© 1972 by Oxford University Press
SWEET'S MECHANISM FOR THE DESTRUCTION OF MAGNETIC FLUX
( Department of Applied Mathematics, University of St. Andrews )
Sweet's mechanism is one of the more efficient ways of converting magnetic energy into other forms by the reconnection of magnetic field lines in a narrow current sheet or boundary layer. This paper presents a more quantitative analysis of the mechanism than hitherto. In particular, it applies the Pohlhausen approximation to the two-dimensional magnetohydrodynamic boundary-layer equations in order to calculate variations along the boundary layer in the boundary-layer thickness 8 and in the components along the boundary layer of magnetic field B and fluid velocity V.
For an incompressible fluid forms are assumed for the profiles of magnetic field and fluid velocity across the layer and the set of resulting ordinary differential equations is integrated numerically. B decreases monotonically to zero along the layer while 8 tends to infinity and V first increases to a maximum and then decreases to zero. About fifty per cent of the energy input goes into ohmic dissipation and thirty-five per cent into kinetic energy of fluid motion.
For compressible flow neglect of the density outside the boundary layer compared with that inside leads to an approximate expression for the variation of the magnetic field across the layer; the y-component increases linearly in an inner region and is constant in an outer region, with a sharp transition between the two. The Pohlhausen approximation then shows that 8 decreases to zero and V tends to infinity as B decreases to zero.