Abyssal recipes II: energetics of tidal and wind mixing

Without deep mixing, the ocean would turn, within a few thousand years, into a stagnant pool of cold salty water with equilibrium maintained locally by near-surface mixing and with very weak convectively driven surface-intensified circulation. (This result follows from Sandström’s theorem for a fluid heated and cooled at the surface.) In this context we revisit the 1966 “Abyssal Recipes”, which called for a diapycnal diffusivity of 10^-4m²/s (1 cgs) to maintain the abyssal stratification against global upwelling associated with 25 Sverdrups of deep water formation. Subsequent microstructure measurements gave a pelagic diffusivity (away from topography) of 10^-5 m²/s — a low value confirmed by dye release experiments.A new solution (without restriction to constant coefficients) leads to approximately the same values of global upwelling and diffusivity, but we reinterpret the computed diffusivity as a surrogate for a small number of concentrated sources of buoyancy flux (regions of intense mixing) from which the water masses (but not the turbulence) are exported into the ocean interior. Using the Levitus climatology we find that 2.1 TW (terawatts) are required to maintain the global abyssal density distribution against 30 Sverdrups of deep water formation.The winds and tides are the only possible source of mechanical energy to drive the interior mixing. Tidal dissipation is known from astronomy to equal 3.7 TW (2.50±0.05 TW from M₂ alone), but nearly all of this has traditionally been allocated to dissipation in the turbulent bottom boundary layers of marginal seas. However, two recent TOPEX/POSEIDON altimetric estimates combined with dynamical models suggest that 0.6–0.9 TW may be available for abyssal mixing. A recent estimate of wind-driving suggests 1 TW of additional mixing power. All values are very uncertain.A surprising conclusion is that the equator-to-pole heat flux of 2000 TW associated with the meridional overturning circulation would not exist without the comparatively minute mechanical mixing sources. Coupled with the findings that mixing occurs at a few dominant sites, there is a host of questions concerning the maintenance of the present climate state, but also that of paleoclimates and their relation to detailed continental configurations, the history of the Earth–Moon system, and a possible great sensitivity to details of the wind system.