  A key issue in stratified turbulence theory concerns the nature of the link
between D(APE), the dissipation rate of available potential energy APE, and
W_{r,turbulent}, the turbulent rate of change of background gravitational
potential energy GPE_r, which are both controlled by molecular diffusion. For
Boussinesq fluids with a linear equation of state, this link is simply
W_{r,turbulent}=D(APE), widely interpreted as implying that GPE_r increases at
the expense of APE, in contrast with the laminar case where GPE_r increases at
the expense of internal energy (IE). This idea is revisited here by regarding
IE as the sum of three distinct subcomponents: available internal energy (AIE),
exergy (IE_{exergy}), and dead internal energy (IE_0). In this new view, D(APE)
is the dissipation rate of APE into IE_0, while both W_{r,laminar} and
W_{r,turbulent} convert IE_{exergy} into GPE_r. The equality
W_{r,turbulent}=D(APE) thus states that IE_{exergy} is converted into GPE_r at
the same rate as APE is dissipated into IE_0. For non-Boussinesq fluids, the
equality D(APE)=W_{r,turbulent} is at best a good approximation, for
W_{r,turbulent} is generally smaller than D(APE), and sometimes even negative
for a strongly nonlinear equation of state. In a second step, the link between
stirring and mixing is examined for a wind-and buoyancy-driven thermally
stratified ocean to determine whether these constrain the mechanical sources of
stirring, as recently advocated. It is established that the coupling between
stirring and mixing cannot refute the traditional buoyancy-driven view of the
so-called meridional overturning circulation, in contrast to recent claims. In
fact, the buoyancy forcing appears to be as important as the mechanical forcing
in stirring and driving the large-scale ocean circulation.
