ALBERT

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: 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: SUMMARYAn experiment was carried out in which each of thirty-six ewes was offered one of six dietary treatments from the 30th to the 140th day of gestation. The treatments supplied two levels of metabolizable energy (ME) intake (128 and 116 kcal/kg W0.75/day) each at three patterns of protein intake, namely equal increments at 22 day intervals, equal decrements at the same intervals and a constant daily intake throughout. The protein intake patterns supplied a mean daily intake of digestible crude protein of 3·74 g/kg W0.75/day. Nitrogen balances were carried out on four ewes from each dietary treatment during the last 10 days of each 22 day period.Thirteen ewes randomly distributed on all dietary treatments were barren. Mean rate of live-weight gain in the pregnant ewes was 123 g/day compared with 66 g/day in the non-pregnant ewes and was not significantly affected by treatments. Lamb birth weights adjusted to the basis of twins were 3·83, 4·02 and 3·56 kg for the increasing, constant and decreasing patterns of protein intake respectively.Within patterns of protein intake there were no significant differences in nitrogen retention between pregnant and non-pregnant ewes until after 90 days of gestation. Thereafter retention increased in the pregnant ewes offered the constant and increasing patterns of crude protein and remained constant in the non-pregnant ewes. During the same period the retention of both pregnant and non-pregnant ewes on the decreasing pattern decreased.The effects of both energy and protein intake on nitrogen retention in early and late pregnancy were assessed by multiple regression analysis. The results are discussed in relation to other recent findings.

Description: SUMMARYThirty-six Border Leicester x Scottish Blackface ewes were separated from their lambs after approximately 12 weeks lactation and brought indoors. They were allocated at random to nine dietary treatments comprising three dietary ratios of chopped roughage to concentrate, each offered at three levels of feeding. During the course of the experiment digestibility and nitrogen balance trials were carried out using three ewes from each dietary treatment.The daily nitrogen intakes required for nitrogen equilibrium were calculated from the regressions of nitrogen intake on nitrogen retained for each of the three ratios. The intakes increased from 0·47 g/kg W0·75 on the diet containing the lowest proportion of roughage to 0·59 g/kg W0·75 on the diet containing the highest proportion of roughage. The corresponding digestible organic matter intakes did not differ significantly from the pooled value of 18·8 g/kg W0·75.The daily digestible organic matter intakes required for the maintenance of live weight on the three ratios did not differ significantly from the pooled estimate of 26·9 g/kg W0·75 which is in close agreement with other published results. The nitrogen intakes required for the maintenance of live weight increased from 0·70 on the diet containing the lowest proportion of roughage to 0·84 g/kg W0·75/day on the diet containing the highest proportion of roughage.The coefficients for live-weight change in the regression equations relating digestible organic matter to live weight and live-weight change for each ratio did not differ significantly from the pooled estimate of 2·0 g DOMI/g live-weight change.The significance of the results are discussed in relation, to the nutritional status of the ewe and other research findings.

Description: SummaryTwelve non-pregnant and 20 pregnant North Country Cheviot ewes due to lamb in April 1969 were subjected to an 18 h daylength during the previous December. Thereafter daylength was reduced by 25 min per week. Eight ewes mated naturally in late May and early June and 22 of the remainder mated within 6 days after treatment with progesterone and gonadotrophin. Five of the photostimulated and 14 of the photostimulated plus hormone-treated ewes subsequently lambed in November 1969. The lambs were weaned at 28 days and 16 of the ewes were returned to fertile rams immediately after weaning. All 16 ewes were re-mated to naturally occurring oestrus during January-February 1970 and 13 proved pregnant.