TY - JOUR
T1 - Stream Helicity in Toroidal Domains
AU - Su , W. D.
AU - Tan , Y.
JO - Advances in Applied Mathematics and Mechanics
VL - 3
SP - 619
EP - 629
PY - 2019
DA - 2019/01
SN - 11
DO - http://doi.org/10.4208/aamm.2018.s06
UR - https://global-sci.org/intro/article_detail/aamm/12985.html
KW - Helicity, magnetic field, streamlines, toroidal domain, helical-wave decomposition.
AB - <p style="text-align: justify;">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.</p>