The impact of variability in mixing efficiency on the abyssal overturning

de Lavergne, C. and Madec, G. and Sommer, J. Le and Nurser, A. J. G. and Naveira Garabato, A. C.

abstract: In studies of ocean mixing, it is generally assumed that small-scale turbulent overturns lose 15% of their energy in eroding the background stratification. Accumulating evidence that this energy fraction, or mixing efficiency R_f, significantly varies depending on flow properties challenges this assumption, however. Here, the authors 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 R_f as a function of a turbulence intensity parameter Re_b = \epsilon_ν/ νN^2, the ratio of dissipation \epsilon_νto stratification N^2 and molecular viscosity ν, it is shown that accounting for reduced mixing efficiencies in regions of weak stratification or energetic turbulence (high Re_b) strongly limits the ability of breaking internal waves to supply oceanic potential energy and drive abyssal upwelling. Moving from a fixed R_f = 1/6 to a variable efficiency R_f(Re_b) causes Antarctic Bottom Water upwelling induced by locally dissipating internal tides and lee waves to fall from 9 to 4 Sverdrups (Sv; 1 Sv ≡10^6 \mboxm^3\mbox s^-1) 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. The 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. These calculations also point to the importance of accurately constraining R_f(Re_b) and including the effect in ocean models.

  author = {de~Lavergne, C. and Madec, G. and Sommer, J. Le and Nurser, A. J. G. and Naveira~Garabato, A. C.},
  title = {The impact of variability in mixing efficiency on the abyssal overturning},
  journal = {J. Phys. Ocean.},
  year = {2016},
  pages = {663--681},
  volume = {46},
  issue = {2},
  doi = {10.1175/JPO-D-14-0259.1},
  url = {}