In this talk, we will consider two classical problems: dynamics of patches on the plane and local energy growth for a solution to 2D Euler and Navier-Stokes on large domains.
For the first problem, we prove the existence of a central pair of patches that merge with a double-exponential rate under the 2D Euler dynamics equipped with regular exterior velocity. For the local energy growth problem, we will discuss Zelik and Gallay's recent results and present the work in progress (with T. Leslie) that concerns "speeding up" the ensemble of point vortices.