Helicity or vortex generation in hydrodynamic (HD), magneto-hydrodynamic (MHD), and electrohydrodynamic (EHD) regimes

Usually the source-origins of helicity or vortex generation have been considered to be thermohydrodynamic in the hydrodynamic (HD) regime and/or magnetohydrodynamic in the magnetohydrodynamic (MHD). Then fluid helicity is defined as h(F) = V (.) Omega (v: fluid velocity, Omega: fluid vorticity, like-wise magnetic helicity is defined as h(M) = v (.) H (H: magnetic field). It has been shown, however, by the present author that an electric quadrupole is also capable for helicity or vortex generation and a new electric helicity defined as h(E) = v (.) E (E: electric field) has been introduced. Accordingly, we have now three kinds of helicity, namely fluid, magnetic, and electric helicity. In many cases of atmospheric and space electricity phenomena in nature, helicity or vortex generation is involved as typically seen in tornadic thunderstorms. Conventional theory of tornadic thunderstorms, however, space-charge and electric fields have never been considered properly so far, surprisingly in spite of their effects of significance, because of no theorv for such cases, although those effects have been recognized implicitly by field experiments. This paper fills up these demands by newly introducing the concept of 'Electric Helicity' based on 'Electrohydrodynamics (EHD) established and developed over the last more than two decades and such a whole theory is applied to tornadic thunderstorms.