Stochastic Transport in Upper Ocean Dynamics II : : STUOD 2022 Workshop, London, UK, September 26-29.
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Superior document: | Mathematics of Planet Earth Series ; v.11 |
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Place / Publishing House: | Cham : : Springer,, 2023. ©2024. |
Year of Publication: | 2023 |
Edition: | 1st ed. |
Language: | English |
Series: | Mathematics of Planet Earth Series
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Physical Description: | 1 online resource (347 pages) |
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Chapron, Bertrand. Stochastic Transport in Upper Ocean Dynamics II : STUOD 2022 Workshop, London, UK, September 26-29. 1st ed. Cham : Springer, 2023. ©2024. 1 online resource (347 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Mathematics of Planet Earth Series ; v.11 Intro -- Preface -- Contents -- Internal Tides Energy Transfers and Interactions with the Mesoscale Circulation in Two Contrasted Areas of the North Atlantic -- 1 Introduction -- 2 Governing Equations and Energy Budget -- 3 Data and Method -- 3.1 eNATL60 Simulation -- 3.2 Filtering and Computing Methods -- 4 Results -- 4.1 Life Cycle of the Internal Tide -- 4.2 Importance of the Different Contributions in the Energy Transfers -- 4.2.1 Detailed View of Coupling Terms -- 4.2.2 Modal Energy Budget -- 5 Conclusion -- References -- Sparse-Stochastic Model Reduction for 2D Euler Equations -- 1 Introduction -- 2 Sparse-Stochastic Model Reduction -- 3 Numerical Simulations -- 4 Conclusions and Outlook -- References -- Effect of Transport Noise on Kelvin-Helmholtz Instability -- 1 Introduction -- 2 Model Formulation -- 2.1 Point Vortex Method for Inviscid Flows -- 2.2 Point Vortex Method for Viscous Flows -- 3 Point Vortex Method with Environmental Noise -- 3.1 Transport Noise and Deterministic Scaling Limit -- 3.2 A Digression on the Theoretical Selection of the Noise -- 4 Numerical Results -- 4.1 Setting: Kelvin-Helmholtz Instability -- 4.1.1 The Role of Intrinsic Instability -- 4.1.2 The Role of Viscosity and Stability Restoration -- 4.2 Numerical Results on Environmental Noise -- 4.2.1 Selection of Divergence Free Field -- 4.2.2 Positions and Intensities of Fixed Vortices -- 4.2.3 Effect of Small Scale Common Noise -- 4.3 Diagnostics -- 5 Concluding Remarks -- References -- On the 3D Navier-Stokes Equations with Stochastic Lie Transport -- Introduction -- 1 Introduction -- 2 Preliminaries -- 2.1 Elementary Notation -- 2.2 Functional Framework -- 2.3 The SALT Operator -- 3 The Velocity Equation on the Torus -- 3.1 Definitions and Results -- 3.2 Operator Bounds -- 3.3 Proof of Proposition 3.2 -- 3.4 Proofs of Theorems 3.1 and 3.6. 4 The Vorticity Equation on a Bounded Main -- 4.1 Deriving the Equation -- 4.2 Definitions and Results -- 4.3 Operator Bounds -- 4.4 Proof of Theorem 4.3 -- 5 Appendices -- 5.1 Proofs from Sects.2.3, 3.2, and 4.3 -- 5.2 A Conversion from Stratonovich to Itô -- 5.3 Abstract Solution Criterion I -- 5.4 Abstract Solution Criterion II -- References -- On the Interactions Between Mean Flows and Inertial Gravity Waves in the WKB Approximation -- 1 Introduction -- 2 Deterministic 3D Euler-Boussinesq (EB) Internal Gravity Waves -- 2.1 Lagrangian Formulation of the WMFI Equations at Leading Order -- 2.2 Hamiltonian Structure for the WMFI Equations at Leading Order -- 3 Stochastic WMFI -- 4 Conclusion -- Appendix: Asymptotic Expansion -- References -- Toward a Stochastic Parameterization for Oceanic Deep Convection -- 1 Introduction -- 2 Stochastic Formulation of Direct Non-hydrostatic Pressure Correction -- 3 Numerical Implementation and Simulations -- 3.1 Stochastic, Non-hydrostatic Pressure Correction -- 3.2 Numerical Experiments -- 4 Results -- 5 Conclusion and Perspectives -- References -- Comparison of Stochastic Parametrization Schemes Using Data Assimilation on Triad Models -- 1 Introduction -- 2 Reduced Order Models for Incompressible Fluids -- 2.1 Reduced Order Models for the 3D Euler Equation -- 2.2 Stochastic Parametrizations for the 3D Euler Equation -- 2.2.1 Modelling Under the Stochastic Advection by Lie Transport Principle -- 2.2.2 Modeling Under the Location Uncertainty Principle -- 2.3 Triad Model Comparison -- 3 Data Assimilation Comparison -- 3.1 Numerical Studies -- 3.1.1 Numerical Implementation -- 3.1.2 Data Assimilation for the Deterministic Model -- 3.1.3 Reduced Order Model Realisations -- 3.1.4 Model Statistics -- 3.1.5 Data Assimilation -- 4 Conclusions -- Appendix 1: Notation and Basic Identities -- Notation -- Vector Identities. Appendix 2: Derivation of Triad Models -- Deterministic Euler -- SALT Euler -- LU Euler -- Appendix 3: Supplementary Numerics -- Calibration of the Noise Amplitude -- Data Assimilation Verification -- References -- An Explicit Method to Determine Casimirs in 2D Geophysical Flows -- 1 Introduction -- 2 Geophysical Flows -- 3 Explicitly Determining the Casimirs -- 4 Conclusion -- References -- Correlated Structures in a Balanced Motion Interacting with an Internal Wave -- 1 Introduction -- 2 Model -- 3 Methods -- 3.1 Spectral Proper Orthogonal Decomposition -- 3.2 Broadband Proper Orthogonal Decomposition -- 3.2.1 Complex Demodulation of the Wave Field -- 3.2.2 Link with SPOD -- 3.2.3 Extended Broadband Proper Orthogonal Decomposition -- 4 Results -- 5 Summary and Perspectives -- References -- Linear Wave Solutions of a Stochastic Shallow Water Model -- 1 Introduction -- 2 Review of RSW-LU -- 3 Stationary Solution -- 4 Stochastic Rotating Shallow Water Waves -- 4.1 Ensemble-Mean Waves Under Homogeneous Noise -- 4.1.1 Mean Poincaré Waves -- 4.1.2 Mean Geostrophic Mode -- 4.2 Path-Wise Waves Under Constant Noise -- 4.2.1 Stochastic Poincaré Waves -- 4.2.2 Stochastic Geostrophic Mode -- 4.3 Approximation of Path-Wise Waves Under Homogeneous Noise -- 4.3.1 Stochastic Poincaré Waves -- 4.3.2 Stochastic Geostrophic Mode -- 4.4 Numerical Illustrations -- 5 Shallow Water PV Dynamics and Geostrophic Adjustment -- 6 Conclusions -- References -- Analysis of Sea Surface Temperature Variability Using Machine Learning -- 1 Introduction -- 2 Method -- 2.1 Deterministic Model Hypothesis -- 2.2 Stochastic Model Hypothesis: The Stochastic NbedDyn -- 3 Numerical Experiments -- 3.1 Data -- 3.2 Analysis of the Deterministic Model -- 3.3 Analysis of the Stochastic Model -- 4 Conclusion -- Appendix 1: Training -- Appendix 2: Parameterization of the Diffusion Function. References -- Data Assimilation: A Dynamic Homotopy-Based Coupling Approach -- 1 Introduction -- 2 Problem Formulation and Background -- 3 Schrödinger Bridge Approach -- 4 Homotopy Induced Dynamic Coupling -- 5 Numerical Implementation -- 5.1 Ensemble Kalman Mean Field Approximation -- 5.2 Particle Approximation and Time-Stepping -- 6 Examples -- 6.1 Pure Diffusion Processes -- 6.2 Purely Deterministic Processes -- 6.3 Linear Gaussian Case -- 6.4 Nonlinear Diffusion Example -- 6.5 Lorenz-63 Example -- 7 Conclusions -- Appendix 1: Derivation of Control Term Equation -- Appendix 2: Ensemble Kalman Filter Approximations -- References -- Constrained Random Diffeomorphisms for Data Assimilation -- 1 Introduction -- 2 Induced Stochastic PDE -- 3 Comparison with Other Perturbation Schemes -- 3.1 Comparison with the LU Equations -- 3.1.1 0-Forms in the LU Framework -- 3.1.2 n-Forms in the LU Framework -- 3.2 The SALT Perturbation Scheme -- 4 Conclusion -- Appendix: Expression of Tt*θ -- References -- Stochastic Compressible Navier-Stokes Equations Under Location Uncertainty -- 1 Introduction -- 2 Stochastic Reynolds Transport Theorem -- 3 Stochastic Compressible Navier-Stokes Equations -- 3.1 Non-dimensioning -- 3.2 Continuity -- 3.3 Momentum -- 3.4 Energy -- 3.5 Equation of State -- 4 Low Mach Approximation -- 5 Boussinesq-Hydrostatic Approximation -- 6 Extension to Non-Boussinesq -- 7 Conclusion -- Appendix A: Stochastic Reynolds Transport Theorem from Stratonovich to Itō -- Appendix B: Calculation Rules -- Distributivity of the Stochastic Transport Operator -- Work of Random Forces -- Appendix C: Displacement of a Transported Control Surface -- References -- Data Driven Stochastic Primitive Equations with Dynamic Modes Decomposition -- 1 Introduction -- 2 Location Uncertainty (LU) -- 3 Stochastic Boussinesq Equations -- 4 Methods. 4.1 High Resolution Data Filtering -- 4.2 Off-Line Noise Modelling Through DMD -- 4.3 On-Line Noise Reconstruction -- 5 Results -- 6 Conclusions -- References -- Index. Description based on publisher supplied metadata and other sources. Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. Electronic books. Crisan, Dan. Holm, Darryl. Mémin, Etienne. Radomska, Anna. Print version: Chapron, Bertrand Stochastic Transport in Upper Ocean Dynamics II Cham : Springer,c2023 9783031400933 ProQuest (Firm) Mathematics of Planet Earth Series https://ebookcentral.proquest.com/lib/oeawat/detail.action?docID=30882864 Click to View |
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English |
format |
