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Toward Understanding Global Flow Structure

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Mathematical Fluid Dynamics, Present and Future

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 183))

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Abstract

Flows in nature are generally coupled with the environment. Also, flow structures in the forms of convection rolls, vortices, boundary layers, for example, are often coupled with flow structures in other form(s) as well as the external environments such as the boundary motion and the temperature gradient. Whole flow structure in such cases is often characterized by multi-scale or hierarchy, therefore, we will term such flow structures “global flow structure”. Clearly, the global flow structure is complex in both space and scales, but there are general viewpoints applicable to this category of the flow, by which we can tackle with new phenomena. In this review, we discuss the global flow structure in both views of typical problems and analysis methods itself.

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Acknowledgements

The authors were major members of the CREST project “A challenge to unsolved problems in fluid engineering with modern mathematical analysis” headed by Professor Yoshihiro Shibata in Waseda University in the JST mathematics program “Alliance for breakthrough between mathematics and sciences” governed by Professor Yasumasa Nishiura in Tohoku University from April 1st, 2010 to March 31st, 2015. We would like to appreciate both financial and academic support for this project. The part of this study was supported by CREST No. PJ74100011, and Grants-in-Aid for Scientific Research (26400396, 25289062, 23540433, 21340019.

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Authors and Affiliations

  1. Graduate School of Science, Hiroshima University, 1-7-1, Kagamiyama, Higashi-hiroshima, 739-8521, Japan

    Makoto Iima

  2. Department of Radiation Oncology, Institute of Biomedical and Health Sciences, Hiroshima University, Higashi-hiroshima, Japan

    Takayuki Yamaguchi

  3. Rocket and Spacecraft Modeling Laboratory, School of Engineering, The University of Tokyo, Tokyo, Japan

    Takeshi Watanabe

  4. Department of Mathematics, Kyoto University of Education, Kyoto, Japan

    Akane Kawaharada

  5. Laboratory for Flow Control, Hokkaido University, Sapporo, Japan

    Yuji Tasaka

  6. Graduate School of Science, Hiroshima University, Higashi-hiroshima, Japan

    Erika Shoji

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  1. Makoto Iima
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  2. Takayuki Yamaguchi
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  3. Takeshi Watanabe
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  4. Akane Kawaharada
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  5. Yuji Tasaka
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  6. Erika Shoji
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Correspondence to Makoto Iima .

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Editors and Affiliations

  1. Department of Mathematics, Waseda University, Tokyo, Japan

    Yoshihiro Shibata

  2. Department of Mathematics, Waseda University, Tokyo, Japan

    Yukihito Suzuki

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Iima, M., Yamaguchi, T., Watanabe, T., Kawaharada, A., Tasaka, Y., Shoji, E. (2016). Toward Understanding Global Flow Structure. In: Shibata, Y., Suzuki, Y. (eds) Mathematical Fluid Dynamics, Present and Future. Springer Proceedings in Mathematics & Statistics, vol 183. Springer, Tokyo. https://doi.org/10.1007/978-4-431-56457-7_6

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