When using many iterative methods, whether for solving linear systems, looking for steady-state convergence in CFD, etc., the semilog plot of the residual often shows "humps" as the residual decays. These humps generally appear in a regular pattern (same number of iterations between them for example). I've seen cases where the valley between the hump can be several orders of magnitude lower than the peak of the hump.
For example, consider this image of a residual vs. iteration count (just the black line is important):
Another example that I can't embed here is Figure 4 in this AIAA paper.
What is it that causes these humps in the residual? Why do they appear with a somewhat regular frequency?