ALBERT

Description: We study the flow of a thin liquid film along a flexible substrate. The flow is modelled using lubrication theory, assuming that gravity is the dominant driving force. The substrate is modelled as an elastic beam that deforms in two dimensions. Steady solutions are found using numerical and perturbation methods, and several different asymptotic regimes are identified. We obtain a complete characterization of how the length and stiffness of the beam and the imposed liquid flux determine the profile of the liquid film and the resulting beam deformation. © 2013 Cambridge University Press.

Description: The Mackenzie River is the seventh longest river in the world and with its tributaries drains a million sq. miles of northern Canada. Its drainage basin includes almost all of that portion of the District of Mackenzie lying south of the so-called “tree line”, two large sections of Yukon Territory and portions of the provinces of Saskatchewan, Alberta, and British Columbia. When flying from Fort Smith, lat. 60° N., to Inuvik near the Arctic Ocean it seems to be an endless expanse of swamp and tundra with almost no possibilities for logging, either now or in the future. Closer inspection, however, shows that there are forested areas capable of supplying timbers suitable for lumber and heavy construction, as well as poles for piling and mining timbers. It is with these forests that this article is primarily concerned.

Description: A boundary-layer model, based on computational results, describes a number of features of two-dimensional convection in a porous medium: the heat flux, velocity, length and temperature scales and the pattern of flow. The cell structure is different from that for convection in a viscous fluid. The model is valid for a limited range of the Rayleigh number. © 1976, Cambridge University Press. All rights reserved.

Description: The problem of the stability of a fluid with time-dependent heating has been investigated by Morton (1957), Lick (1965) and Foster (1965). Morton and Lick assumed that the rate of change of the temperature profile is small compared with the growth rate of the disturbances (quasi-static assumption). This assumption is invalid near the onset of instability (as defined by ∂/∂t = 0), and Foster has therefore used an initial-value approach.In this paper the range of validity of the quasi-static assumption is discussed, and results of a time-scaled analysis and calculations based on this are compared with the work of Foster; the agreement is found to be good. We restrict our attention to a semi-infinite fluid initially at a constant temperature; at time t = 0 a temperature difference ΔT is applied at the (lower) horizontal boundary (case (A) of Foster).

Description: In this paper we consider two-dimensional steady cellular motion in a fluid heated from below at large Rayleigh number and Prandtl number of order unity. This is a boundary-layer problem and has been considered by Weinbaum (1964) for the case of rigid boundaries and circular cross-section. Here we consider cells of rectangular cross-section with three sets of velocity boundary conditions: all boundaries free, rigid horizontal boundaries and free vertical boundaries (referred to here as periodic rigid boundary conditions), and all boundaries rigid; the vertical boundaries of the cells are insulated. It is shown that the geometry of the cell cross-section is important, such steady motion being not possible in the case of free boundaries and circular cross-section; also that the dependence of the variables of the problem on the Rayleigh number is determined by the balances in the vertical boundary layers.We assume only those boundary layers necessary to satisfy the boundary conditions and obtain a Nusselt number dependence $N sim R^{frac{1}{3}}$ for free vertical boundaries. For the periodic rigid case, Pillow (1952) has assumed that the buoyancy torque is balanced by the shear stress on the horizontal boundaries; this is equivalent to assuming velocity boundary layers beside the vertical boundaries (rather than the vorticity boundary layers demanded by the boundary conditions) and leads to a Nusselt number dependence N ∼ R¼. If it is assumed that the flow will adjust itself to give the maximum heat flux possible the two models are found to be appropriate for different ranges of the Rayleigh number and there is good agreement with experiment.An error in the application of Rayleigh's method in this paper is noted and the correct method for carrying the boundary-layer solutions round the corners is given. Estimates of the Nusselt numbers for the various boundary conditions are obtained, and these are compared with the computed results of Fromm (1965). The relevance of the present work to the theory of turbulent convection is discussed and it is suggested that neglect of the momentum convection term, as in the mean field equations, leads to a decrease in the heat flux at very high Rayleigh numbers. A physical argument is given to derive Gill's model for convection in a vertical slot from the Batchelor model, which is appropriate in the present work.

Description: In this paper we assume the existence of a nonlinear boundary layer centred on the critical point, and explore its effect on the development of unstable parallel shear flows. A velocity matching condition derived in a qualitative discussion suggests a growth of harmonics which differs from that predicted by previous theories; however, the prediction is in excellent agreement with experimental data. A hyperbolic-tangent velocity profile, subjected to perturbations with wavenumbers and frequencies close to marginal values, is then chosen as a mathematical model of the nonlinear development, both temporal and spatial instability growth being considered. A singularity in the analysis which has been treated in previous theories by the introduction of viscosity is dealt with in the present work by the introduction of a growth boundary layer. The asymptotics are non-uniform and the time-dependent solution does not resemble the steady viscous solutions, even as the growth rate tends to zero. The theory suggests that the instability will develop as a series of temporally growing spiral vortices, a description differing from that of a cat's-eye pattern predicted by existing theories, but in accord with experimental and field observations. © 1974, Cambridge University Press. All rights reserved.