eBook |
author |
Chapron, Bertrand. |
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Chapron, Bertrand. Stochastic Transport in Upper Ocean Dynamics II : STUOD 2022 Workshop, London, UK, September 26-29. Mathematics of Planet Earth Series ; Intro -- Preface -- Contents -- Internal Tides Energy Transfers and Interactions with the Mesoscale Circulation in Two Contrasted Areas of the North Atlantic -- 1 Introduction -- 2 Governing Equations and Energy Budget -- 3 Data and Method -- 3.1 eNATL60 Simulation -- 3.2 Filtering and Computing Methods -- 4 Results -- 4.1 Life Cycle of the Internal Tide -- 4.2 Importance of the Different Contributions in the Energy Transfers -- 4.2.1 Detailed View of Coupling Terms -- 4.2.2 Modal Energy Budget -- 5 Conclusion -- References -- Sparse-Stochastic Model Reduction for 2D Euler Equations -- 1 Introduction -- 2 Sparse-Stochastic Model Reduction -- 3 Numerical Simulations -- 4 Conclusions and Outlook -- References -- Effect of Transport Noise on Kelvin-Helmholtz Instability -- 1 Introduction -- 2 Model Formulation -- 2.1 Point Vortex Method for Inviscid Flows -- 2.2 Point Vortex Method for Viscous Flows -- 3 Point Vortex Method with Environmental Noise -- 3.1 Transport Noise and Deterministic Scaling Limit -- 3.2 A Digression on the Theoretical Selection of the Noise -- 4 Numerical Results -- 4.1 Setting: Kelvin-Helmholtz Instability -- 4.1.1 The Role of Intrinsic Instability -- 4.1.2 The Role of Viscosity and Stability Restoration -- 4.2 Numerical Results on Environmental Noise -- 4.2.1 Selection of Divergence Free Field -- 4.2.2 Positions and Intensities of Fixed Vortices -- 4.2.3 Effect of Small Scale Common Noise -- 4.3 Diagnostics -- 5 Concluding Remarks -- References -- On the 3D Navier-Stokes Equations with Stochastic Lie Transport -- Introduction -- 1 Introduction -- 2 Preliminaries -- 2.1 Elementary Notation -- 2.2 Functional Framework -- 2.3 The SALT Operator -- 3 The Velocity Equation on the Torus -- 3.1 Definitions and Results -- 3.2 Operator Bounds -- 3.3 Proof of Proposition 3.2 -- 3.4 Proofs of Theorems 3.1 and 3.6. 4 The Vorticity Equation on a Bounded Main -- 4.1 Deriving the Equation -- 4.2 Definitions and Results -- 4.3 Operator Bounds -- 4.4 Proof of Theorem 4.3 -- 5 Appendices -- 5.1 Proofs from Sects.2.3, 3.2, and 4.3 -- 5.2 A Conversion from Stratonovich to Itô -- 5.3 Abstract Solution Criterion I -- 5.4 Abstract Solution Criterion II -- References -- On the Interactions Between Mean Flows and Inertial Gravity Waves in the WKB Approximation -- 1 Introduction -- 2 Deterministic 3D Euler-Boussinesq (EB) Internal Gravity Waves -- 2.1 Lagrangian Formulation of the WMFI Equations at Leading Order -- 2.2 Hamiltonian Structure for the WMFI Equations at Leading Order -- 3 Stochastic WMFI -- 4 Conclusion -- Appendix: Asymptotic Expansion -- References -- Toward a Stochastic Parameterization for Oceanic Deep Convection -- 1 Introduction -- 2 Stochastic Formulation of Direct Non-hydrostatic Pressure Correction -- 3 Numerical Implementation and Simulations -- 3.1 Stochastic, Non-hydrostatic Pressure Correction -- 3.2 Numerical Experiments -- 4 Results -- 5 Conclusion and Perspectives -- References -- Comparison of Stochastic Parametrization Schemes Using Data Assimilation on Triad Models -- 1 Introduction -- 2 Reduced Order Models for Incompressible Fluids -- 2.1 Reduced Order Models for the 3D Euler Equation -- 2.2 Stochastic Parametrizations for the 3D Euler Equation -- 2.2.1 Modelling Under the Stochastic Advection by Lie Transport Principle -- 2.2.2 Modeling Under the Location Uncertainty Principle -- 2.3 Triad Model Comparison -- 3 Data Assimilation Comparison -- 3.1 Numerical Studies -- 3.1.1 Numerical Implementation -- 3.1.2 Data Assimilation for the Deterministic Model -- 3.1.3 Reduced Order Model Realisations -- 3.1.4 Model Statistics -- 3.1.5 Data Assimilation -- 4 Conclusions -- Appendix 1: Notation and Basic Identities -- Notation -- Vector Identities. Appendix 2: Derivation of Triad Models -- Deterministic Euler -- SALT Euler -- LU Euler -- Appendix 3: Supplementary Numerics -- Calibration of the Noise Amplitude -- Data Assimilation Verification -- References -- An Explicit Method to Determine Casimirs in 2D Geophysical Flows -- 1 Introduction -- 2 Geophysical Flows -- 3 Explicitly Determining the Casimirs -- 4 Conclusion -- References -- Correlated Structures in a Balanced Motion Interacting with an Internal Wave -- 1 Introduction -- 2 Model -- 3 Methods -- 3.1 Spectral Proper Orthogonal