Sack Lunch Seminar (SLS)

The evolution equation of potential temperature has to date been treated as an approximation to the oceanic version of the First Law of Thermodynamics. That is, we oceanographers have regarded the advection and diffusion of potential temperature as the advection and diffusion of "heat''. However the non-conservative source terms that arise in the evolution equation for potential temperature are estimated to be two orders of magnitude larger than the corresponding source terms for Conservative Temperature. In this talk the non-conservative source terms of potential temperature, Conservative Temperature and entropy for a stratified turbulent fluid are introduced, then quantified using the output of a coarse resolution ocean model, and compared to the rate of dissipation of mechanical energy, epsilon. It is shown that the error incurred in ocean models by assuming that Conservative Temperature is 100% conservative is approximately 120 times smaller than the corresponding error for potential temperature and at least 1200 times smaller than the corresponding error for entropy. Furthermore, the error in assuming that Conservative Temperature is 100% conservative is approximately 6 times smaller than the error in ignoring epsilon. Hence Conservative Temperature can be quite accurately regarded as a conservative variable and can be treated as being proportional to the ''heat content'' per unit mass of seawater, and therefore should now be used in place of potential temperature in physical oceanography, including as the prognostic temperature variable in ocean models.