摘要：There exist two central measures of turbulent mixing in turbulent stratified fluids that are both caused by molecular diffusion: 1) the dissipation rate D (APE) of available potential energy APE; 2) the turbulent rate of change W r , turbulent of background gravitational potential energy GPE r . So far, these two quantities have often been regarded as the same energy conversion, namely the irreversible conversion of APE into GPE r , owing to the well known exact equality D (APE)= W r , turbulent for a Boussinesq fluid with a linear equation of state. Recently, however, Tailleux (2009) pointed out that the above equality no longer holds for a thermally-stratified compressible, with the ratio ξ= W r , turbulent / D (APE) being generally lower than unity and sometimes even negative for water or seawater, and argued that D (APE) and W r , turbulent actually represent two distinct types of energy conversion, respectively the dissipation of APE into one particular subcomponent of internal energy called the "dead" internal energy IE 0 , and the conversion between GPE r and a different subcomponent of internal energy called "exergy" IE exergy . In this paper, the behaviour of the ratio ξ is examined for different stratifications having all the same buoyancy frequency N vertical profile, but different vertical profiles of the parameter Υ=α P /(ρ C p ), where α is the thermal expansion coefficient, P the hydrostatic pressure, ρ the density, and C p the specific heat capacity at constant pressure, the equation of state being that for seawater for different particular constant values of salinity. It is found that ξ and W r , turbulent depend critically on the sign and magnitude of d Υ/ 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 in practice, which are discussed.
