SUMMARYAn idealized case-study has been designed to investigate the modelling of the diurnal cycle of deep precipitating convection over land. A simulation of this case was performed by seven single-column models (SCMs) and three cloud-resolving models (CRMs). Within this framework, a quick onset of convective rainfall is found in most SCMs, consistent with the results from general-circulation models. In contrast, CRMs do not predict rainfall before noon. A joint analysis of the results provided by both types of model indicates that convection occurs too early in most SCMs, due to crude triggering criteria and quick onsets of convective precipitation. In the CRMs, the first clouds appear before noon, but surface rainfall is delayed by a few hours to several hours. This intermediate stage, missing in all SCMs except for one, is characterized by a gradual moistening of the free troposphere and an increase of cloud-top height. Later on, convective downdraughts efficiently cool and dry the boundary layer (BL) in the CRMs. This feature is also absent in most SCMs, which tend to adjust towards more unstable states, with moister (and often more cloudy) low levels and a drier free atmosphere. This common behaviour of most SCMs with respect to deep moist convective processes occurs even though each SCM simulates a different diurnal cycle of the BL and atmospheric stability. The scatter among the SCMs results from the wide variety of representations of BL turbulence and moist convection in these models. Greater consistency is found among the CRMs, despite some differences in their representation of the daytime BL growth, which are linked to their parametrizations of BL turbulence and/or resolution.

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: 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.

The entropy budget is calculated of the coupled atmosphere-ocean general circulation model HadCM3. Estimates of the different entropy sources and sinks of the climate system are obtained directly from the diabatic heating terms, and an approximate estimate of the planetary entropy production is also provided. The rate of material entropy production of the climate system is found to be *50 mW m -2 K -1 , a value intermediate in the range 30-70 mW m -2 K -1 previously reported from different models. The largest part of this is due to sensible and latent heat transport (*38 mW m -2 K -1 ). Another 13 mW m -2 K -1 is due to dissipation of kinetic energy in the atmosphere by friction and Reynolds stresses. Numerical entropy production in the atmosphere dynamical core is found to be about 0.7 mW m -2 K -1 . The material entropy production within the ocean due to turbulent mixing is *1 mW m -2 K -1 , a very small contribution to the material entropy production of the climate system. The rate of change of entropy of the model climate system is about 1 mW m -2 K -1 or less, which is comparable with the typical size of the fluctuations of the entropy sources due to interannual variability, and a more accurate closure of the budget than achieved by previous analyses. Results are similar for FAMOUS, which has a lower spatial resolution but similar formulation to HadCM3, while more substantial differences are found with respect to other models, suggesting that the formulation of the model has an important influence on the climate entropy budget. Since this is the first diagnosis of the entropy budget in a climate model of the type and complexity used for projection of twenty-first century climate change, it would be valuable if similar analyses were carried out for other such models.

In this paper, a theory for constructing quasi-neutral density variables γ directly in thermodynamic space is formulated, which is based on minimising the absolute value of a purely thermodynamic quantity J n. Physically, J n has a dual dynamic/thermodynamic interpretation as the quantity controlling the energy cost of adiabatic and isohaline parcel exchanges on material surfaces, as well as the dependence of in-situ density on spiciness, in a description of water masses based on γ, spiciness and pressure. Mathematically, minimising |J n | in thermodynamic space is showed to be equivalent to maximising neutrality in physical space. The physics of epineutral dispersion is also reviewed and discussed. It is argued, in particular, that epineutral dispersion is best understood as the aggregate effect of many individual non-neutral stirring events (being understood here as adiabatic and isohaline events with non-zero buoyancy), so that it is only the net displacement aggregated over many events that is approximately neutral. This new view resolves an apparent paradox between the focus in neutral density theory on zero-buoyancy motions and the overwhelming evidence that lateral dispersion in the ocean is primarily caused by non-zero buoyancy processes such as tides, residual currents and sheared internal waves. The efficiency by which a physical process contributes to lateral dispersion can be characterised by its energy signature, with those processes releasing available potential energy (negative energy cost) being more efficient than purely neutral processes with zero energy cost. The latter mechanism occurs in the wedge of instability, and its source of energy is the coupling between baroclinicity, thermobaricity, and density compensated temperature/salinity anomalies. Such a mechanism, which can only exist in a salty ocean, is speculated to be important for dissipating spiciness anomalies and neutral helicity. The paper also discusses potential conceptual difficulties with the use of neutral rotated diffusion tensors in numerical ocean models, as well as with the construction of neutral density variables in physical space. It also emphasises the irreducible character of thermobaric forces in the ocean. These are argued to be the cause for adiabatic thermobaric dianeutral dispersion, and to forbid the existence of density surfaces along which fluid parcels can be exchanged without experiencing buoyancy forces, in contrast to what is assumed in the theory of neutral surfaces.

The North Atlantic eddy-driven jet exhibits latitudinal variability with evidence of three preferred latitudinal locations: south, middle, and north. Here the authors examine the drivers of this variability and the variability of the associated storm track. The authors investigate the changes in the storm-track characteristics for the three jet locations and propose a mechanism by which enhanced storm-track activity, as measured by upstream heat flux, is responsible for cyclical downstream latitudinal shifts in the jet. This mechanism is based on a nonlinear oscillator relationship between the enhanced meridional temperature gradient (and thus baroclinicity) and the meridional high-frequency (periods of shorter than 10 days) eddy heat flux. Such oscillations in baroclinicity and heat flux induce variability in eddy anisotropy, which is associated with the changes in the dominant type of wave breaking and a different latitudinal deflection of the jet. The authors' results suggest that high heat flux is conducive to a northward deflection of the jet, whereas low heat flux is conducive to a more zonal jet. This jet-deflecting effect was found to operate most prominently downstream of the storm-track maximum, while the storm track and the jet remain anchored at a fixed latitudinal location at the beginning of the storm track. These cyclical changes in storm-track characteristics can be viewed as different stages of the storm track's spatiotemporal life cycle.