ALBERT

Description: We have performed numerical calculations of fluid mixing driven by Rayleigh-Taylor instability for density profiles based on the stratified density experiments of Lawrie & Dalziel (J. Fluid Mech., vol. 688, 2011, pp. 507-527) and Davies Wykes & Dalziel (J. Fluid Mech., vol. 756, 2014, pp. 1027-1057). We find that the late-time mixing profiles are similar to their experimental results for similar initial conditions; we consider a range of additional initial conditions to investigate the robustness of the results. A model for the late-time structure of the mixing layer, based on the maximization of configurational entropy, is compared with the results of the numerical calculations, and shows good agreement. © British Crown Owned Copyright 2016/AWE.

Description: Both experiments and numerical simulations pertinent to the study of self-similarity in shock-induced turbulent mixing often do not cover sufficiently long times for the mixing layer to become developed in a fully turbulent manner. When the Mach number of the flow is sufficiently low, numerical simulations based on the compressible flow equations tend to become less accurate due to inherent numerical cancellation errors. This paper concerns a numerical study of the late-time behaviour of a single-shocked Richtmyer-Meshkov instability (RMI) and the associated compressible turbulent mixing using a new technique that addresses the above limitation. The present approach exploits the fact that the RMI is a compressible flow during the early stages of the simulation and incompressible at late times. Therefore, depending on the compressibility of the flow field, the most suitable model, compressible or incompressible, can be employed. This motivates the development of a hybrid compressible-incompressible solver that removes the low-Mach-number limitations of the compressible solvers, thus allowing numerical simulations of late-time mixing. Simulations have been performed for a multi-mode perturbation at the interface between two fluids of densities corresponding to an Atwood number of 0.5, and results are presented for the development of the instability, mixing parameters and turbulent kinetic energy spectra. The results are discussed in comparison with previous compressible simulations, theory and experiments. © Crown Owned Copyright. Published by Cambridge University Press 2015.

Description: This paper investigates the influence of different three-dimensional multi-mode initial conditions on the rate of growth of a mixing layer initiated via a Richtmyer-Meshkov instability through a series of well-controlled numerical experiments. Results are presented for large-eddy simulation of narrowband and broadband perturbations at grid resolutions up to 3 10 9 points using two completely different numerical methods, and comparisons are made with theory and experiment. It is shown that the mixing-layer growth is strongly dependent on initial conditions, the narrowband case giving a power-law exponent θ≈0.26 at low Atwood and θ≈0.3 at high Atwood numbers. The broadband case uses a perturbation power spectrum of the form P(k) k2 with a proposed theoretical growth rate of θ= 2/3. The numerical results confirm this; however, they highlight the necessity of a very fine grid to capture an appropriately broad range of initial scales. In addition, an analysis of the kinetic energy decay rates, fluctuating kinetic energy spectra, plane-averaged volume fraction profiles and mixing parameters is presented for each case. © 2010 Cambridge University Press.

Description: 1. The amounts of N, P and K recovered by five arable crops and by permanent grass from soil alone, and from fertilizer and farmyard manure (FYM) dressings were measured. All the crops responded well to P and K fertilizers and all except clover responded to N. Uptakes from soil alone are therefore the maximum amounts of each nutrient that each crop could remove when supplied with other fertilizer nutrients (the exchangeable Ca and Mg in the soil were adequate).2. Permanent grass (free from legumes) obtained about 114 lb. N/acre each year from soil and other natural sources; winter wheat obtained 1001b. N, kale and potatoes about 80 lb. N and spring barley only 57 lb. A 1 year ley of clover and grass fixed at least 1 cwt. N/aere/year. Permanent grass removed most P from soil (17 lb./acre a year), potatoes removed least (6 lb. of P) and other crops intermediate amounts. Most K was taken from soil by kale (70 lb. K/acre/year) and least (20 lb.) by potatoes. Annual variations in the amounts of nutrients recovered from soil by any one crop were much greater with K than with N or P.3. Most fertilizer N was recovered by kale and least by potatoes; with these crops two-thirds and one-third respectively of the light dressing was recovered, percentage recovery from the higher rate of N tested was less. Kale and the 1 year ley recovered nearly one-quarter of the P applied, permanent grass recovered little more than one-tenth. Clover-grass ley recovered most fertilizer K, apparently taking up four-fifths of that applied. Potatoes, kale and permanent grass all recovered more than half of the fertilizer K given, cereals were least efficient although both responded well to K dressings.4. Farmyard manure supplied large amounts of nutrients to all crops. Similar amounts of N, P and K appeared to be recovered from FYM whether or not NPK fertilizer was also used. A rough estimate was that crops like kale, potatoes and permanent grass, which received FYM each year, recovered about 30 lb. of N, 4 lb. of P and 75 lb. of K from a 10 tons/acre dressing.

