The theory of non-linear oscillator applied to the BiOS mechanism

The observed pseudo-periodic reversal of the upper layer circulation of the Ionian Sea has been assumed to be related to some internal feedback processes (density driven) by the so called BiOS (Adriatic-Ionian Bimodal Oscillating System) hypothesis. The mechanism seems to be very well described by a non-linear oscillator dynamical system. By setting the state variables as the salinity of Adriatic deep water and the sea level anomaly in the Ionian region a Van der Pol equation has been obtained. The periodic cycle so obtained is of the order of a decade as observed in the data. Furthermore, a periodic term, which mimics the decadal variability of the forcing (mainly atmospheric), produces a period doubling phenomenon which is typical of the forced Van der Pol oscillator. By considering also a stochastic gaussian noise acting as a forcing and a decadal periodic input term, having an amplitude much smaller than the noise variance, a sub-harmonic stochastic resonance appears in the solution for a certain range of the values of the parameters. This yields the possibility of a longer time scale variability of the BiOS mechanism.