Decomposition -- 3.2 Broadband Proper Orthogonal Decomposition -- 3.2.1 Complex Demodulation of the Wave Field -- 3.2.2 Link with SPOD -- 3.2.3 Extended Broadband Proper Orthogonal Decomposition -- 4 Results -- 5 Summary and Perspectives -- References -- Linear Wave Solutions of a Stochastic Shallow Water Model -- 1 Introduction -- 2 Review of RSW-LU -- 3 Stationary Solution -- 4 Stochastic Rotating Shallow Water Waves -- 4.1 Ensemble-Mean Waves Under Homogeneous Noise -- 4.1.1 Mean Poincaré Waves -- 4.1.2 Mean Geostrophic Mode -- 4.2 Path-Wise Waves Under Constant Noise -- 4.2.1 Stochastic Poincaré Waves -- 4.2.2 Stochastic Geostrophic Mode -- 4.3 Approximation of Path-Wise Waves Under Homogeneous Noise -- 4.3.1 Stochastic Poincaré Waves -- 4.3.2 Stochastic Geostrophic Mode -- 4.4 Numerical Illustrations -- 5 Shallow Water PV Dynamics and Geostrophic Adjustment -- 6 Conclusions -- References -- Analysis of Sea Surface Temperature Variability Using Machine Learning -- 1 Introduction -- 2 Method -- 2.1 Deterministic Model Hypothesis -- 2.2 Stochastic Model Hypothesis: The Stochastic NbedDyn -- 3 Numerical Experiments -- 3.1 Data -- 3.2 Analysis of the Deterministic Model -- 3.3 Analysis of the Stochastic Model -- 4 Conclusion -- Appendix 1: Training -- Appendix 2: Parameterization of the Diffusion Function. References -- Data Assimilation: A Dynamic Homotopy-Based Coupling Approach -- 1 Introduction -- 2 Problem Formulation and Background -- 3 Schrödinger Bridge Approach -- 4 Homotopy Induced Dynamic Coupling -- 5 Numerical Implementation -- 5.1 Ensemble Kalman Mean Field Approximation -- 5.2 Particle Approximation and Time-Stepping -- 6 Examples -- 6.1 Pure Diffusion Processes -- 6.2 Purely Deterministic Processes -- 6.3 Linear Gaussian Case -- 6.4 Nonlinear Diffusion Example -- 6.5 Lorenz-63 Example -- 7 Conclusions -- Appendix 1: Derivation of Control Term Equation -- Appendix 2: Ensemble Kalman Filter Approximations -- References -- Constrained Random Diffeomorphisms for Data Assimilation -- 1 Introduction -- 2 Induced Stochastic PDE -- 3 Comparison with Other Perturbation Schemes -- 3.1 Comparison with the LU Equations -- 3.1.1 0-Forms in the LU Framework -- 3.1.2 n-Forms in the LU Framework -- 3.2 The SALT Perturbation Scheme -- 4 Conclusion -- Appendix: Expression of Tt*θ -- References -- Stochastic Compressible Navier-Stokes Equations Under Location Uncertainty -- 1 Introduction -- 2 Stochastic Reynolds Transport Theorem -- 3 Stochastic Compressible Navier-Stokes Equations -- 3.1 Non-dimensioning -- 3.2 Continuity -- 3.3 Momentum -- 3.4 Energy -- 3.5 Equation of State -- 4 Low Mach Approximation -- 5 Boussinesq-Hydrostatic Approximation -- 6 Extension to Non-Boussinesq -- 7 Conclusion -- Appendix A: Stochastic Reynolds Transport Theorem from Stratonovich to Itō -- Appendix B: Calculation Rules -- Distributivity of the Stochastic Transport Operator -- Work of Random Forces -- Appendix C: Displacement of a Transported Control Surface -- References -- Data Driven Stochastic Primitive Equations with Dynamic Modes Decomposition -- 1 Introduction -- 2 Location Uncertainty (LU) -- 3 Stochastic Boussinesq Equations -- 4 Methods. 4.1 High Resolution Data Filtering -- 4.2 Off-Line Noise Modelling Through DMD -- 4.3 On-Line Noise Reconstruction -- 5 Results -- 6 Conclusions -- References -- Index. |
author_facet |
Chapron, Bertrand. Crisan, Dan. Holm, Darryl. Mémin, Etienne. Radomska, Anna. |
author_variant |
b c bc |
author2 |
Crisan, Dan. Holm, Darryl. Mémin, Etienne. Radomska, Anna. |
author2_variant |
d c dc d h dh e m em a r ar |
author2_role |
TeilnehmendeR TeilnehmendeR TeilnehmendeR TeilnehmendeR |
author_sort |
Chapron, Bertrand. |
title |
Stochastic Transport in Upper Ocean Dynamics II : STUOD 2022 Workshop, London, UK, September 26-29. |
title_sub |
STUOD 2022 Workshop, London, UK, September 26-29. |
title_full |
Stochastic Transport in Upper Ocean Dynamics II : STUOD 2022 Workshop, London, UK, September 26-29. |
title_fullStr |
Stochastic Transport in Upper Ocean Dynamics II : STUOD 2022 Workshop, London, UK, September 26-29. |
title_full_unstemmed |
Stochastic Transport in Upper Ocean Dynamics II : STUOD 2022 Workshop, London, UK, September 26-29. |
title_auth |
Stochastic Transport in Upper Ocean Dynamics II : STUOD 2022 Workshop, London, UK, September 26-29. |
title_new |
Stochastic Transport in Upper Ocean Dynamics II : |
title_sort |
stochastic transport in upper ocean dynamics ii : stuod 2022 workshop, london, uk, september 26-29. |