Description: To obtain large yields of grass much N fertilizer is usually needed, and when such grass is cut and conserved large amounts of K soon are removed from the soil. Some soils contain so little ‘available’ K that yields are soon limited unless grass is given enough K fertilizer, but other soils supply more K and so need less K fertilizer. Soils differ so greatly in their ability to supply crops with K that it is difficult to generalize about the fertilizer K requirements of grass, especially as the use to which the grass is put greatly affects the soil K ‘balance sheet’. On average, grass in England grows well for not much more than 6 months each year. This implies that, when cattle are maintained on hay or silage for much of the remainder of the year, on average one-third of the grass product each year may have to be cut, removed from the field, and conserved. Much of the N, P and K contained in this grass is not returned to the soil.

Description: 1. Fourteen experiments with winter wheat on heavy-land farms from 1958–60 compared autumn dressings of sulphate of ammonia with equivalent early (March) or late (May) spring top-dressings. Dressings applied on two or all three dates of application were also compared.2. Consistent and significant gains in yield from low (0·5 or 0·6 cwt. N/acre) and high (1·0 or 1·2 cwt. N/acre) levels were obtained at most centres, which were on fields under arable rotation.3. With the low level of N, gains in yield were greatest from a single May top-dressing. There was no gain from dividing the dressing.4. With the high level of N, dressings divided between autumn-May or March-May were best. March-May was the most consistently satisfactory treatment and gave the highest mean increases in yield in 1959 and 1960, but in 1958 autumn-May was better. Single May dressings gave slightly lower yields. There was no advantage from dividing N between all three dates of application.5. Single applications of N in autumn gave lower yields than single applications in spring; supplementing autumn N with a late spring top-dressing gave almost the same yield as giving all the N in spring. Dividing the dressing in this way may be convenient on many heavy-land farms.6. The percentage of N in the grain was highest with a late top-dressing of fertilizer-N, lowest with autumn N and intermediate with March top-dressings.

Description: Two degrees of compaction, 'heavy' with a flattyred vehicle wheel, and 'light' with a ring roller, were given to the seed beds after sowing barley and globe beet on three contrasted soils. Changes in pore space of the soils and the responses of the crop to the changed physical properties were measured. The sites used were: Barnfield at Rothamsted, a heavy clay loam long under arable cultivation and having little organic matter; Pastures Field at Rothamsted, a field of silty clay loam ploughed after an 8-year ley; Stackyard field at Woburn, a light sandy loam long in arable cultivation and containing little organic matter.

