Irreversible compressible work and APE dissipation in turbulent stratified fluid
Tailleux, R. (2013) Irreversible compressible work and APE dissipation in turbulent stratified fluid. Physica Scripta, T155. 014033. ISSN 1402-4896
To link to this article DOI: 10.1088/0031-8949/2013/T155/014033
Although it plays a key role in the theory of stratiﬁed turbulence, the concept of available potential energy (APE) dissipation has remained until now a rather mysterious quantity, owing to the lack of rigorous result about its irreversible character or energy conversion type. Here, we show by using rigorous energetics considerations rooted in the analysis of the Navier-Stokes for a fully compressible ﬂuid with a nonlinear equation of state that the APE dissipation is an irreversible energy conversion that dissipates kinetic energy into internal energy, exactly as viscous dissipation. These results are established by showing that APE dissipation contributes to the irreversible production of entropy, and by showing that it is a part of the work of expansion/contraction. Our results provide a new interpretation of the entropy budget, that leads to a new exact deﬁnition of turbulent eﬀective diﬀusivity, which generalizes the Osborn-Cox model, as well as a rigorous decomposition of the work of expansion/contraction into reversible and irreversible components. In the context of turbulent mixing associated with parallel shear ﬂow instability, our results suggests that there is no irreversible transfer of horizontal momentum into vertical momentum, as seems to be required when compressible eﬀects are neglected, with potential consequences for the parameterisations of momentum dissipation in the coarse-grained Navier-Stokes equations.