Thermodynamics/dynamics coupling and thermodynamic consistency of Boussinesq and anelastic binary fluids with an arbitrary nonlinear equation of state

摘要: This paper shows that the energetics of Boussinesq and anelastic fluids possesses a term can be identified as approximation $\delta W_{ba}$ to compressible work expansion/contraction W =-P {\rm d}\upsilon$, where $P$ is pressure $\upsilon$ specific volume. It follows admit explicit effects conversions between internal energy mechanical energy, under form apparent changes in gravitational potential resulting from density by diabatic adiabatic effects. From knowledge W_{ba}$, corresponding "heat" Q_{ba}$ constructed consistent way requiring Maxwell relationships satisfied, ultimately leading construction well defined full range known thermodynamic potentials. These properties make it possible endow common forms approximations with fully thermodynamics, even when an arbitrary nonlinear equation state for binary fluid are retained, without loss accuracy. In case, shown sum kinetic enthalpy conservative quantity, which plays role total both motions. implies regarded difference hence pure property fluid. The results have implications our understanding turbulent mixing stratified fluids, correcting current numerical ocean general circulation models, discussed.