  The nature of current sheet formation in the vicinity of three-dimensional
(3D) magnetic null points is investigated. The particular focus is upon the
effect of the compressibility of the plasma on the qualitative and quantitative
properties of the current sheet. An initially potential 3D null is subjected to
shearing perturbations, as in a previous paper [Pontin et al., Phys. Plasmas,
in press (2007)]. It is found that as the incompressible limit is approached,
the collapse of the null point is suppressed, and an approximately planar
current sheet aligned to the fan plane is present instead. This is the case
regardless of whether the spine or fan of the null is sheared. Both the peak
current and peak reconnection rate are reduced. The results have a bearing on
previous analytical solutions for steady-state reconnection in incompressible
plasmas, implying that fan current sheet solutions are dynamically accessible,
while spine current sheet solutions are not.
