Lower bounds on the mix norm of passive scalars advected by incompressible enstrophy-constrained flows

Gautam Iyer, Alexander Kiselev, Xiaoqian Xu

Consider a diffusion-free passive scalar $\theta$ being mixed by an incompressible flow $u$ on the torus ${\mathbb{T}}^d$. Our aim is to study how well this scalar can be mixed under an e…