -- 3.3.2.2 The Hydrostatic Approximation -- 3.3.2.3 The Hydrostatic Primitive Equations -- 3.3.3 Ocean Turbulence -- 3.3.4 Subgrid-Scale Parameterization -- 3.3.5 Classi cation of Ocean Models -- 3.3.6 Initial and Boundary Conditions -- References -- Chapter 4: Studying the Baltic Sea Circulation with Eulerian Tracers -- 4.1 Introduction -- 4.1.1 Motivation -- 4.1.2 Eulerian Versus Lagrangian Approaches -- 4.2 Ocean Circulation Modelling -- 4.2.1 Model Dynamics -- 4.2.1.1 Basic Equations -- 4.2.1.2 Equation of State -- 4.2.1.3 Sea Surface Boundary Conditions -- Wind Stress -- Heat Flux -- Fresh Water Flux -- 4.2.1.4 Insolation -- 4.2.1.5 Horizontal Mixing -- 4.2.1.6 Turbulence Model -- 4.2.1.7 Bottom Friction -- 4.2.2 Model Setup -- 4.2.2.1 Introduction -- 4.2.2.2 Bottom Topography -- 4.2.2.3 Initial Conditions and Spin-Up -- 4.2.2.4 Lateral Boundary Conditions -- 4.2.2.5 Sea Level in the Kattegat -- 4.2.2.6 Atmospheric Forcing -- 4.2.2.7 River Runoff -- 4.2.2.8 Numerical Implementation and Shortcomings -- 4.3 Eulerian Tracer Methods -- 4.4 Oil Spill Modelling Using Eulerian Methods -- 4.4.1 Ensemble Approach -- 4.4.2 Multi-tracer Approach -- 4.4.3 Hybrid Approach -- 4.5 Outlook -- References -- Chapter 5: European Semi-enclosed Seas: Basic Physical Processes and Their Numerical Modelling -- 5.1 Introduction -- 5.1.1 Fresh Water Fluxes -- 5.1.2 The Role of Topography -- 5.1.3 Wind-Driven and Thermohaline Circulation -- 5.1.4 Numerical Modelling of the Three Major European Seas -- 5.2 Straits -- 5.2.1 Theoretical Considerations. , 5.2.2 The Danish Straits and Baltic Sea Underwater Passages -- 5.2.3 The Bosporus Straits -- 5.2.4 Gibraltar -- 5.2.5 Modelling Strait Processes and Out ows -- 5.3 Water Mass Formation -- 5.3.1 Numerical Modelling of Wind and Thermohaline Circulation -- 5.3.1.1 Models -- 5.3.1.2 Parameterization of the Vertical Exchange in Estuarine Basins -- 5.3.2 Numerical Modelling of Thermohaline Circulation -- 5.3.2.1 Baltic Sea -- 5.3.2.2 Black Sea -- 5.3.2.3 Mediterranean Sea -- 5.3.3 Numerical Modelling of the Estuarine Circulation: The Baltic Sea Case -- 5.3.4 Intermediate Water Mass Formation: The Black Sea Example -- 5.3.5 The Eastern Mediterranean Transient -- 5.4 Concluding Remarks -- References -- Chapter 6: The Gulf of Finland, Its Hydrography and Circulation Dynamics -- 6.1 Introduction -- 6.2 General Features of the Gulf of Finland Affecting the Circulation Dynamics: The Forcing -- 6.2.1 Topography -- 6.2.2 Water Budget -- 6.2.3 Horizontal and Vertical Structure of Salinity -- 6.2.4 Temperature -- 6.2.5 Upwelling and Turbulence -- 6.3 Meteorological Forcing -- 6.3.1 Wind Forcing -- 6.3.2 Ice Conditions -- 6.3.3 Energy Budget -- 6.4 Circulation Dynamics -- 6.4.1 Scaling of the Equations of Motions and the Rossby Radius -- 6.4.2 In Search of the Mean Residual Circulation -- 6.4.3 Complexity of Observed Motion Patterns -- 6.4.4 Advanced Numerical Modelling of Mesoscale Dynamics -- 6.4.5 The Intriguing Entrance to the Gulf of Finland -- 6.4.6 Water Age -- 6.5 Concluding Remarks -- References -- Part II: Lagrangian Dynamics and Inverse Problems -- Chapter 7: TRACMASS-A Lagrangian Trajectory Model -- 7.1 Introduction -- 7.2 Trajectory Solution for Rectangular Grids -- 7.3 Scheme for Volume or Mass Transports and Non-rectangular Grids -- 7.4 Scheme for Atmospheric Hybrid Vertical Coordinates -- 7.5 Time Integration -- 7.5.1 Time-Stepping Method. , 7.5.2 Analytical Time Integration -- 7.5.3 Evaluation of the Two Time Integration Methods -- 7.6 Subgrid Turbulence Parameterizations -- 7.6.1 Turbulence Parameterization -- 