Every climate index, from ENSO to obscure indices such as the PNA, will reveal this characteristic. It's also a known property of nonlinear fluid dynamics at all scales, capable of being reproduced in the lab -- see geoenergymath.com/2020/05/17/d....
The only question is what causes the magnitude and sign in the strength of the "overturning" signal (I put quotes around overturning because its likely not the same process as fresh-water lake overturning but perhaps analogous).
I place all my money into tidal forces synchronizing the resultant signal profile, much like tidal forces control the signal profile of ocean tides. imageshack.com/a/mLK17/1
24 models of various degrees of cross-validation imageshack.com/a/mLK17/1
