On the energetics of stratified turbulent mixing, irreversible thermodynamics, Boussinesq models and the ocean heat engine controversy

In this paper, the available potential energy (APE) framework of Winters et al. (J. Fluid Mech., vol. 289, 1995, p. 115) is extended to the fully compressible Navier– Stokes equations, with the aims of clarifying (i) the nature of the energy conversions taking place in turbulent thermally stratified fluids; and (ii) the role of surface buoyancy fluxes in the Munk & Wunsch (Deep-Sea Res., vol. 45, 1998, p. 1977) constraint on the mechanical energy sources of stirring required to maintain diapycnal mixing in the oceans. The new framework reveals that the observed turbulent rate of increase in the background gravitational potential energy GPEr , commonly thought to occur at the expense of the diffusively dissipated APE, actually occurs at the expense of internal energy, as in the laminar case. The APE dissipated by molecular diffusion, on the other hand, is found to be converted into internal energy (IE), similar to the viscously dissipated kinetic energy KE. Turbulent stirring, therefore, does not introduce a new APE/GPEr mechanical-to-mechanical energy conversion, but simply enhances the existing IE/GPEr conversion rate, in addition to enhancing the viscous dissipation and the entropy production rates. This, in turn, implies that molecular diffusion contributes to the dissipation of the available mechanical energy ME =APE +KE, along with viscous dissipation. This result has important implications for the interpretation of the concepts of mixing efficiency γmixing and flux Richardson number Rf , for which new physically based definitions are proposed and contrasted with previous definitions. The new framework allows for a more rigorous and general re-derivation from the first principles of Munk & Wunsch (1998, hereafter MW98)’s constraint, also valid for a non-Boussinesq ocean: G(KE) ≈ 1 − ξ Rf ξ Rf Wr, forcing = 1 + (1 − ξ )γmixing ξ γmixing Wr, forcing , where G(KE) is the work rate done by the mechanical forcing, Wr, forcing is the rate of loss of GPEr due to high-latitude cooling and ξ is a nonlinearity parameter such that ξ =1 for a linear equation of state (as considered by MW98), but ξ <1 otherwise. The most important result is that G(APE), the work rate done by the surface buoyancy fluxes, must be numerically as large as Wr, forcing and, therefore, as important as the mechanical forcing in stirring and driving the oceans. As a consequence, the overall mixing efficiency of the oceans is likely to be larger than the value γmixing =0.2 presently used, thereby possibly eliminating the apparent shortfall in mechanical stirring energy that results from using γmixing =0.2 in the above formula.

Evaluating the efficacy of planktonic foraminifer calcite and 18O data for sea surface temperature reconstruction for the Late Miocene

This study examines the efficacy of published δ18O data from the calcite of Late Miocene surface dwelling planktonic foraminifer shells, for sea surface temperature estimates for the pre-Quaternary. The data are from 33 Late Miocene (Messinian) marine sites from a modern latitudinal gradient of 64°N to 48°S. They give estimates of SSTs in the tropics/subtropics (to 30°N and S) that are mostly cooler than present. Possible causes of this temperature discrepancy are ecological factors (e.g. calcification of shells at levels below the ocean mixed layer), taphonomic effects (e.g. diagenesis or dissolution), inaccurate estimation of Late Miocene seawater oxygen isotope composition, or a real Late Miocene cool climate. The scale of apparent cooling in the tropics suggests that the SST signal of the foraminifer calcite has been reset, at least in part, by early diagenetic calcite with higher δ18O, formed in the foraminifer shells in cool sea bottom pore waters, probably coupled with the effects of calcite formed below the mixed layer during the life of the foraminifera. This hypothesis is supported by the markedly cooler SST estimates from low latitudes—in some cases more than 9 °C cooler than present—where the gradients of temperature and the δ18O composition of seawater between sea surface and sea bottom are most marked, and where ocean surface stratification is high. At higher latitudes, particularly N and S of 30°, the temperature signal is still cooler, though maximum temperature estimates overlap with modern SSTs N and S of 40°. Comparison of SST estimates for the Late Miocene from alkenone unsaturation analysis from the eastern tropical Atlantic at Ocean Drilling Program (ODP) Site 958—which suggest a warmer sea surface by 2–4 °C, with estimates from oxygen isotopes at Deep Sea Drilling Project (DSDP) Site 366 and ODP Site 959, indicating cooler than present SSTs, also suggest a significant impact on the δ18O signal. Nevertheless, much of the original SST variation is clearly preserved in the primary calcite formed in the mixed layer, and records secular and temporal oceanographic changes at the sea surface, such as movement of the Antarctic Polar Front in the Southern Ocean. Cooler SSTs in the tropics and sub-tropics are also consistent with the Late Miocene latitude reduction in the coral reef belt and with interrupted reef growth on the Queensland Plateau of eastern Australia, though it is not possible to quantify absolute SSTs with the existing oxygen isotope data. Reconstruction of an accurate global SST dataset for Neogene time-slices from the existing published DSDP/ODP isotope data, for use in general circulation models, may require a detailed re-assessment of taphonomy at many sites.

Evaluating the efficacy of planktonic foraminifer calcite and 18O data for sea surface temperature reconstruction for the Late Miocene

This study examines the efficacy of published δ18O data from the calcite of Late Miocene surface dwelling planktonic foraminifer shells, for sea surface temperature estimates for the pre-Quaternary. The data are from 33 Late Miocene (Messinian) marine sites from a modern latitudinal gradient of 64°N to 48°S. They give estimates of SSTs in the tropics/subtropics (to 30°N and S) that are mostly cooler than present. Possible causes of this temperature discrepancy are ecological factors (e.g. calcification of shells at levels below the ocean mixed layer), taphonomic effects (e.g. diagenesis or dissolution), inaccurate estimation of Late Miocene seawater oxygen isotope composition, or a real Late Miocene cool climate. The scale of apparent cooling in the tropics suggests that the SST signal of the foraminifer calcite has been reset, at least in part, by early diagenetic calcite with higher δ18O, formed in the foraminifer shells in cool sea bottom pore waters, probably coupled with the effects of calcite formed below the mixed layer during the life of the foraminifera. This hypothesis is supported by the markedly cooler SST estimates from low latitudes—in some cases more than 9 °C cooler than present—where the gradients of temperature and the δ18O composition of seawater between sea surface and sea bottom are most marked, and where ocean surface stratification is high. At higher latitudes, particularly N and S of 30°, the temperature signal is still cooler, though maximum temperature estimates overlap with modern SSTs N and S of 40°. Comparison of SST estimates for the Late Miocene from alkenone unsaturation analysis from the eastern tropical Atlantic at Ocean Drilling Program (ODP) Site 958—which suggest a warmer sea surface by 2–4 °C, with estimates from oxygen isotopes at Deep Sea Drilling Project (DSDP) Site 366 and ODP Site 959, indicating cooler than present SSTs, also suggest a significant impact on the δ18O signal. Nevertheless, much of the original SST variation is clearly preserved in the primary calcite formed in the mixed layer, and records secular and temporal oceanographic changes at the sea surface, such as movement of the Antarctic Polar Front in the Southern Ocean. Cooler SSTs in the tropics and sub-tropics are also consistent with the Late Miocene latitude reduction in the coral reef belt and with interrupted reef growth on the Queensland Plateau of eastern Australia, though it is not possible to quantify absolute SSTs with the existing oxygen isotope data. Reconstruction of an accurate global SST dataset for Neogene time-slices from the existing published DSDP/ODP isotope data, for use in general circulation models, may require a detailed re-assessment of taphonomy at many sites.