. . "For a 2d flow, for example, the (total) enstrophy is a surface integral over the whole domain, not a line integral (and for a $D$-dimensional flow, it is $\\int_{\\mathcal{D} \\subset \\mathbb{R}^D} |\\vec{\\omega}|^2 ext{d}^{D} x$), with $\\vec{\\omega}$ the vorticity). (We could also consider the local enstrophy $|\\vec{\\omega}|^2$ ...)" . .