Convective adjustment in box models

We find that a salt oscillator does not occur in the most common box-model configurations. In one of our models, however, we find wide parameter ranges in which all steady states calculated for the model fail to satisfy the CA scheme, the situation which is expected to result in CA-induced oscillations. The model in question corresponds to a hemispheric shallow thermohaline flow over a deep reservoir. However, we find that oscillations occur in these parameter ranges only if the density threshold for convection is negative, i.e., if the CA scheme turns on convection between vertically adjacent boxes when the density stratification between them is still slightly stable. In this situation, the amplitude and period of the oscillations depend strongly on the size of the density threshold, both vanishing as the threshold is taken toward zero. We also show that the same is true in the Welander flip-flop model of a single salt oscillator. For positive values of the threshold, that is, when the CA scheme is allowed to ignore small unstable stratification changes, oscillations do not occur in the limit of integration time step going to zero, but can still be seen when the time step is finite, even if small. Moreover, the system evolves toward a new steady state, one in which the stratification in one box is exactly the threshold value itself. We show how to calculate these new steady states, and explain why they give way to oscillations when the density threshold is negative.