  The background potential energy (BPE) is the only reservoir that double
diffusive instabilities can tap their energy from when developing from an
unforced motionless state with no available potential energy (APE). Recently,
Middleton and Taylor linked the extraction of BPE into APE to the sign of the
diapycnal component of the buoyancy flux, but their criterion can only predict
diffusive convection instability, not salt finger instability. Here, we show
that the problem can be corrected if the sign of the APE dissipation rate is
used instead, making it emerge as the most fundamental criterion for double
diffusive instabilities. A theory for the APE dissipation rate for a
two-component fluid relative to its single-component counterpart is developed
as a function of three parameters: the diffusivity ratio, the density ratio,
and a spiciness parameter. The theory correctly predicts the occurrence of both
salt finger and diffusive convection instabilities in the laminar unforced
regime, while more generally predicting that the APE dissipation rate for a
two-component fluid can be enhanced, suppressed, or even have the opposite sign
compared to that for a single-component fluid, with important implications for
the study of ocean mixing. Because negative APE dissipation can also occur in
stably stratified single-component and doubly stable two-component stratified
fluids, we speculate that only the thermodynamic theory of exergy can explain
its physics; however, this necessitates accepting that APE dissipation is a
conversion between APE and the internal energy component of BPE, in contrast to
prevailing assumptions.
