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.

Influence of foliar diseases and their control by fungicides on grain yield and quality in wheat

Twenty-eight field experiments on sandy-loam soils in the UK (1982-2003) are reviewed by relating the extension of the green area duration of the flag leaf (GLADF) by fungicides to effects on yield and quality of winter wheat. Over all experiments mean grain yield = 8.85t ha(-1) at 85% DM. With regards quality, mean values were: thousand grain weight (TGW) = 44.5 g; specific weight (SWT) = 76.9 kg hl(-1); crude protein concentration (CP (N x 5.7)) = 12.5 % DM; Hagberg falling number (HFN) = 285 s; and sodium dodecyl sulphate (SDS)-sedimentation volume = 69ml. For each day (d) that fungicides increased GLADF there were associated average increases in yield (0.144 1 ha(-1) d(-1), se 0.0049, df = 333), TGW (0.56 gd(-1), se = 0.017) and SWT (0.22 kg hl(-1) d(-1), se 0.011). Some curvature was evident in all these relationships. When GLADF was delayed beyond 700 degrees Cd after anthesis, as was possible in cool wet seasons, responses were curtailed, or less reliable. Despite this apparent terminal sink limitation, fungicide effects on sink size, eg endosperm cell numbers or maximum water mass per grain, were not prerequisites for large effects on grain yield, TGW or SWT. Fungicide effects on CP were variable. Although the average response of CP was negative (-0.029%DM/d; se = 0.00338), this depended on cultivar and disease controlled. Controlling biotrophs such as rusts, (Puccinia spp.) tended to increase CP, whereas controlling a more necrotrophic pathogen (Septoria tritici) usually reducedCP. Irrespective of pathogen controlled, delaying senescence of the flag leaf was associated with increased nitrogen yields in the grain (averaging 2.24 kg N ha-1 d(-1), se = 0.0848) due to both increased N uptake into the above ground crop, and also more efficient remobilisation of N from leaf laminas. When sulphur availability appeared to be adequate, fungicide x cultivar interactions were similar on S as for CP, although N:S ratios tended to decline (i.e. improve for bread making) when S. tritici was controlled. On average, SDS-sedimentation volume declined (-0. 18 ml/d, se = 0.027) with increased GLADF, broadly commensurate with the average effect on CP. Hagberg falling number decreased as fungicide increased GLADF (-2.73 s/d, se = 0.178), indicating an increase in alpha-amylase activity.