  There exist two central measures of turbulent mixing in turbulent stratified
fluids, both caused by molecular diffusion: 1) the dissipation rate D(APE) of
available potential energy (APE); 2) the turbulent rate of change Wr,turbulent
of background potential energy GPEr. So far, these two quantities have often
been regarded as the same energy conversion, namely the irreversible conversion
of APE into GPEr, owing to D(APE)=Wr,turbulent holding exactly for a Boussinesq
fluid with a linear equation of state. It was recently pointed out, however,
that this equality no longer holds for a thermally-stratified compressible
fluid, the ratio \xi=Wr,turbulent/D(APE) being then lower than unity and
sometimes even negative for water/seawater. In this paper, the behavior of the
ratio \xi is examined for different stratifications having the same buoyancy
frequency N(z), but different vertical profiles of the parameter \Upsilon =
\alpha P/(\rho C_p), where \alpha is the thermal expansion, P the hydrostatic
pressure, \rho the density, and C_p the isobaric specific heat capacity, the
equation of state considered being that for seawater for different particular
constant values of salinity. It is found that \xi and Wr,turbulent depend
critically on the sign and magnitude of d\Upsilon/dz, in contrast with D(APE),
which appears largely unaffected by the latter. These results have important
consequences for how the mixing efficiency should be defined and measured.
