# $L^p$-weighted enstrophy calculations

Mathematician here, only somewhat familiar with physics, but finding myself involved in a research project on fluid dynamics. I'm studying a 3D simulation of turbulent fluid flow, and we are currently using the enstrophy calculation to study the system. That is, we look at $$\mathcal{E}(\omega) = \frac{1}{2}\int_V |\omega|^2 dV,$$ the integral of the square of the magnitude of the vorticity field. Mathematically, we see that $$2\mathcal{E}(\omega) = ||\omega||_2^2,$$ the square of the $L^2$-norm of the magnitude of the vorticity field.

My question: Do physicists ever look at other $L^p$-norms of the vorticity field? Is this something of interest? Intuitively, it would be like a weighted enstrophy calculation, placing more weight on regions of high vorticity.