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Turbulence, Transport and Reconnection

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Topics in Magnetohydrodynamic Topology, Reconnection and Stability Theory

Part of the book series: CISM International Centre for Mechanical Sciences ((CISM,volume 591))

Abstract

Turbulence is a multi-scale phenomenon that is ubiquitous in our universe. Strong nonlinearity in a system enhances coupling among modes, leading to a very broad spectrum in the spatial domain which contains an energy cascade and dissipation. We have to deal with all the scales of motions from the largest energy-containing scale to the smallest dissipation scales simultaneously. One of the subjects of this chapter is to show how to treat nonlinearity beyond the quasi-linear approximation. Turbulence of practical interest is almost always inhomogeneous and accompanied by non-uniform global structures, such as density stratification, velocity shear, rotation and magnetic field. Therefore, another subject of this chapter is to present how to tackle strongly nonlinear and inhomogeneous magnetohydrodynamic turbulence. Turbulence modelling provides a strong tool for studying realistic turbulent flow. A way to construct a turbulence model on the basis of the fundamental equations, beyond the heuristic ad hoc modelling, is shown. With these preparations, the magnetic reconnection problem is addressed from the viewpoint of turbulent transport.

The author would like to cordially dedicate this chapter to the memory of his mentor and great friend, Akira Yoshizawa (25 August 1942–3 June 2018), who kept inspiring him through heartfelt and thoughtful encouragement from the beginning of his research career. Part of this work was conducted under the support of the JSPS Grants-in-Aid Scientific Research 18H01212.

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Notes

  1. 1.

    As a parody of a poem by Jonathan Swift, Richardson wrote: “We realize thus that: big whirls have little whirls that feed on their velocity, and little whirls have lesser whirls and so on to viscosity – in the molecular sense” (Richardson 1922).

  2. 2.

    Arnold Sommerfeld proposed this name (Rott 1990).

  3. 3.

    Due to the frequent appearance of dyadic products, u ⊗u will appear as uu.

  4. 4.

    Hereafter, the internal energy is denoted as q not e, sincee is used for the electric field in MHD.

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Authors and Affiliations

  1. Institute of Industrial Science, University of Tokyo, Tokyo, Japan

    Nobumitsu Yokoi

  2. Nordic Institute for Theoretical Physics (NORDITA), Stockholm, Sweden

    Nobumitsu Yokoi

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  1. Nobumitsu Yokoi
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Correspondence to Nobumitsu Yokoi .

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Editors and Affiliations

  1. School of Mathematics and Statistics, University of Glasgow, Glasgow, UK

    David MacTaggart

  2. College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, UK

    Andrew Hillier

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Yokoi, N. (2020). Turbulence, Transport and Reconnection. In: MacTaggart, D., Hillier, A. (eds) Topics in Magnetohydrodynamic Topology, Reconnection and Stability Theory. CISM International Centre for Mechanical Sciences, vol 591. Springer, Cham. https://doi.org/10.1007/978-3-030-16343-3_6

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