series |
Mathematics of Planet Earth Series ; |
series2 |
Mathematics of Planet Earth Series ; |
publisher |
Springer, |
publishDate |
2023 |
physical |
1 online resource (347 pages) |
edition |
1st ed. |
contents |
Intro -- Preface -- Contents -- Internal Tides Energy Transfers and Interactions with the Mesoscale Circulation in Two Contrasted Areas of the North Atlantic -- 1 Introduction -- 2 Governing Equations and Energy Budget -- 3 Data and Method -- 3.1 eNATL60 Simulation -- 3.2 Filtering and Computing Methods -- 4 Results -- 4.1 Life Cycle of the Internal Tide -- 4.2 Importance of the Different Contributions in the Energy Transfers -- 4.2.1 Detailed View of Coupling Terms -- 4.2.2 Modal Energy Budget -- 5 Conclusion -- References -- Sparse-Stochastic Model Reduction for 2D Euler Equations -- 1 Introduction -- 2 Sparse-Stochastic Model Reduction -- 3 Numerical Simulations -- 4 Conclusions and Outlook -- References -- Effect of Transport Noise on Kelvin-Helmholtz Instability -- 1 Introduction -- 2 Model Formulation -- 2.1 Point Vortex Method for Inviscid Flows -- 2.2 Point Vortex Method for Viscous Flows -- 3 Point Vortex Method with Environmental Noise -- 3.1 Transport Noise and Deterministic Scaling Limit -- 3.2 A Digression on the Theoretical Selection of the Noise -- 4 Numerical Results -- 4.1 Setting: Kelvin-Helmholtz Instability -- 4.1.1 The Role of Intrinsic Instability -- 4.1.2 The Role of Viscosity and Stability Restoration -- 4.2 Numerical Results on Environmental Noise -- 4.2.1 Selection of Divergence Free Field -- 4.2.2 Positions and Intensities of Fixed Vortices -- 4.2.3 Effect of Small Scale Common Noise -- 4.3 Diagnostics -- 5 Concluding Remarks -- References -- On the 3D Navier-Stokes Equations with Stochastic Lie Transport -- Introduction -- 1 Introduction -- 2 Preliminaries -- 2.1 Elementary Notation -- 2.2 Functional Framework -- 2.3 The SALT Operator -- 3 The Velocity Equation on the Torus -- 3.1 Definitions and Results -- 3.2 Operator Bounds -- 3.3 Proof of Proposition 3.2 -- 3.4 Proofs of Theorems 3.1 and 3.6. 4 The Vorticity Equation on a Bounded Main -- 4.1 Deriving the Equation -- 4.2 Definitions and Results -- 4.3 Operator Bounds -- 4.4 Proof of Theorem 4.3 -- 5 Appendices -- 5.1 Proofs from Sects.2.3, 3.2, and 4.3 -- 5.2 A Conversion from Stratonovich to Itô -- 5.3 Abstract Solution Criterion I -- 5.4 Abstract Solution Criterion II -- References -- On the Interactions Between Mean Flows and Inertial Gravity Waves in the WKB Approximation -- 1 Introduction -- 2 Deterministic 3D Euler-Boussinesq (EB) Internal Gravity Waves -- 2.1 Lagrangian Formulation of the WMFI Equations at Leading Order -- 2.2 Hamiltonian Structure for the WMFI Equations at Leading Order -- 3 Stochastic WMFI -- 4 Conclusion -- Appendix: Asymptotic Expansion -- References -- Toward a Stochastic Parameterization for Oceanic Deep Convection -- 1 Introduction -- 2 Stochastic Formulation of Direct Non-hydrostatic Pressure Correction -- 3 Numerical Implementation and Simulations -- 3.1 Stochastic, Non-hydrostatic Pressure Correction -- 3.2 Numerical Experiments -- 4 Results -- 5 Conclusion and Perspectives -- References -- Comparison of Stochastic Parametrization Schemes Using Data Assimilation on Triad Models -- 1 Introduction -- 2 Reduced Order Models for Incompressible Fluids -- 2.1 Reduced Order Models for the 3D Euler Equation -- 2.2 Stochastic Parametrizations for the 3D Euler Equation -- 2.2.1 Modelling Under the Stochastic Advection by Lie Transport Principle -- 2.2.2 Modeling Under the Location Uncertainty Principle -- 2.3 Triad Model Comparison -- 3 Data Assimilation Comparison -- 3.1 Numerical Studies -- 3.1.1 Numerical Implementation -- 3.1.2 Data Assimilation for the Deterministic Model -- 3.1.3 Reduced Order Model Realisations -- 3.1.4 Model Statistics -- 3.1.5 Data Assimilation -- 4 Conclusions -- Appendix 1: Notation and Basic Identities -- Notation -- Vector Identities. Appendix 2: Derivation of Triad Models -- Deterministic Euler -- SALT Euler -- LU Euler -- Appendix 3: Supplementary Numerics -- Calibration of the Noise Amplitude -- Data Assimilation Verification -- References -- An Explicit Method to Determine Casimirs in 2D Geophysical Flows -- 1 Introduction -- 2 Geophysical Flows -- 3 Explicitly Determining the Casimirs -- 4 Conclusion -- References -- Correlated Structures in a Balanced Motion Interacting with an Internal Wave -- 1 Introduction -- 2 Model -- 3 Methods -- 3.1 Spectral Proper Orthogonal Decomposition -- 3.2 Broadband