Negative available potential energy dissipation as the fundamental criterion for double diffusive instabilities

Tailleux, R. ORCID: https://orcid.org/0000-0001-8998-9107 (2024) Negative available potential energy dissipation as the fundamental criterion for double diffusive instabilities. Journal Of Fluid Mechanics, 994. A5. ISSN 1469-7645 doi: 10.1017/jfm.2024.647

Abstract/Summary

The background potential energy (BPE) is the only reservoir that double diffusive instabilities can tap their energy from when developing from an unforced motionless state with no available potential energy (APE). Recently, Middleton and Taylor linked the extraction of BPE into APE to the sign of the diapycnal component of the buoyancy flux, but their criterion can only predict diffusive convection instability, not salt finger instability. Here, we show that the problem can be corrected if the sign of the APE dissipation rate is used instead, making it emerge as the most fundamental criterion for double diffusive instabilities. A theory for the APE dissipation rate for a two-component fluid relative to its single-component counterpart is developed as a function of three parameters: the diffusivity ratio, the density ratio, and a spiciness parameter. The theory correctly predicts the occurrence of both salt finger and diffusive convection instabilities in the laminar unforced regime, while more generally predicting that the APE dissipation rate for a two-component fluid can be enhanced, suppressed, or even have the opposite sign compared to that for a single-component fluid, with important implications for the study of ocean mixing. Because negative APE dissipation can also occur in stably stratified single-component and doubly stable two-component stratified fluids, we speculate that only the thermodynamic theory of exergy can explain its physics; however, this necessitates accepting that APE dissipation is a conversion between APE and the internal energy component of BPE, in contrast to prevailing assumptions.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/116978
Item Type	Article
Refereed	Yes
Divisions	Interdisciplinary Research Centres (IDRCs) > Walker Institute Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
Uncontrolled Keywords	negative dissipation, mixing, double-diffusion, salt fingers, diffusive convection, thermohaline staircases, available potential energy
Publisher	Cambridge University Press
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