  We study the distribution of spatial extrema of vorticity and the determinant
of the strain rate tensor for a two-dimensional turbulent flow forced by a
Kolmogorov forcing. The distribution of these quantities follow non-Gaussian
behaviour and they do not fall into the Generalised Extreme value
distributions. It is found that for the truncated Euler equations the spatial
extrema of vorticity and strain rate tensor are well described by the Gumbel
distribution. The spatial extrema for the vorticity is found to be at the core
of the vortices while the velocity gradients are found near the edges of the
vortices or at the shear layers in the regions between the vortices. Temporal
correlations of the velocity gradients shed light on the extreme value
distributions obtained for turbulence and the truncated Euler equations.