Proper Orthogonal Decomposition -- 3.2.1 Complex Demodulation of the Wave Field -- 3.2.2 Link with SPOD -- 3.2.3 Extended Broadband Proper Orthogonal Decomposition -- 4 Results -- 5 Summary and Perspectives -- References -- Linear Wave Solutions of a Stochastic Shallow Water Model -- 1 Introduction -- 2 Review of RSW-LU -- 3 Stationary Solution -- 4 Stochastic Rotating Shallow Water Waves -- 4.1 Ensemble-Mean Waves Under Homogeneous Noise -- 4.1.1 Mean Poincaré Waves -- 4.1.2 Mean Geostrophic Mode -- 4.2 Path-Wise Waves Under Constant Noise -- 4.2.1 Stochastic Poincaré Waves -- 4.2.2 Stochastic Geostrophic Mode -- 4.3 Approximation of Path-Wise Waves Under Homogeneous Noise -- 4.3.1 Stochastic Poincaré Waves -- 4.3.2 Stochastic Geostrophic Mode -- 4.4 Numerical Illustrations -- 5 Shallow Water PV Dynamics and Geostrophic Adjustment -- 6 Conclusions -- References -- Analysis of Sea Surface Temperature Variability Using Machine Learning -- 1 Introduction -- 2 Method -- 2.1 Deterministic Model Hypothesis -- 2.2 Stochastic Model Hypothesis: The Stochastic NbedDyn -- 3 Numerical Experiments -- 3.1 Data -- 3.2 Analysis of the Deterministic Model -- 3.3 Analysis of the Stochastic Model -- 4 Conclusion -- Appendix 1: Training -- Appendix 2: Parameterization of the Diffusion Function. References -- Data Assimilation: A Dynamic Homotopy-Based Coupling Approach -- 1 Introduction -- 2 Problem Formulation and Background -- 3 Schrödinger Bridge Approach -- 4 Homotopy Induced Dynamic Coupling -- 5 Numerical Implementation -- 5.1 Ensemble Kalman Mean Field Approximation -- 5.2 Particle Approximation and Time-Stepping -- 6 Examples -- 6.1 Pure Diffusion Processes -- 6.2 Purely Deterministic Processes -- 6.3 Linear Gaussian Case -- 6.4 Nonlinear Diffusion Example -- 6.5 Lorenz-63 Example -- 7 Conclusions -- Appendix 1: Derivation of Control Term Equation -- Appendix 2: Ensemble Kalman Filter Approximations -- References -- Constrained Random Diffeomorphisms for Data Assimilation -- 1 Introduction -- 2 Induced Stochastic PDE -- 3 Comparison with Other Perturbation Schemes -- 3.1 Comparison with the LU Equations -- 3.1.1 0-Forms in the LU Framework -- 3.1.2 n-Forms in the LU Framework -- 3.2 The SALT Perturbation Scheme -- 4 Conclusion -- Appendix: Expression of Tt*θ -- References -- Stochastic Compressible Navier-Stokes Equations Under Location Uncertainty -- 1 Introduction -- 2 Stochastic Reynolds Transport Theorem -- 3 Stochastic Compressible Navier-Stokes Equations -- 3.1 Non-dimensioning -- 3.2 Continuity -- 3.3 Momentum -- 3.4 Energy -- 3.5 Equation of State -- 4 Low Mach Approximation -- 5 Boussinesq-Hydrostatic Approximation -- 6 Extension to Non-Boussinesq -- 7 Conclusion -- Appendix A: Stochastic Reynolds Transport Theorem from Stratonovich to Itō -- Appendix B: Calculation Rules -- Distributivity of the Stochastic Transport Operator -- Work of Random Forces -- Appendix C: Displacement of a Transported Control Surface -- References -- Data Driven Stochastic Primitive Equations with Dynamic Modes Decomposition -- 1 Introduction -- 2 Location Uncertainty (LU) -- 3 Stochastic Boussinesq Equations -- 4 Methods. 4.1 High Resolution Data Filtering -- 4.2 Off-Line Noise Modelling Through DMD -- 4.3 On-Line Noise Reconstruction -- 5 Results -- 6 Conclusions -- References -- Index. |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>09437nam a22004933i 4500</leader><controlfield tag="001">50030882864</controlfield><controlfield tag="003">MiAaPQ</controlfield><controlfield tag="005">20240229073851.0</controlfield><controlfield tag="006">m o d | </controlfield><controlfield tag="007">cr cnu||||||||</controlfield><controlfield tag="008">240229s2023 xx o ||||0 eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783031400940</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">9783031400933</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(MiAaPQ)50030882864</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(Au-PeEL)EBL30882864</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1409704950</subfield></datafield><datafield 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ind1=" " ind2=" "><subfield code="a">1 online resource (347 pages)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Mathematics of Planet Earth Series ;</subfield><subfield code="v">v.11</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Intro -- Preface -- Contents -- Internal Tides Energy Transfers and Interactions with the Mesoscale Circulation in Two Contrasted Areas