Nonlinear saturation of baroclinic instability: part II: continuously stratified fluid

Rigorous upper bounds are derived that limit the finite-amplitude growth of arbitrary nonzonal disturbances to an unstable baroclinic zonal flow in a continuously stratified, quasi-geostrophic, semi-infinite fluid. Bounds are obtained bath on the depth-integrated eddy potential enstrophy and on the eddy available potential energy (APE) at the ground. The method used to derive the bounds is essentially analogous to that used in Part I of this study for the two-layer model: it relies on the existence of a nonlinear Liapunov (normed) stability theorem, which is a finite-amplitude generalization of the Charney-Stern theorem. As in Part I, the bounds are valid both for conservative (unforced, inviscid) flow, as well as for forced-dissipative flow when the dissipation is proportional to the potential vorticity in the interior, and to the potential temperature at the ground. The character of the results depends on the dimensionless external parameter γ = f02ξ/β0N2H, where ξ is the maximum vertical shear of the zonal wind, H is the density scale height, and the other symbols have their usual meaning. When γ ≫ 1, corresponding to “deep” unstable modes (vertical scale ≈H), the bound on the eddy potential enstrophy is just the total potential enstrophy in the system; but when γ≪1, corresponding to ‘shallow’ unstable modes (vertical scale ≈γH), the eddy potential enstrophy can be bounded well below the total amount available in the system. In neither case can the bound on the eddy APE prevent a complete neutralization of the surface temperature gradient which is in accord with numerical experience. For the special case of the Charney model of baroclinic instability, and in the limit of infinitesimal initial eddy disturbance amplitude, the bound states that the dimensionless eddy potential enstrophy cannot exceed (γ + 1)2/24&gamma2h when γ ≥ 1, or 1/6;&gammah when γ ≤ 1; here h = HN/f0L is the dimensionless scale height and L is the width of the channel. These bounds are very similar to (though of course generally larger than) ad hoc estimates based on baroclinic-adjustment arguments. The possibility of using these kinds of bounds for eddy-amplitude closure in a transient-eddy parameterization scheme is also discussed.

Deep Convective System Evolution over Africa and the Tropical Atlantic

In the tropical African and neighboring Atlantic region there is a strong contrast in the properties of deep convection between land and ocean. Here, satellite radar observations are used to produce a composite picture of the life cycle of convection in these two regions. Estimates of the broadband thermal flux from the geostationary Meteosat-8 satellite are used to identify and track organized convective systems over their life cycle. The evolution of the system size and vertical extent are used to define five life cycle stages (warm and cold developing, mature, cold and warm dissipating), providing the basis for the composite analysis of the system evolution. The tracked systems are matched to overpasses of the Tropical Rainfall Measuring Mission satellite, and a composite picture of the evolution of various radar and lightning characteristics is built up. The results suggest a fundamental difference in the convective life cycle between land and ocean. African storms evolve from convectively active systems with frequent lightning in their developing stages to more stratiform conditions as they dissipate. Over the Atlantic, the convective fraction remains essentially constant into the dissipating stages, and lightning occurrence peaks late in the life cycle. This behavior is consistent with differences in convective sustainability in land and ocean regions as proposed in previous studies. The area expansion rate during the developing stages of convection is used to provide an estimate of the intensity of convection. Reasonable correlations are found between this index and the convective system lifetime, size, and depth.

A stochastic parameterization for deep convection based on equilibrium statistics

A stochastic parameterization scheme for deep convection is described, suitable for use in both climate and NWP models. Theoretical arguments and the results of cloud-resolving models, are discussed in order to motivate the form of the scheme. In the deterministic limit, it tends to a spectrum of entraining/detraining plumes and is similar to other current parameterizations. The stochastic variability describes the local fluctuations about a large-scale equilibrium state. Plumes are drawn at random from a probability distribution function (pdf) that defines the chance of finding a plume of given cloud-base mass flux within each model grid box. The normalization of the pdf is given by the ensemble-mean mass flux, and this is computed with a CAPE closure method. The characteristics of each plume produced are determined using an adaptation of the plume model from the Kain-Fritsch parameterization. Initial tests in the single column version of the Unified Model verify that the scheme is effective in producing the desired distributions of convective variability without adversely affecting the mean state.

