Threshold dependence in the flip-flop model

The flip-flop salt oscillator model¹ is a simplified dynamical model describing buoyancy-induced oscillations in the ocean. In this model, coupling to the atmosphere can increase the density of water at the surface to the point that it becomes denser than the water beneath, at which point vigorous vertical convection sets in and restores stable stratification. One parameter in this model quantifies the strength of the atmospheric forcing; the dependence of the amplitude and period of the oscillations in vertical mixing on this parameter has been well studied. However, in order for the model to produce oscillations at all, it must allow convective mixing to begin when the stratification is still slightly stable; a "threshold" parameter must be given to specify how close to unstable the stratification must be for convection to begin. The geophysical significance of this parameter is unclear, and typically it is set to some arbitrary small value. We show, however, that the amplitude and period of oscillations in the model depend strongly on this parameter, being proportional to its value and its square root, respectively. Thus numerical results from the flip-flop model need to be interpreted with care.

¹P. Welander, Dyn. Atmos. Oceans 6, 233 (1982).