The only earth science class I took in college was limnology.

Of course I was a casual student of freshwater activities before that time, but certain behaviors of lakes were hammered home by taking this class. For example, the idea behind seasonal lake overturning. The overturning occurs as a singular event at a particular time of the year (monomictic once per year and dimictic twice per year, see figure to the right).

Saltwater doesn’t show the same predilection for overturning as freshwater does, mainly because of the higher density differences above and below the thermocline, but the thermocline does vary, especially at latitudes located off the equator.

The ENSO model that appears so promising might be pointing to a partial overturning  showing a bimictic behavior.  The bi-prefix implies a biennial impulse that reverses direction every year, tied into a biennial Mathieu modulation associated with fluid sloshing dynamics. The Mathieu modulation is partially induced from the forcing conditions [1][2].

The following figure shows the modulation and impulse forcing that generates the best fit for the ENSO model. The BLUE is the Mathieu modulation while the ORANGE is the impulse.

The impulse may be related to a rapidly changing slope when the bimictic partial-overturning kicks in. The positive impulse as the Mathieu modulation moves from high to low, and the negative impulse as the modulation moves from low to high, both occurring at the same relative time late in the year.  Note that the polarity of this may be reversed, as the lunar tidal forcing at the impulse time provides the strength of this forcing through a multiplicative effect. This is shown below.

Whether to call it sloshing or a partial overturning remains to be determined. Yet overall this piece of the puzzle is the primary ansatz behind the entire model — since if we don’t include it, the model does not generate the sharply distinct ENSO peaks and valleys. In other words, this is what causes the physical aliasing necessary to transform the monthly and fortnightly tidal cycles into a more erratic interannual cycling. This is in fact a simple model that shows more complex but still predictable dynamics.

References

[1] T. B. Benjamin and F. Ursell, “The stability of the plane free surface of a liquid in vertical periodic motion,” presented at the Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 1954, vol. 225, pp. 505–515.

[2] S. Bale, K. Clavin, M. Sathe, A. S. Berrouk, F. C. Knopf, and K. Nandakumar, “Mixing in oscillating columns: Experimental and numerical studies,” Chemical Engineering Science, vol. 168, pp. 78–89, 2017.