A detailed analysis of deep-decoupling/deep-coupling oscillations in the Welander model

We revisit the conceptual Welander model for the evolution of temperature and salinity in two vertically stacked boxes for surface and deep water, which interact through diffusion and/or convective adjustment. When the switching between them is assumed to be instantaneous, the model exhibits oscillations with phases of weak diffusive mixing (deep-decoupling) interspersed with strong convective mixing (deep-coupling). We present a comprehensive study of oscillations in the Welander model with a smooth, non-instantaneous switching function, where we distinguish four types in terms of their phases of diffusive vs convective mixing and show where they exist in parameter space. The characteristic Welander deep-(de)coupling oscillations still exist, but they require switching that is considerably faster than needed for sustaining oscillatory behavior. We also demonstrate how a gradual freshwater influx can lead to transitions between different types of oscillations.