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Short-Time Correlation Approximations for Diffusing Tracers in Random Velocity Fields: A Functional Approach

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Stochastic Modelling in Physical Oceanography

Part of the book series: Progress in Probability ((PRPR,volume 39))

Abstract

The paper studies statistical characteristics of the passive tracer concentration field, and of its spatial gradient, in random velocity fields. Those include mean values, correlation functions as well as probability distributions. The functional approach is used. Influence of the mean flow (on the example of linear shear flow) and of the molecular diffusion coefficient on the statistical characteristics is analysed. Most of our analysis is conducted in the framework of the delta-correlated (in time) approximation and conditions for its applicabillity are established. We also consider approximations taking account of the positive but finite correlation radius, such as the telegraph process approximation and the diffusion approximation.

The authors made an effort to provide a broad perspective of and the background for the issues under consideration. To make the material accessible to physical scientists they tried to avoid use of overly abstract mathematical structures and conduct their presentation in the language and an idiom common in the physical and applied mathematics literature.

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Author information

Authors and Affiliations

  1. Institute of Atmospheric Physics, Russian Academy of Sciences, Moscow, 109017, Russia

    V. I. Klyatskin

  2. Pacific Oceanological Institute, Russian Academy of Sciences, Vladivostok, 690041, Russia

    V. I. Klyatskin

  3. Department of Statistics and Center for Stochastic and Chaotic Processes in Science and Technology, Case Western Reserve University, Cleveland, OH, 44106, USA

    W. A. Woyczynski & D. Gurarie

Authors
  1. V. I. Klyatskin
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  2. W. A. Woyczynski
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  3. D. Gurarie
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Editor information

Editors and Affiliations

  1. Faculty of Industrial Engineering and Management, Technion University, Haifa, 32000, Israel

    Robert J. Adler

  2. Department of Oceanography, University of Hawaii, Honolulu, HI, 96822, USA

    Peter MĂĽller

  3. Center for Applied Mathematical Sciences, University of Southern California, Los Angeles, CA, 90089-1113, USA

    Boris L. Rozovskii

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© 1996 Birkhäuser Boston

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Klyatskin, V.I., Woyczynski, W.A., Gurarie, D. (1996). Short-Time Correlation Approximations for Diffusing Tracers in Random Velocity Fields: A Functional Approach. In: Adler, R.J., Müller, P., Rozovskii, B.L. (eds) Stochastic Modelling in Physical Oceanography. Progress in Probability, vol 39. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2430-3_9

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  • DOI: https://doi.org/10.1007/978-1-4612-2430-3_9

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4612-7533-6

  • Online ISBN: 978-1-4612-2430-3

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