  In this note we study locally self-similar blow up for the Euler equation.
The main result states that under a mild $L^p$-growth assumption on the profile
$v$, namely, $\int_{|y| \sim L} |v|^p dy \lesssim L^{\g}$ for some $\g <p-2$,
the self-similar solution carries a positive amount of energy up to the time of
blow-up $T$, namely, $\int_{|y| \sim L} |v|^2 dy \sim L^{N-2\a}$. The result
implies and extends several previously known exclusion criteria. It also
supports a general conjecture relating fractal local dimensions of the energy
measure with the rate of velocity growth at the time of possible blowup.
