Sorry ignore what I wrote below. For some reason I thought it was a transient simulation. Maybe plot contours of the residuals to see where it is not converging. Could there be some inherent unsteadiness in the solution, such as vortex shedding? Also, in my experience, mesh quality can be a cause for a solution failing when moving from first order to second order. The numerical dissipation of first order meshes sometimes overcome mesh quality problems, whereas the second order discretization will amplify it. Also consider moving to the segregated solver and see if you get better convergence there.

~~You are plotting those each iteration. If instead you plotted those per time step those spike will smooth out. If you plot every iteration the plot will be corrupted by intermediate “incorrect” solutions.~~

~~Trying to look at the last iteration per timestep in your plots, I can imagine some sort of convergence to a fixed value.~~