Note: Zusammenfassung in deutscher und englischer Sprache

Note: Intro -- List of Symbols -- Part I Fundamental Laws -- 1 Preliminaries -- - -- 1.1 Flow Kinematics -- 1.1.1 Lagrangian and Eulerian Representation -- 1.1.2 Deformation and Rotation -- 1.2 Thermodynamics of Sea Water -- 1.2.1 Salt Concentration and Salinity -- 1.2.2 Additive State Variables -- 1.2.3 First Law of Thermodynamics -- 1.2.4 Second Law of Thermodynamics -- 1.2.5 Thermodynamic Potentials -- 1.2.6 Equation of State -- 1.2.7 Specific Heat -- 2 Conservation Laws for Moving Fluids -- - -- 2.1 General Form of Conservation Equations -- 2.2 Mass Conservation -- 2.2.1 Total Mass and Salt Conservation Equation -- 2.2.2 Boundary Conditions for the Fluxes of Total Mass and Salt -- 2.3 Conservation of Momentum -- 2.3.1 Stresses, Pressure and Frictional Forces -- 2.3.2 Boundary Condition for the Momentum Flux -- 2.3.3 Conservation Equations on the Rotating Earth -- 2.3.4 The Force of Gravity on the Earth -- 2.4 Energy Conservation -- 2.4.1 Contributions to the Change of Energy in a Material Volume -- 2.4.2 Mechanical Energy -- 2.4.3 Internal Energy and Enthalpy -- 2.4.4 Total Energy and Total Enthalpy -- 2.4.5 Boundary Condition for the Enthalpy Flux -- 2.5 Entropy Budget -- 2.5.1 Entropy Sources and Flux-Gradient Relations -- 2.5.2 Onsager Relations -- 2.6 Temperature Equations -- 2.6.1 In-situ Temperature -- 2.6.2 Conservative Temperature -- 2.6.3 Potential Temperature -- 2.6.4 Conservative Temperature as a State Variable -- 2.7 Density Variables -- 2.7.1 Potential Density -- 2.7.2 Neutral Surface Elements -- 2.8 Molecular and Turbulent Transports -- 2.8.1 Magnitude of Molecular Transports -- 2.8.2 Reynolds and Hesselberg Averaging -- 2.9 The State of Rest -- 2.9.1 Hydrostatic Balance -- 2.9.2 Static Stability -- 2.10 * Some Differences to Atmospheric Thermodynamics -- 2.10.1 Differences in Thermodynamics -- 2.10.2 Differences in Conservation Laws. , 2.11 Vorticity -- 2.11.1 Kinematical Properties -- 2.11.2 Dynamical Properties -- 2.11.3 Ertel's Potential Vorticity -- 2.12 * Lagrangian Concepts in Fluid Mechanics -- 2.12.1 Incompressible Fluid -- 2.12.2 Compressible Isentropic Fluid -- 2.12.3 Rotating Fluid with Gravity -- 2.12.4 Rotating Stratified Fluid -- 2.12.5 A Variational Principle for Eulerian Coordinates -- Part II Common Approximations -- 3 Approximations Derived from Mode Filtering -- - -- 3.1 A Prognostic Equation for the Pressure -- 3.2 Linear Waves -- 3.3 Filtering of Modes -- 4 Approximations Relating to Density Changes and Geometric Conditions -- - -- 4.1 Approximations Involving Density -- 4.1.1 Inelastic Approximation -- 4.1.2 Boussinesq Approximation -- 4.1.3 Dynamical Role of Sea Water Compressibility -- 4.1.4 Energetics in the Boussinesq Approximation -- 4.1.5 Potential Vorticity in the Boussinesq Approximation -- 4.1.6 Full Incompressibility and Combination of Salt and Heat Budgets -- 4.2 Shallow Water Approximation -- 4.2.1 Oblate Spheroidal Coordinates -- 4.2.2 Spherical Approximation -- 4.2.3 Thin-Shell Approximation -- 4.2.4 Small Aspect Ratio -- 4.2.5 Primitive Equations -- 4.2.6 Energetics and Potential