of the North Atlantic -- 1 Introduction -- 2 Governing Equations and Energy Budget -- 3 Data and Method -- 3.1 eNATL60 Simulation -- 3.2 Filtering and Computing Methods -- 4 Results -- 4.1 Life Cycle of the Internal Tide -- 4.2 Importance of the Different Contributions in the Energy Transfers -- 4.2.1 Detailed View of Coupling Terms -- 4.2.2 Modal Energy Budget -- 5 Conclusion -- References -- Sparse-Stochastic Model Reduction for 2D Euler Equations -- 1 Introduction -- 2 Sparse-Stochastic Model Reduction -- 3 Numerical Simulations -- 4 Conclusions and Outlook -- References -- Effect of Transport Noise on Kelvin-Helmholtz Instability -- 1 Introduction -- 2 Model Formulation -- 2.1 Point Vortex Method for Inviscid Flows -- 2.2 Point Vortex Method for Viscous Flows -- 3 Point Vortex Method with Environmental Noise -- 3.1 Transport Noise and Deterministic Scaling Limit -- 3.2 A Digression on the Theoretical Selection of the Noise -- 4 Numerical Results -- 4.1 Setting: Kelvin-Helmholtz Instability -- 4.1.1 The Role of Intrinsic Instability -- 4.1.2 The Role of Viscosity and Stability Restoration -- 4.2 Numerical Results on Environmental Noise -- 4.2.1 Selection of Divergence Free Field -- 4.2.2 Positions and Intensities of Fixed Vortices -- 4.2.3 Effect of Small Scale Common Noise -- 4.3 Diagnostics -- 5 Concluding Remarks -- References -- On the 3D Navier-Stokes Equations with Stochastic Lie Transport -- Introduction -- 1 Introduction -- 2 Preliminaries -- 2.1 Elementary Notation -- 2.2 Functional Framework -- 2.3 The SALT Operator -- 3 The Velocity Equation on the Torus -- 3.1 Definitions and Results -- 3.2 Operator Bounds -- 3.3 Proof of Proposition 3.2 -- 3.4 Proofs of Theorems 3.1 and 3.6.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">4 The Vorticity Equation on a Bounded Main -- 4.1 Deriving the Equation -- 4.2 Definitions and Results -- 4.3 Operator Bounds -- 4.4 Proof of Theorem 4.3 -- 5 Appendices -- 5.1 Proofs from Sects.2.3, 3.2, and 4.3 -- 5.2 A Conversion from Stratonovich to Itô -- 5.3 Abstract Solution Criterion I -- 5.4 Abstract Solution Criterion II -- References -- On the Interactions Between Mean Flows and Inertial Gravity Waves in the WKB Approximation -- 1 Introduction -- 2 Deterministic 3D Euler-Boussinesq (EB) Internal Gravity Waves -- 2.1 Lagrangian Formulation of the WMFI Equations at Leading Order -- 2.2 Hamiltonian Structure for the WMFI Equations at Leading Order -- 3 Stochastic WMFI -- 4 Conclusion -- Appendix: Asymptotic Expansion -- References -- Toward a Stochastic Parameterization for Oceanic Deep Convection -- 1 Introduction -- 2 Stochastic Formulation of Direct Non-hydrostatic Pressure Correction -- 3 Numerical Implementation and Simulations -- 3.1 Stochastic, Non-hydrostatic Pressure Correction -- 3.2 Numerical Experiments -- 4 Results -- 5 Conclusion and Perspectives -- References -- Comparison of Stochastic Parametrization Schemes Using Data Assimilation on Triad Models -- 1 Introduction -- 2 Reduced Order Models for Incompressible Fluids -- 2.1 Reduced Order Models for the 3D Euler Equation -- 2.2 Stochastic Parametrizations for the 3D Euler Equation -- 2.2.1 Modelling Under the Stochastic Advection by Lie Transport Principle -- 2.2.2 Modeling Under the Location Uncertainty Principle -- 2.3 Triad Model Comparison -- 3 Data Assimilation Comparison -- 3.1 Numerical Studies -- 3.1.1 Numerical Implementation -- 3.1.2 Data Assimilation for the Deterministic Model -- 3.1.3 Reduced Order Model Realisations -- 3.1.4 Model Statistics -- 3.1.5 Data Assimilation -- 4 Conclusions -- Appendix 1: Notation and Basic Identities -- Notation -- Vector Identities.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">Appendix 2: Derivation of Triad Models -- Deterministic Euler -- SALT Euler -- LU Euler -- Appendix 3: Supplementary Numerics -- Calibration of the Noise Amplitude -- Data Assimilation Verification -- References -- An Explicit Method to Determine Casimirs in 2D Geophysical Flows -- 1 Introduction -- 2 Geophysical Flows -- 3 Explicitly Determining the Casimirs -- 4 Conclusion -- References -- Correlated Structures in a Balanced Motion Interacting with an Internal Wave -- 1 Introduction -- 2 Model -- 3 Methods -- 3.1 Spectral Proper Orthogonal Decomposition -- 3.2 Broadband Proper Orthogonal Decomposition -- 3.2.1 Complex Demodulation of the Wave Field -- 3.2.2 Link with SPOD -- 3.2.3 Extended Broadband Proper Orthogonal Decomposition -- 4 Results -- 5 Summary and Perspectives -- References -- Linear Wave Solutions