Variation in dynamic elastic shear modulus of sandstone upon fluid saturation and substitution

Experimental acoustic measurements on sandstone rocks at both sonic and ultrasonic frequencies show that fluid saturation can cause a noticeable change in both the dynamic bulk and shear elastic moduli of sandstones. We observed that the change in dynamic shear modulus upon fluid saturation is highly dependent on the type of saturant, its viscosity, rock microstructure, and applied pressures. Frequency dispersion has some influence on dynamic elastic moduli too, but its effect is limited to the ultrasonic frequency ranges and above. We propose that viscous coupling, reduction in free surface energy, and, to a limited extent, frequency dispersion due to both local and global flow are the main mechanisms responsible for the change in dynamic shear elastic modulus upon fluid saturation and substitution, and we quantify influences.

Consistent approximate models of the global atmosphere: shallow, deep, hydrostatic, quasi-hydrostatic and non-hydrostatic

We study global atmosphere models that are at least as accurate as the hydrostatic primitive equations (HPEs), reviewing known results and reporting some new ones. The HPEs make spherical geopotential and shallow atmosphere approximations in addition to the hydrostatic approximation. As is well known, a consistent application of the shallow atmosphere approximation requires omission of those Coriolis terms that vary as the cosine of latitude and of certain other terms in the components of the momentum equation. An approximate model is here regarded as consistent if it formally preserves conservation principles for axial angular momentum, energy and potential vorticity, and (following R. Müller) if its momentum component equations have Lagrange's form. Within these criteria, four consistent approximate global models, including the HPEs themselves, are identified in a height-coordinate framework. The four models, each of which includes the spherical geopotential approximation, correspond to whether the shallow atmosphere and hydrostatic (or quasi-hydrostatic) approximations are individually made or not made. Restrictions on representing the spatial variation of apparent gravity occur. Solution methods and the situation in a pressure-coordinate framework are discussed. © Crown copyright 2005.

Feeding rumen-inert fats differing in their degree of saturation decreases intake and increases plasma concentrations of gut peptides in lactating dairy cows

Our objective was to determine the effect of feeding rumen-inert fats differing in their degree of saturation on dry matter intake (DMI), milk production, and plasma concentrations of insulin, glucagon-like peptide 1 (7-36) amide (GLP-1), glucose-dependent insulinotropic polypeptide (GIP), and cholecystokinin (CCK) in lactating dairy cows. Four midlactation, primiparous Holstein cows were used in a 4 x 4 Latin square experiment with 2-wk periods. Cows were fed a control mixed ration ad libitum, and treatments were the dietary addition (3.5% of ration dry matter) of 3 rumen-inert fats as sources of mostly saturated fatty acids (SFA), monounsaturated fatty acids (MUFA), or polyunsaturated fatty acids (PUFA). Daily DMI, milk yield, and composition were measured on the last 4 d of each period. Jugular vein blood was collected every 30 min over a 7-h period on d 12 and 14 of each period for analysis of plasma concentrations of hormones, glucose, and nonesterified fatty acids. Feeding fat decreased DMI, and the decrease tended to be greater for MUFA and PUFA compared with SFA. Plasma concentration of GLP-1 increased when fat was fed and was greater for MUFA and PUFA. Feeding fat increased plasma glucose-dependent insulinotropic polypeptide and CCK concentrations and decreased plasma insulin concentration. Plasma CCK concentration was greater for MUFA and PUFA than for SFA and was greater for MUFA than PUFA. Decreases in DMI in cows fed fat were associated with increased plasma concentrations of GLP-1 and CCK and a decreased insulin concentration. The role of these peptides in regulating DMI in cattle fed fat requires further investigation.

Structure oil-absorption relationships during deep-fat frying

Analysis of the oil-absorption process in deep-fat fried potato cylinders (frying temperatures of 155degreesC, 170degreesC, and 185degreesC) allowed to distinguish 3 oil fractions: structural oil (absorbed during frying), penetrated surface oil (suctioned during cooling), and surface oil. Results showed that a small amount of oil penetrates during frying because most of the oil was picked up at the end of the process, suggesting that oil uptake and water removal are not synchronous phenomena. After cooling, oil was located either on the surface of the chip or suctioned into the porous crust microstructure, with an inverse relationship between them for increasing frying times.

Search space pruning and global optimization of multiple gravity assist trajectories with deep space manoeuvres

This paper deals with the design of optimal multiple gravity assist trajectories with deep space manoeuvres. A pruning method which considers the sequential nature of the problem is presented. The method locates feasible vectors using local optimization and applies a clustering algorithm to find reduced bounding boxes which can be used in a subsequent optimization step. Since multiple local minima remain within the pruned search space, the use of a global optimization method, such as Differential Evolution, is suggested for finding solutions which are likely to be close to the global optimum. Two case studies are presented.