7.6.2 Diffusion -- 7.6.3 Subgrid Parameterization Questions -- 7.7 Mass Transport and Lagrangian Stream Functions -- 7.8 Conclusion and Discussion -- References -- Chapter 8: Evaluation and Tuning of Model Trajectories and Spreading Rates in the Baltic Sea Using Surface Drifter Observations -- 8.1 Background -- 8.2 Surface Drifters in the Baltic Sea -- 8.3 Simulated Drifters -- 8.4 Lagrangian Statistics -- 8.5 Results -- 8.5.1 The Surface Drifters -- 8.5.2 Model Evaluation -- 8.6 Tuning the Trajectories -- 8.7 Spreading Rates in the Uppermost Layer of the Gulf of Finland -- 8.8 Power Law Representation of the Spreading Rate -- 8.9 Discussion and Conclusions -- References -- Chapter 9: Statistics of Lagrangian Transport Reveals Hidden Features of Velocity Fields -- 9.1 Introduction -- 9.2 Hydrodynamics of the Test Regions -- 9.2.1 South-Western Baltic Sea -- 9.2.2 The Gulf of Finland -- 9.2.3 Aperiodic Flow Patterns and Subsurface Currents -- 9.3 Tools for the Search for the Patterns of Lagrangian Transport -- 9.3.1 Semi-persistent Patterns -- 9.3.2 Circulation Models -- 9.3.3 Reconstruction of Trajectories of Water Particles -- 9.3.4 Splitting the Simulation Periods -- 9.3.5 Simulating Statistically Independent Trajectories -- 9.3.6 Subgrid Processes and Spreading of Trajectories -- 9.3.7 Overlapping Simulations -- 9.4 Simulations of Environmental Risks -- 9.4.1 The Coast as the Vulnerable Region -- 9.4.2 Time to Reach the Coast and the Hitting Rate Re ect the Surface Dynamics -- 9.4.3 Temporal Scales for Transport Patterns in the Gulf of Finland -- 9.4.4 Patterns of Net and Bulk Lagrangian Transport -- 9.5 Concluding Remarks -- References. , Chapter 10: Applications of the Inverse Problem of Pollution Propagation -- 10.1 Introduction -- 10.1.1 The Hidden Potential of Currents -- 10.1.2 The Value of Different Sea Areas -- 10.1.3 The Inverse Problem -- 10.2 The Use of Lagrangian Trajectories of Current-Driven Transport in the Surface Layer -- 10.2.1 Quanti cation of Environmental Risks -- 10.2.2 Preventive Optimization of Dangerous Activities -- 10.3 Components of the Technique and Properties of Test Areas -- 10.3.1 The Baltic Sea Under Pressure -- 10.3.2 The Western and Eastern Gateways to the Baltic Sea -- 10.4 Circulation and Trajectory Models -- 10.4.1 The Rossby Centre Ocean Model RCO -- 10.4.2 The OAAS Model -- 10.4.3 The DMI/BSHcmod Model -- 10.4.4 Trajectory Simulations Using TRACMASS -- 10.4.5 Trajectory Simulations in the OAAS Model -- 10.5 Quanti cation of the Risk of Coastal Pollution -- 10.5.1 Launching the Particles -- 10.5.2 Indicators of Coastal Hit and Drift Time -- 10.5.3 Long-Term Course of Probability and Particle Age -- 10.5.4 Spatial Distributions of Probability and Particle Age -- 10.5.5 Dependence on Spatial Resolution -- 10.6 Applications for Decision-Making -- 10.6.1 Sharing the Costs: the Equiprobability Line -- 10.6.2 Cross-Sections -- 10.6.3 Simplest Optimum Fairways -- 10.6.4 Following Local Decisions -- 10.7 The Bene t and Uncertainties -- 10.7.1 Quanti cation of the Bene t -- 10.7.2 Critically Questioning the Recommendations -- 10.7.3 Robustness and Uncertainty -- 10.7.4 Nearly Optimal Solutions -- 10.7.5 Limitations of Modelling -- 10.7.6 Sensitivity to the Resolution of the Ocean Model -- 10.8 Concluding Remarks -- References -- Chapter 11: Applications of an Oil Drift and Fate Model for Fairway Design -- 11.1 Introduction -- 11.2 Oil at Sea -- 11.2.1 Oil Spills -- 11.2.2 Oil Drift -- 11.2.3 Oil Fate -- 11.3 Modelling of Circulation and Oil Spill. , 11.3.1 DMI's Ocean Circulation and Oil Spill Modelling System.