Volume 11, Issue 3
Stream Helicity in Toroidal Domains

W. D. Su & Y. Tan

Adv. Appl. Math. Mech., 11 (2019), pp. 619-629.

Published online: 2019-01

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  • Abstract

As the analogue of helicity, the concept of stream helicity proposed in 2007 provides a quantitative measurement for entanglement of streamlines for an incompressible flow field or magnetic field lines for a magnetic field. It is found that the helical-wave decomposition can serve as a convenient mathematical physics tool for the calculation of helicity and stream helicity. However, for a multiply connected domain such as a torus under the background of TOKAMAK, the analysis presents some peculiarities due to the nature of multiple-value of some involving potentials. Here we give a full derivation of stream helicity for such a case, together with some detailed analysis. Particularly, it is found that a maximum of absolute helicity under prescribed energy could be attained by a pure potential field.

  • Keywords

Helicity, magnetic field, streamlines, toroidal domain, helical-wave decomposition.

  • AMS Subject Headings

76F20, 76F25, 76W05, 82D10, 85A30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-11-619, author = {}, title = {Stream Helicity in Toroidal Domains}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2019}, volume = {11}, number = {3}, pages = {619--629}, abstract = {

As the analogue of helicity, the concept of stream helicity proposed in 2007 provides a quantitative measurement for entanglement of streamlines for an incompressible flow field or magnetic field lines for a magnetic field. It is found that the helical-wave decomposition can serve as a convenient mathematical physics tool for the calculation of helicity and stream helicity. However, for a multiply connected domain such as a torus under the background of TOKAMAK, the analysis presents some peculiarities due to the nature of multiple-value of some involving potentials. Here we give a full derivation of stream helicity for such a case, together with some detailed analysis. Particularly, it is found that a maximum of absolute helicity under prescribed energy could be attained by a pure potential field.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2018.s06}, url = {http://global-sci.org/intro/article_detail/aamm/12985.html} }
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