Advection and Diffusion in Random Media

1. Front Matter

   Pages i-xii

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2. Problem Statement

   • Leonid I. Piterbarg, Alexander G. Ostrovskii

   Pages 1-23

3. Scale Classification of Turbulent Diffusion Models

   • Leonid I. Piterbarg, Alexander G. Ostrovskii

   Pages 25-41

4. Delta-Correlation Approximation

   • Leonid I. Piterbarg, Alexander G. Ostrovskii

   Pages 43-70

5. Homogenization and Superdiffusion

   • Leonid I. Piterbarg, Alexander G. Ostrovskii

   Pages 71-101

6. Finite Correlation Time

   • Leonid I. Piterbarg, Alexander G. Ostrovskii

   Pages 103-117

7. The Inverse Problem: Maximum Likelihood Method

   • Leonid I. Piterbarg, Alexander G. Ostrovskii

   Pages 119-144

8. Maximum Likelihood Estimators: Numerical Simulations

   • Leonid I. Piterbarg, Alexander G. Ostrovskii

   Pages 145-177

9. The Inverse Problem: Autoregressive Estimators

   • Leonid I. Piterbarg, Alexander G. Ostrovskii

   Pages 179-190

10. A Stochastic Model for SST Anomaly Transport

    • Leonid I. Piterbarg, Alexander G. Ostrovskii

    Pages 191-233

11. Advection and Diffusion Inferred from SST Anomaly Time Series

    • Leonid I. Piterbarg, Alexander G. Ostrovskii

    Pages 235-303

12. Back Matter

    Pages 305-330

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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.

• Ocean
• Oceanography
• fluid dynamics
• partial differential equation
• statistics
• partial differential equations
• fluid- and aerodynamics

• Center for Applied Mathematical Sciences, University of Southern California, Los Angeles, USA

  Leonid I. Piterbarg

• Research Institute for Applied Mechanics, Kyushu University, Kasuga, Japan

  Alexander G. Ostrovskii

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