The impact of a variable mixing efficiency on the abyssal overturning

In studies of ocean mixing, it is generally assumed that small-scale turbulent overturns lose 15-20 % of their energy in eroding the background stratification. Accumulating evidence that this energy fraction, or mixing efficiency Rf, significantly varies depending on flow properties challenges this assumption, however. Here, we examine the implications of a varying mixing efficiency for ocean energetics and deep water mass transformation. Combining current parameterizations of internal wave-driven mixing with a recent model expressing Rf as a function of a turbulence intensity parameter Reb = εν/νN2, we show that accounting for reduced mixing efficiencies in regions of weak stratification or energetic turbulence (high Reb) strongly limits the ability of breaking internal waves to supply oceanic potential energy and drive abyssal upwelling. Moving from a fixed Rf = 1/6 to a variable efficiency Rf(Reb) causes Antarctic Bottom Water upwelling induced by locally-dissipating internal tides and lee waves to fall from 9 to 4 Sv, and the corresponding potential energy source to plunge from 97 to 44 GW. When adding the contribution of remotely-dissipating internal tides under idealized distributions of energy dissipation, the total rate of Antarctic Bottom Water upwelling is reduced by about a factor of 2, reaching 5-15 Sv compared to 10-33 Sv for a fixed efficiency. Our results suggest that distributed mixing, overflow-related boundary processes and geothermal heating are more effective in consuming abyssal waters than topographically-enhanced mixing by breaking internal waves. Our calculations also point to the importance of accurately constraining Rf(Reb) and including the effect in ocean models.