Vorticity in the Shallow Water Approximation -- 5 Geostrophic and Quasi-Geostrophic Motions -- - -- 5.1 Geostrophic Scaling -- 5.2 Quasi-Geostrophic Approximation -- 5.2.1 Expansion for Small Parameters -- 5.2.2 Quasi-Geostrophic Vorticity Equation -- 5.2.3 Quasi-Geostrophic Potential Vorticity -- 5.2.4 Boundary Conditions -- 5.2.5 Energetics of Quasi-Geostrophic Motions -- 5.2.6 Available Potential Energy -- 5.3 Planetary-Scale Geostrophic Motions -- 5.3.1 The M-Representation -- 5.3.2 Thermal Wind-Equations -- 5.3.3 Planetary Ideal Fluid Equations -- Part III Ocean Waves -- 6 Sound Waves -- - -- 6.1 Approximations and Perturbation Expansion -- 6.2 Plane Waves. , 6.2.1 Group Velocity I: Interference of Waves -- 6.2.2 Energy Conservation I: Kinetic and Elastic Energy -- 6.2.3 Sound Waves in a Mean Current -- 6.3 Propagation in a Variable Environment: WKBJ Approximation -- 6.3.1 General Wave Kinematics -- 6.3.2 Group Velocity II: Rays and Wave Packages -- 6.3.3 Energy Conservation II: Energy Flux and Group Velocity -- 6.3.4 Pathways of Sound Wave Propagation in the Ocean -- 7 Gravity Waves -- - -- 7.1 Governing Equations -- 7.2 Plane Gravity Waves -- 7.2.1 Propagation Characteristics -- 7.2.2 Energy Conservation -- 7.3 Propagation in Variable Stratification -- 7.3.1 WKBJ Approximation for Internal Waves -- 7.3.2 Turning Points -- 7.4 The Influence of Boundaries -- 7.4.1 Reflection at a Plane Interface -- 7.4.2 Reflection at a Sloping Bottom -- 7.4.3 Vertical Modes -- 7.4.4 Accuracy of the Rigid-Lid Condition -- 7.5 Surface Waves -- 7.6 Group Velocity III: Initial Value Problems and Stationary Phase Method -- 7.7 Influence of a Mean Flow -- 7.7.1 Critical Layer Absorption -- 7.7.2 Propagation in a Geostrophic Current -- 7.7.3 Stability of Shear Flows -- 8 Long Waves -- - -- 8.1 Long Gravity Waves -- 8.1.1 Barotropic and Baroclinic Modes -- 8.1.2 Dispersion Relation and Group Velocity -- 8.1.3 Geostrophic Adjustment -- 8.1.4 Influence of Horizontal Boundaries -- 8.1.5 Kelvin Waves -- 8.1.6 Hydraulic Control: Wave Propagation and Nonlinearity -- 8.2 Planetary Waves in Midlatitudes -- 8.2.1 Propagation Characteristics -- 8.2.2 Energy of Planetary Waves -- 8.2.3 Reflection at Meridional Boundaries -- 8.2.4 Topographic-Planetary Waves -- 8.2.5 Stationary Rossby Waves in a Baroclinic Flow over a Ridge -- 8.2.6 Spin-up of the Wind-Driven Basin Circulation -- 8.3 Equatorial Waves -- 8.3.1 Refraction due to Variations of the Coriolis Parameter -- 8.3.2 Equation for the Meridional Velocity. , 8.3.3 Meridional Eigenfunctions -- 8.3.4 Wave Solutions -- 8.3.5 Equatorial Kelvin Waves -- 8.3.6 Yanai Waves -- 8.3.7 Equatorial Rossby and Gravity Waves -- 8.3.8 Reflection at Meridional Boundaries -- 8.4 The Oceanic Waveguide -- 8.5 Influence of a Mean Flow on Planetary Waves -- 8.5.1 Modification of the Doppler Shift -- 8.5.2 Energy Transfer Between Waves and Mean Flow -- 8.5.3 Conditions for Instability -- 8.5.4 Energetics of Parcel Exchanges -- 9 * Lagrangian Theory of Ocean Waves -- - -- 9.1 Sound Waves as Example -- 9.2 Adiabatic Invariants -- 9.3 Variational Approach to Wave Trains -- 9.4 A Rigorous Derivation -- 9.5 Rossby Waves and Internal Gravity Waves as Examples -- 9.6 Wave-Wave Interactions -- 9.6.1 Resonant Wave Triads -- 9.6.2 Interaction Theory for Random Wave Fields -- 10 Forced Waves -- - -- 10.1 The Forcing Functions of Long Waves -- 10.2 Forced Midlatitude Waves -- 10.3 Forced Equatorial Waves -- 10.4 * Energetics of a Random Gravity Wave Field -- 10.4.1 Generation Processes -- 10.4.2 Dissipation Mechanisms -- 10.4.3 Some Prototype Balances -- 10.4.4 Resonant Transfer -- 10.4.5 The Link to Mixing -- Part IV Oceanic Turbulence and Eddies -- 11 Small-Scale Turbulence -- - -- 11.1 Kolmogorov's Theory of Homogeneous Turbulence -- 11.1.1 Isotropy -- 11.1.2 Momentum and Kinetic Energy in Homogeneous Turbulence -- 11.1.3 Large and Small Length Scales -- 11.1.4 Equilibrium Range and Inertial Subrange -- 11.2 Turbulent Mixing -- 11.2.1 Heuristic Approaches -- 11.2.2 Turbulent Diffusion in the Lagrangian Reference System -- 11.2.3 Eulerian Diffusion by Small-Scale Turbulence -- 11.3 Inhomogeneous Three-Dimensional Turbulence -- 11.3.1 Energetic Constraints -- 11.3.2 Turbulence Models for the Surface Boundary Layer -- 11.3.3 Turbulence in the Ocean Interior -- 12 Geostrophic Turbulence -- - -- 12.1 Homogeneous Turbulence in Two Dimensions. , 12.1.1 Inverse Energy Cascade -- 12.1.2 A Numerical Example of Two-Dimensional Turbulence -- 12.1.3 Equilibrium Range -- 12.2 Mesoscale Eddies and Their Impact on the Mean Flow -- 12.2.1 Energetics of Mesoscale Eddies and the Lorenz Cycle -- 12.2.2 Isopycnal Mixing Tensor -- 12.2.3 Transformed Eulerian Mean -- 12.2.4 Gent and McWilliams Parameterization and the Bolus Velocity -- 12.2.5 Isopycnal Mixing and Transformed Eulerian Mean -- 12.2.6 * Mesoscale Eddy Effects in the Momentum Equation -- 12.3 * Alternative Averaging Frameworks -- 12.3.1 Temporal Residual Mean -- 12.3.2 Rotational Eddy Fluxes -- 12.3.3 Generalized Osborn-Cox Relation -- 12.3.4 Generalized Lagrangian Mean -- 12.3.5 Semi-Lagrangian (Isopycnal) Mean -- 12.3.6 Relating Lagrangian, Eulerian, and Semi-Lagrangian Mean -- Part V Aspects of Ocean Circulation Theory -- 13 Forcing of the Ocean -- - -- 13.1 Bulk Formulae as Boundary Conditions -- 13.2 Simplified Boundary Conditions -- 14 The Wind-Driven Circulation -- - -- 14.1 The Flat-Bottom Wind-Driven Circulation -- 14.1.1 The Elementary Current System -- 14.1.2 Ekman Spiral -- 14.1.3 Ekman Transport -- 14.1.4 Ekman Pumping -- 14.1.5 Equilibrium Wind-Driven Model Regimes -- 14.1.6 The Western Boundary Current -- 14.2 The Role of Stratification and Topography -- 14.2.1 The JEBAR Term -- 14.2.2 The f/h Contours -- 14.2.3 Sverdrup's Catastrophe -- 14.2.4 The Bottom Pressure Torque -- 14.2.5 A Realistic Application of the BARBI Model -- 14.2.6 The Baroclinic Stommel Equation -- 14.3 Main Thermocline Dynamics -- 14.3.1 Scaling Considerations -- 14.3.2 Similarity Solutions -- 14.3.3 Ideal Fluid Solutions -- 14.3.4 Thermocline Ventilation in an Isopycnal Layer Model -- 14.3.5 Circulation in Unventilated Regions -- 15 The Meridional Overturning of the Oceans -- - -- 15.1 Basic Ingredients of the Meridional Overturning. , 15.1.1 Water Masses of the Ocean.

