  The variability of the strength of the Atlantic Meridional Overturning
Circulation is influenced substantially by the formation of deep water in the
North Atlantic. In many ocean models, so-called deep-decoupling oscillations
have been found, whose timescale depends on the characteristics of convective
vertical mixing processes. Their precise origin and sensitivity to the
representation of mixing have remained unclear so far. To study this problem,
we revisit a 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. The model is known to
exhibit several types of deep-decoupling oscillations, with phases of weak
diffusive mixing interspersed with strong convective mixing, when the switching
between them is assumed to be instantaneous. We present a comprehensive study
of oscillations in Welander's model with non-instantaneous switching between
mixing phases, as described by a smooth switching function. A dynamical systems
approach allows us to distinguish four types of oscillations, in terms of their
phases of diffusive versus convective mixing, and to identify the regions in
the relevant parameter plane where they exist. The characteristic
deep-decoupling oscillations still exist for non-instantaneous switching, but
they require switching that is considerably faster than needed for sustaining
oscillatory behaviour. Furthermore, we demonstrate how a gradual freshwater
influx can lead to transitions between different vertical mixing oscillations.
Notably, the convective mixing phase becomes shorter and even disappears,
resulting in long periods of much reduced deep water formation. The results are
relevant for the interpretation of ocean-climate variability in models and
(proxy) observations.
