Yudovich proved that the 2D incompressible Euler equation has a unique solution for integrable and bounded initial vorticity.  While solutions are known to exist for integrable but unbounded  vorticity, it remains open whether such initial data admits multiple solutions. In this talk, we construct two distinct solutions of the 2D  Euler equation with the same initial vorticity in $\bigcap_{1\le p<\infty}L^p(\mathbb R^2)$. The vorticities are compactly supported in  space and have mean zero, so the corresponding velocities have finite  energy. The nonuniqueness mechanism is a cascade of transitions in quadrupole dynamics across infinitely many scales.