Description: 1. Laboratory incubation studies with topsoil samples of the Kikuyu red loam coffee soil have shown that active nitrification of the natural soil nitrogen stops at a soil moisture level just below the permanent wilting percentage. Ammonification of natural nitrogen in this soil does not cease at this moisture level and ammonia nitrogen accumulates substantially, although the values found at the end of the 32-day incubation period, and the rate of ammonification are significantly lower as the moisture level is decreased from ⅚ to of the permanent wilting percentage.

Description: SUMMARYEwo milk yield data obtained by the lamb suckling technique from nutritional experiments were analysed statistically to obtain estimates of the several components of variation. Diurnal variation was studied. The fitting of a sinusoidal curve removed a significant amount of variation.There was a highly significant correlation between successive milk yields obtained at 4 h intervals. Number of lambs suckled and body weight of ewe at parturition had a significant effect on total daily milk yield.The variation within ewes after the removal of diurnal variation and between ewes after the removal of the effects of number of lambs suckled and body weight at parturition were computed. These sources of variation were combined in a general equation which enabled the prediction of the standard errors associated with daily milk production for a given sampling technique. The practical application of the predicted standard errors is discussed.

Description: SummaryThe effect of altering the level of protein intake on urea excretion in ewes was assessed in two separate experiments.In Expt 1, 14 pregnant (during the last 20 days of gestation) and 10 non-pregnant ewes were each offered a different level of digested N intake in the range 5–25 g/day. At all levels of protein intake urea N excretion was lower in pregnant than in nonpregnant ewes.In Expt 2, 21 pregnant ewe lambs were each offered one of three diets supplying mean intakes of 83 (T1), 113 (T2) or 147 (T3) g crude protein/day. During the last 100 days of gestation the mean levels of urea N excretion were 6·9, 11·0 and 15·2 g/day for T1, T 2 and T 3, respectively. The corresponding values for urinary N excretion were 9·3, 13·8 and 18·2 g/day. At all levels of protein intake urea N excretion was lower just prior to parturition than 95 days prepartum; the difference was correlated with lamb birth weight and maternal body-weight change.A notable feature of both experiments was the low level of urea N excretion by the pregnant ewes in late gestation, at low protein intakes. It would appear that when energy intake is adequate the decrease in urea N excretion associated with pregnancy is a direct result of an increased N requirement for maternal and/or foetal growth.

Description: SUMMARYSeventy-nine Finnish Landrace x Dorset Horn ewes in lamb to Suffolk rams were used in a comparative slaughter experiment to assess the effects of numbers of foetuses on the growth of the products of conception. The mean number of foetuses was 2·7, with a range from 1 to 5. The ewes were individually penned and given a standard diet with metabolizable energy concentration 7·7 MJ/kg and N concentration 21 g/kg, rationed at 2 kg/day during the first month and 1·25 kg/day during the second and third. Allowances beyond that time were on two scales and depended on the number of foetuses being carried as diagnosed by radiography. The ewes were slaughtered between 50 and 145 days of gestation. The gravid uterus was dissected into foetal, placental, foetal fluid and empty uterus components. Equations were fitted to the weights of each component to describe the effects of stage of gestation, litter size and ewe weight. For the mean weight per foetus (Y, kg) the preferred equation isIn (Y)= 2·419–17·574e-0.01976t–00079ft+0–0046w,where tis the time in days from conception, / is the number of foetuses and wis the weight (kg) of the ewe at mating. This is a version of the Gompertz equation, with additional terms to express the effects of / and w.The weights of the placenta and of the empty uterus were similarly fitted by versions of the Gompertz equation but the mean weight of fluids per foetus (Z, kg) or, rather, its natural logarithm was best described by a third degree polynomial, which isIn(Z) = –11·518 + 0–326t;–0·00316t2+0·0000102t3.None of the weights was significantly affected by the level of feeding in late pregnancy.Estimates of mean weights from the equations and of daily rates of gain in weight from the first differentials of the equations are tabulated against stage of gestation and litter size, and the forms of the weight, growth rate and specific growth-rate curves are illustrated graphically.The equation for foetal weight estimates that at the end of pregnancy the mean weight per foetus is reduced by a factor of 0–89 for each additional foetus being carried. The mathematical model implies that the differences originate in early pregnancy, when the factor is very close to unity, and that the mean weights gradually diverge. In the absence of direct evidence this would appear to be the simplest hypothesis, rather than the assumption in most of the earlier literature that the effect is entirely confined to the last 4 or 5 weeks of gestation.Just before parturition the total daily weight gain of quadruplet foetuses was about 250 g and was associated with a similar gain in weight of foetal fluids, the ratio of fluid weight to foetal weight appearing to increase with litter size. The ewes were clearly under considerable physical stress. It is suggested that this aspect must be closely considered when greater prolificacy is sought.