Description: Soil samples from 179 field experiments testing phosphate fertilizers on potatoes, swedes and grass were analysed for total phosphorus, and for phosphorus soluble in the following solutions: 0·3 N-HCl, 0·002 N-H2SO4, 1% citric acid (H3Ci), 0·5 N acetic acid (HAc), acetic acid-sodium acetate buffer (HAc-NaAc) at pH 4·8, 0·5 M-NaHCO3, and 0·01 M CaCl2.Average values for soluble P were closely related to average crop responses to superphosphate in the experiments on swedes, but not in the grass and potato experiments. The extractants that differentiated best between responsive and unresponsive groups of experiments were HAc, HAc-NaAc, and NaHCO3 for potatoes, and HCl, H2S04, HAc–NaAc, NaHCO3 and CaCl2 for grass.For the experiments as a whole 0·5 M-NaHCO3 was the ‘best’ extractant. The HCl, H2SO4, and HAc-NaAc buffer solution methods were roughly equally effective, though inferior to NaHCO3; the other three extractants (HAc, H3Ci, CaCl2) were of little general use. Total P in soil was also related to response to superphosphate, though less well than values for soluble P obtained by the better methods.Estimates of soluble P by different solvents were often related. Estimates by HCl and H2SO4 methods were most closely related; values for P soluble in H2SO4 and in HAc-NaAc were also often significantly correlated, as were estimates by HAc–NaAc and CaCl2. The H3Ci and CaCl2 methods gave results that were least related to those with other methods.The use of soil analyses in advising on P-manuring is discussed and a tentative method is proposed of establishing the analytical limits for soluble P that define ‘deficient’ soils. If the confidence attached to the limiting values that separate ‘deficient’ and ‘non-deficient’ soils is stated, farmers will be able to assess the risk entailed in accepting advice based on soil analysis.

Description: SummaryNinety-four British liming materials were examined. The contents of Ca, Mg, K, P, S, Sr, B, Fe, Mn, Zn, Cu, Co, Mo, Ni, Cd and Na in the acid-soluble fraction, and Mn, Cu, Co, Mo, Ni, Sr, Ti, Cr, Ga, Pb, Sn, V, Y, Zr and Ba in the acid-insoluble fraction were determined by chemical and spectrographic analysis. Water soluble nitrate was also determined.Only manganese, providing on average 3 kg Mn/ha for a 10 t/ha dressing, was found in agriculturally significant quantities in the acid-soluble fraction of the limestones or shell-sands analysed. Magnesium, present only in significant amounts in the dolomitic limestones, provided on average 27 kg Mg/ha from a 10 t/ha dressing.The acid-insoluble fraction of the limestones contained, on average, a twentieth of the concentration of Mn in the acid-soluble fraction. The concentration of K was much larger and depended on the amounts and nature of the insoluble fraction. The acidinsoluble fraction contained no significant amounts of other plant nutrients. The relative concentrations of Mn and K in both fractions emphasize that results based on the total amounts of elements in limestones could overestimate their potential value as sources of plant nutrients.

Description: SUMMARYThe effects of N, P and K fertilizers on the yield and N, P and K contents of grass cut for conservation, measured during 1958–63, were again measured during 1964–7. Grass given 38 kg N/ha per cut needed 31 kg K/ha per cut for full yield, grass given 75 or 113 kg N/ha per cut needed twice as much K. With sufficient K, at least 75 kg N/ha per cut was justified. The grass responded little to P.Percentage N in the grass, though greatly increased by N fertilizer, was little altered by K fertilizer. Percentage K, whilst greatly increased by K fertilizer, was decreased by N unless 62 kg K/ha per cut also was given. Percentage P in the grass was little increased by P fertilizer.Exchangeable K in the surface soil (0–20 cm) was maintained with time where the grass was given either 38 kg N plus 31 kg K or 75 kg N plus 62 kg K/ha per cut, corresponding to an N:K ratio of 1:0·82. Percentage K in the grass decreased with time throughout. Whereas a N:K ratio of 1:1·66 best maintained % K in grass during 1958–63 it was no better than an N:K ratio of 1:0·82 during 1964–7.Although exchangeable Mg in the surface soil decreased markedly between 1958 and 1967 (Mg fertilizer was not applied), % Mg in the grass did not. Mg in the grass was increased by N, but decreased by K fertilizer, and exceeded 0·2% (in dry matter) only in 1967 and then only where 75 or 113 kg N/ha per cut was applied.