Vorticity squared integrated over the whole computational domain as a function of simulation time for the thin-layer case. The various lines correspond to simulations with different levels of refinement in the AMR scheme: 1 (black dot-dashed line), 2 (brown dotted line), 3 (green dashed line), and 4 (blue solid line). For comparison purposes, the linear analytical value is also shown (red dashed line). Vorticity is normalized to the value at t = 0.