Understanding mixing efficiency in the oceans. Do the nonlinearities of the equation of state matter?

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 Wr, turbulent of background gravitational potential energy GPEr. So far, these two quantities have often been regarded as the same energy conversion, namely the irreversible conversion of APE into GPEr, owing to the well known exact equality D(APE)=Wr, 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=Wr, turbulent/D(APE) being generally lower than unity and sometimes even negative for water or seawater, and argued that D(APE) and Wr, 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 IE0, and the conversion between GPEr and a different subcomponent of internal energy called "exergy" IEexergy. 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/(ρCp), where α is the thermal expansion coefficient, P the hydrostatic pressure, ρ the density, and Cp 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 Wr, turbulent depend critically on the sign and magnitude of dΥ/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.

Proceedings of the Ninth Annual Conference of the British Association for Biological Anthropology and Osteoarchaeology, Department of Archaeology, University of Reading

The Proceedings of the Ninth Annual Conference of the British Association for Biological Anthropology and Osteoarchaeology (BABAO) held at the University of Reading in 2007. Contents: 1) A life course perspective of growing up in medieval London: evidence of sub-adult health from St Mary Spital (London) (Rebecca Redfern and Don Walker); 2) Preservation of non-adult long bones from an almshouse cemetery in the United States dating to the late nineteenth to the early twentieth centuries (Colleen Milligan, Jessica Zotcavage and Norman Sullivan); 3) Childhood oral health: dental palaeopathology of Kellis 2, Dakhleh, Egypt. A preliminary investigation (Stephanie Shukrum and JE Molto); 4) Skeletal manifestation of non-adult scurvy from early medieval Northumbria: the Black Gate cemetery, Newcastle-upon-Tyne (Diana Mahoney-Swales and Pia Nystrom); 5) Infantile cortical hyperostosis: cases, causes and contradictions (Mary Lewis and Rebecca Gowland); 6) Biological Anthropology Tuberculosis of the hip in the Victorian Britain (Benjamin Clarke and Piers Mitchell); 7) The re-analysis of Iron Age human skeletal material from Winnall Down (Justine Tracey); 8) Can we estimate post-mortem interval from an individual body part? A field study using sus scrofa (Branka Franicevec and Robert Pastor); 9) The expression of asymmetry in hand bones from the medieval cemetery at Écija, Spain (Lisa Cashmore and Sonia Zakrezewski); 10) Returning remains: a curator’s view (Quinton Carroll); 11) Authority and decision making over British human remains: issues and challenges (Piotr Bienkowski and Malcolm Chapman); 12) Ethical dimensions of reburial, retention and repatriation of archaeological human remains: a British perspective (Simon Mays and Martin Smith); 13) The problem of provenace: inaccuracies, changes and misconceptions (Margaret Clegg); 14) Native American human remains in UK collections: implications of NAGPRA to consultation, repatriation, and policy development (Myra J Giesen); 15) Repatriation – a view from the receiving end: New Zealand (Nancy Tayles).