Chaos in the lid-driven square cavity

As the Reynolds number Re⟶∞ the primary eddy switches from clockwise- to counterclockwise-rotating, a switching repeatedly reversing as the time t⟶∞. The primary eddy is the eddy leading the dynamics. Marking the genesis of chaos, the switching first is observed at Re=307,000 at the upper side of the total kinetic energy range. But then, it is observed at Re=310,000 at the lower side of the total kinetic energy range and unexpectedly relies upon the occurrence of a unique lowest spike in the total kinetic energy range. However, this reliance is not observed at Re=307,000, even when the lowest spike is more pronounced herein, but continues occurring systematically beyond Re=310,000. At extreme Reynolds numbers Re=O(1eps)=O(1015), where eps is the machine epsilon in double precision, as the time t⟶∞, an interesting dynamics still endures where the switching repeatedly reverses or where it stays put, the primary eddy rotating solely counterclockwise.