Note: Enth. Literaturangaben und Index

Note: Hamburg, Univ. Hamburg, FB Geowiss., Diss., 2013

Note: Intro -- Preface -- Acknowledgements -- Contents -- Contributors -- 1 Multi-scale Methods for Geophysical Flows -- 1.1 Introduction -- 1.2 The Governing Equations -- 1.2.1 Rotating Boussinesq Equations -- 1.2.2 Imbalance Variables -- 1.2.3 Mid-latitude Scalings -- 1.2.4 Hydrostatic Approximation -- 1.2.5 The Quasi-geostrophic Approximation on the β-plane -- 1.2.6 Rotating Shallow Water Equations -- 1.2.7 Geostrophic Scalings -- 1.2.8 Equatorial Scalings -- 1.3 Variational Principles and Hamiltonian Mechanics -- 1.3.1 Variational Principles -- 1.3.2 Variational Model Reduction -- 1.3.3 Poisson Formulation -- 1.3.4 Nambu Formulation -- 1.4 Dissipation, Turbulence, and Nonlinear Waves -- 1.4.1 Viscosity and Dissipation -- 1.4.2 Nonlinear Waves and Dynamical Systems Methods -- 1.5 Stochastic Model Reduction -- 1.5.1 Basic Setup -- 1.5.2 Slow Dynamics via the Kolmogorov Backward Equation -- 1.5.3 Direct Averaging -- 1.6 Outlook -- References -- 2 The Interior Energy Pathway: Inertia-Gravity Wave Emission by Oceanic Flows -- 2.1 Introduction -- 2.2 Rotating Shallow Water Equations and Spontaneous Emission -- 2.2.1 Shallow Water on the f-Plane -- 2.2.2 Spontaneous Emission -- 2.2.3 Beyond Shallow Water -- 2.3 Ray Equations and Wave Capture -- 2.4 Interactions Between IGWs and Density Fronts -- 2.4.1 Wave Capture in Frontal Strain -- 2.4.2 Role of IGWs in Frontal Geostrophic Adjustment -- 2.5 Diagnostics -- 2.5.1 Characterization of Flow Regimes via the Rossby Number -- 2.5.2 Linear Filters -- 2.5.3 Optimal Potential Vorticity Balance -- 2.5.4 A Simple Model for Optimal Balance -- 2.6 High-resolution Ocean General Circulation Models as a Novel Tool for Studying Spontaneous Emission -- 2.7 Discussion -- References -- 3 The IDEMIX Model: Parameterization of Internal Gravity Waves for Circulation Models of Ocean and Atmosphere. , 3.1 Internal Waves in Ocean and Atmosphere -- 3.2 The IDEMIX Model -- 3.2.1 Details of the Oceanic IDEMIX -- 3.2.2 The IDEMIX Concept Applied to Atmospheric Gravity Waves -- 3.3 Oceanic Processes in Present and Future IDEMIX -- 3.3.1 Including Energy Transfers from Mesoscale Eddies to Internal Waves -- 3.3.2 Including Wave-Mean Flow Interaction -- 3.3.3 Including Anisotropic Tidal Forcing -- 3.3.4 Including High-Frequency Compartments -- 3.3.5 Evaluation with Available Observations -- 3.4 Atmospheric Processes in IDEMIX -- 3.5 Summary -- References -- 4 Observations and Models of Low-Mode Internal Waves in the Ocean -- 4.1 Introduction -- 4.2 Numerical Modeling -- 4.2.1 Wind -- 4.2.2 Tides -- 4.3 Dissipation -- 4.4 Observations -- 4.4.1 Satellite Altimetry -- 4.4.2 Shipboard Observations -- 4.4.3 Moorings -- 4.5 Summary and Outlook -- References -- 5 Toward Consistent Subgrid Momentum Closures in Ocean Models -- 5.1 Introduction -- 5.2 Subgrid Momentum Closures -- 5.3 Quasigeostrophic Turbulence and Ocean Eddies -- 5.3.1 Two-Dimensional Turbulence -- 5.3.2 Two-Layer Geostrophic Flows -- 5.3.3 Continuously Stratified and Surface QG Dynamics -- 5.3.4 Ocean Models and Observational Evidence -- 5.4 Energy Backscatter -- 5.4.1 Models with Scalar Subgrid Energy Budget -- 5.4.2 Stochastic Superparameterizations -- 5.5 Other Closures -- 5.5.1 The Mana-Zanna Parameterization of Ocean Mesoscale Eddies -- 5.5.2 α-Models -- 5.6 Concluding Remarks -- References -- 6 Diagnosing and Parameterizing the Effects of Oceanic Eddies -- 6.1 Introduction -- 6.1.1 Isopycnal and Diapycnal Diffusion -- 6.1.2 Skew Diffusion -- 6.1.3 Diagnosing and Parameterizing the Diffusivities -- 6.2 Eddy Diffusivity Diagnostics -- 6.2.1 Lagrangian Particle Dispersion -- 6.2.2 Quasigeostrophic Linear Stability Analysis -- 6.2.3 Diffusivities from Eulerian Eddy Fluxes. , 6.3 Eddy Diffusivity Estimates in the Global Ocean -- 6.4 Limits of the Eddy Diffusion Model and Anomalous Diffusion -- 6.5 Eddy Diffusivity Parameterization -- 6.5.1 EKE Equation -- 6.6 Conclusions -- References -- 7 Entropy Production in Turbulence Parameterizations -- 7.1 The Numerically Modeled Atmosphere as a Forced-Dissipative System -- 7.2 The Entropy Budget Equation in Numerical Models of the Atmosphere -- 7.3 Moisture and Precipitation Fluxes -- 7.4 Thermal Fluxes -- 7.5 Momentum Fluxes -- 7.6 Fluctuation Theorem -- 7.7 Applicability of the Fluctuation Theorem in Geophysical Flows -- References -- 8 Reducing Spurious Diapycnal Mixing in Ocean Models -- 8.1 Introduction -- 8.2 Diagnosing Spurious Mixing -- 8.2.1 An Analytical Example -- 8.2.2 Variance Decay as a Measure for Mixing and Dissipation -- 8.2.3 Discrete Variance Decay -- 8.2.4 Applications -- 8.3 Arbitrary Lagrangian Eulerian Vertical Coordinate -- 8.3.1 tildez-Vertical Coordinate and its Effect on Spurious Mixing -- 8.3.2 Additional Techniques for Adaptive Vertical Model Layers -- 8.4 Advection Algorithms Stabilized with Isoneutral Mixing -- 8.5 ADER High Order Flux Evaluation and WENO Reconstruction -- 8.5.1 The Generalized Riemann Problem -- 8.5.2 Kernel-Based WENO Reconstruction -- 8.6 Discussion and Conclusions -- References -- 9 Diffuse Interface Approaches in Atmosphere and Ocean-Modeling and Numerical Implementation -- 9.1 Introduction -- 9.2 Diffuse Interface Approach -- 9.2.1 Notation -- 9.2.2 The Mathematical Model -- 9.3 Discretization -- 9.3.1 The Temporal Discretization -- 9.3.2 The Spatial Discretization and Energy Inequalities -- 9.3.3 A posteriori Error Estimation -- 9.4 Numerics -- 9.5 Outlook on the Direction of Research -- References -- Index.

Note: Kiel, Univ., Diss., 2012