Advection and Diffusion in Random Media
Implications for Sea Surface Temperature Anomalies
(Sprache: Englisch)
This book originated from our interest in sea surface temperature variability. Our initial, though entirely pragmatic, goal was to derive adequate mathemat ical tools for handling certain oceanographic problems. Eventually, however, these considerations...
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Klappentext zu „Advection and Diffusion in Random Media “
This book originated from our interest in sea surface temperature variability. Our initial, though entirely pragmatic, goal was to derive adequate mathemat ical tools for handling certain oceanographic problems. Eventually, however, these considerations went far beyond oceanographic applications partly because one of the authors is a mathematician. We found that many theoretical issues of turbulent transport problems had been repeatedly discussed in fields of hy drodynamics, plasma and solid matter physics, and mathematics itself. There are few monographs concerned with turbulent diffusion in the ocean (Csanady 1973, Okubo 1980, Monin and Ozmidov 1988). While selecting material for this book we focused, first, on theoretical issues that could be helpful for understanding mixture processes in the ocean, and, sec ond, on our own contribution to the problem. Mathematically all of the issues addressed in this book are concentrated around a single linear equation: the stochastic advection-diffusion equation. There is no attempt to derive universal statistics for turbulent flow. Instead, the focus is on a statistical description of a passive scalar (tracer) under given velocity statistics. As for applications, this book addresses only one phenomenon: transport of sea surface temperature anomalies. Hopefully, however, our two main approaches are applicable to other subjects.
The book presents the foundations of the theory of turbulent transport within the context of stochastic partial differential equations. It serves to establish a firm connection between rigorous and non-rigorous results concerning turbulent diffusion. Mathematically all of the issues addressed in this book are concentrated around a single linear equation: stochastic advection-diffusion (transport) equation. There is no attempt made to derive universal statistics for turbulent flow. Instead emphasis is placed on a statistical description of a passive scalar (tracer) under given velocity statistics. An application concerning transport of sea surface temperature anomalies reconciles the developed theory and a highly practical issue of modern physical oceanography by using the newly designed inversion techniques which take advantage of powerful maximum likelihood and autoregressive estimators. Audience: Graduate students and researchers in mathematics, fluid dynamics, and physical oceanography.
Inhaltsverzeichnis zu „Advection and Diffusion in Random Media “
- Preface1. Problem Statement
2. Scale Classification of Turbulent Diffusion Models
3. Delta-Correlation Approximation
4. Homogenization and Superdiffusion
5. Finite Correlation Time
6. The Inverse Problem: Maximum Likelihood Method
7. Maximum Likelihood Estimators: Numerical Simulations
8. The Inverse Problem: Autoregressive Estimators
9. A Stochastic Model for SST Anomaly Transport
10. Advection and Diffusion Inferred From SST Anomaly Time Series
- References
- Index
Bibliographische Angaben
- Autoren: Leonid Piterbarg , A. Ostrovskii
- 2010, XII, 330 Seiten, Maße: 15,5 x 23,5 cm, Kartoniert (TB), Englisch
- Verlag: Springer, Berlin
- ISBN-10: 1441947736
- ISBN-13: 9781441947734
Sprache:
Englisch
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