In Kolmogorov’s theory of turbulence there is a "cascade" of energy from large to small scales where energy is dissipated by viscosity. In two-dimensional flows (which have been used for example to model geophysical flows if rotation can be neglected), the flow is dominated by the formation of small stable vortices and what cascades to small scales is not energy but enstrophy. Informally, enstrophy can be thought of as the energy associated to vortices. In both cases, there must be a finite rate of dissipation as viscosity vanishes, as observed experimentally and in simulations. Mathematically, this is the case if there are irregular solutions to the Euler equations, modeling inviscid fluid flow, which do not conserve energy in 3D or enstrophy in 2D. We will discuss some results concerning the behavior of enstrophy in 2D Euler solutions, in particular how to reconcile turbulence with the fact Euler solutions conserve enstrophy exactly. This is joint work with Milton Lopes and Helena Nussenzveig Lopes.