Understanding mixing efficiency in the oceans: Do the nonlinearities of the equation of state matter?
arXiv:0906.4190 · doi:10.5194/os-5-271-2009
Abstract
There exist two central measures of turbulent mixing in turbulent stratified fluids, 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 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 D(APE)=Wr,turbulent holding exactly for a Boussinesq fluid with a linear equation of state. It was recently pointed out, however, that this equality no longer holds for a thermally-stratified compressible fluid, the ratio ξ=Wr,turbulent/D(APE) being then lower than unity and sometimes even negative for water/seawater. In this paper, the behavior of the ratio ξis examined for different stratifications having the same buoyancy frequency N(z), but different vertical profiles of the parameter Υ= αP/(ρC_p), where αis the thermal expansion, P the hydrostatic pressure, ρthe density, and C_p the isobaric specific heat capacity, the equation of state considered being that for seawater for different particular constant values of salinity. It is found that ξand 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.
17 pages, 5 figures, 1 Table, accepted in Ocean Science (special issue on seawater) on July 10th 2009