Rotational and Irrotational Wind Forcing as dual drivers of El Nino Southern Oscillation variability

Abstract

El Ni\~no Southern Oscillation (ENSO) is the Earth's strongest source of interannual climate variability. Although its center of action is in the tropical Pacific, it has significant influences on the climate at the planetary scale. ENSO is sustained by a feedback process between equatorial winds, vertical displacements of the thermocline, and sea surface temperature (SST) anomaly gradients. This produces an oscillation in the SST anomaly between a warm (El Ni\~no) and a cold phase (La Ni\~na). While the natural time-scale of ENSO variability is interannual, variations in its behavior and characteristics have been observed over longer time scales, including decadal and interdecadal. Here, we use the Helmholtz decomposition to break down the wind stress into two components: irrotational (curl free) and solenoidal (divergence free). We show that the irrotational component of the wind stress drives the dynamics of the thermocline on the interannual time-scale, while the solenoidal component, whose action is influenced by the stratification of the water column, affects the variability of the thermocline over decadal or interdecadal time-scales. Furthermore, we develop an integral relation that links the variability of the thermocline depth anomaly across the entire tropical Pacific to the variability of the average SST anomaly in the central tropical Pacific (known as the Ni\~no-3.4 index) and conclude that the irrotational component of the wind stress determines the interannual variability of the Ni\~no-3.4 index, while the solenoidal component determines its long-term variability.