The El Niño-Southern Oscillation (ENSO) is a climate oscillation in the tropical Pacific sustained by a positive feedback between sea surface temperature (SST) gradient and the Walker circulation, known as the Bjerknes feedback. This results in an oscillation in the SST anomaly between warm (El Niño) and cold (La Niña) phases. In traditional ENSO theories, the Bjerknes feedback amplifies an initial disturbance to produce a full El Niño or La Niña, while the Sverdrup transport, caused by off-equatorial wind stress (WS) curl, determines the slow charging of the equatorial Pacific through deepening of the thermocline. However, recent research has emphasized the role played by the WS divergence in generating Kelvin waves that initiate El Niño. To account for changes in the action of the WS over a varying ocean stratification, we introduce a dimensionless WS (DWS) and use the Helmholtz decomposition to break it down into an irrotational (curl-free) and solenoidal (divergence-free) component to study ENSO variability over the interannual-to-interdecadal time scale. We show that the irrotational component of the DWS drives the thermocline dynamics on interannual time-scales, while the solenoidal component, which drives Sverdrup transport, determines off-equatorial internal waves, referred to as q-waves, that induce changes in the thermocline depth over longer time-scales. Furthermore, we develop an integral relation that links the variability of the thermocline depth anomaly across the tropical Pacific to the Niño-3.4 index variability. We conclude that the DWS irrotational component determines the Niño-3.4 index interannual variability, while the solenoidal component determines its long-term variability.