English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This paper shows that the energetics of Boussinesq and anelastic fluidspossesses a term that can be identified as the approximation $\delta W_{ba}$ tothe compressible work of expansion/contraction $\delta W =-P {\rm d}\upsilon$,where $P$ is the pressure and $\upsilon$ is the specific volume. It followsthat Boussinesq and anelastic fluids admit explicit compressible effects andconversions between internal energy and mechanical energy, under the form ofapparent changes in gravitational potential energy resulting from changes indensity by diabatic and adiabatic effects. From the knowledge of $\deltaW_{ba}$, the corresponding approximation to the "heat" $\delta Q_{ba}$ can beconstructed in a consistent way by requiring that the Maxwell relationships besatisfied, ultimately leading to the construction of a well definedapproximation to the internal energy and ultimately of the full range of knownthermodynamic potentials. These properties make it possible to endow commonforms of the Boussinesq and anelastic approximations with fully consistentenergetics and thermodynamics, even when diabatic effects and an arbitrarynonlinear equation of state for a binary fluid are retained, without loss ofaccuracy. In that case, it can be shown that the sum of kinetic energy andenthalpy is a conservative quantity, which plays the role of the total energyin the Boussinesq and anelastic approximations for both diabatic and adiabaticmotions. This implies that gravitational potential energy can be regarded asthe difference between enthalpy and internal energy, and hence as a purethermodynamic property of the fluid.  The results have implications for our understanding of turbulent mixing instratified fluids, as well as for correcting the energetics of currentnumerical ocean general circulation models, which are discussed.

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