of a Stochastic Shallow Water Model -- 1 Introduction -- 2 Review of RSW-LU -- 3 Stationary Solution -- 4 Stochastic Rotating Shallow Water Waves -- 4.1 Ensemble-Mean Waves Under Homogeneous Noise -- 4.1.1 Mean Poincaré Waves -- 4.1.2 Mean Geostrophic Mode -- 4.2 Path-Wise Waves Under Constant Noise -- 4.2.1 Stochastic Poincaré Waves -- 4.2.2 Stochastic Geostrophic Mode -- 4.3 Approximation of Path-Wise Waves Under Homogeneous Noise -- 4.3.1 Stochastic Poincaré Waves -- 4.3.2 Stochastic Geostrophic Mode -- 4.4 Numerical Illustrations -- 5 Shallow Water PV Dynamics and Geostrophic Adjustment -- 6 Conclusions -- References -- Analysis of Sea Surface Temperature Variability Using Machine Learning -- 1 Introduction -- 2 Method -- 2.1 Deterministic Model Hypothesis -- 2.2 Stochastic Model Hypothesis: The Stochastic NbedDyn -- 3 Numerical Experiments -- 3.1 Data -- 3.2 Analysis of the Deterministic Model -- 3.3 Analysis of the Stochastic Model -- 4 Conclusion -- Appendix 1: Training -- Appendix 2: Parameterization of the Diffusion Function.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">References -- Data Assimilation: A Dynamic Homotopy-Based Coupling Approach -- 1 Introduction -- 2 Problem Formulation and Background -- 3 Schrödinger Bridge Approach -- 4 Homotopy Induced Dynamic Coupling -- 5 Numerical Implementation -- 5.1 Ensemble Kalman Mean Field Approximation -- 5.2 Particle Approximation and Time-Stepping -- 6 Examples -- 6.1 Pure Diffusion Processes -- 6.2 Purely Deterministic Processes -- 6.3 Linear Gaussian Case -- 6.4 Nonlinear Diffusion Example -- 6.5 Lorenz-63 Example -- 7 Conclusions -- Appendix 1: Derivation of Control Term Equation -- Appendix 2: Ensemble Kalman Filter Approximations -- References -- Constrained Random Diffeomorphisms for Data Assimilation -- 1 Introduction -- 2 Induced Stochastic PDE -- 3 Comparison with Other Perturbation Schemes -- 3.1 Comparison with the LU Equations -- 3.1.1 0-Forms in the LU Framework -- 3.1.2 n-Forms in the LU Framework -- 3.2 The SALT Perturbation Scheme -- 4 Conclusion -- Appendix: Expression of Tt*θ -- References -- Stochastic Compressible Navier-Stokes Equations Under Location Uncertainty -- 1 Introduction -- 2 Stochastic Reynolds Transport Theorem -- 3 Stochastic Compressible Navier-Stokes Equations -- 3.1 Non-dimensioning -- 3.2 Continuity -- 3.3 Momentum -- 3.4 Energy -- 3.5 Equation of State -- 4 Low Mach Approximation -- 5 Boussinesq-Hydrostatic Approximation -- 6 Extension to Non-Boussinesq -- 7 Conclusion -- Appendix A: Stochastic Reynolds Transport Theorem from Stratonovich to Itō -- Appendix B: Calculation Rules -- Distributivity of the Stochastic Transport Operator -- Work of Random Forces -- Appendix C: Displacement of a Transported Control Surface -- References -- Data Driven Stochastic Primitive Equations with Dynamic Modes Decomposition -- 1 Introduction -- 2 Location Uncertainty (LU) -- 3 Stochastic Boussinesq Equations -- 4 Methods.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">4.1 High Resolution Data Filtering -- 4.2 Off-Line Noise Modelling Through DMD -- 4.3 On-Line Noise Reconstruction -- 5 Results -- 6 Conclusions -- References -- Index.</subfield></datafield><datafield tag="588" ind1=" " ind2=" "><subfield code="a">Description based on publisher supplied metadata and other sources.</subfield></datafield><datafield tag="590" ind1=" " ind2=" "><subfield code="a">Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. </subfield></datafield><datafield tag="655" ind1=" " ind2="4"><subfield code="a">Electronic books.</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Crisan, Dan.</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Holm, Darryl.</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Mémin, Etienne.</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Radomska, Anna.</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Print version:</subfield><subfield code="a">Chapron, Bertrand</subfield><subfield code="t">Stochastic Transport in Upper Ocean Dynamics II</subfield><subfield code="d">Cham : Springer,c2023</subfield><subfield code="z">9783031400933</subfield></datafield><datafield tag="797" ind1="2" ind2=" "><subfield code="a">ProQuest (Firm)</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Mathematics of Planet Earth Series</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://ebookcentral.proquest.com/lib/oeawat/detail.action?docID=30882864</subfield><subfield code="z">Click to View</subfield></datafield></record></collection> |