ALBERT

Description: The work is concerned with the problem of the linear instability of symmetric short-crested water waves, the simplest three-dimensional wave pattern. Two complementary basic approaches were used. The first, previously developed by Ioualalen & Kharif (1993, 1994), is based on the application of the Galerkin method to the set of Euler equations linearized around essentially nonlinear basic states calculated using the Stokes-like series for the short-crested waves with great precision. An alternative analytical approach starts with the so-called Zakharov equation, i.e. an integro-differential equation for potential water waves derived by means of an asymptotic procedure in powers of wave steepness. Both approaches lead to the analysis of an eigenvalue problem of the type where A and B are infinite square matrices. The first approach should deal with matrices of quite general form although the problem is tractable numerically. The use of the proper canonical variables in our second approach turns the matrix B into the unit one, while the matrix A gets a very specific ‘nearly diagonal’ structure with some additional (Hamiltonian) properties of symmetry. This enables us to formulate simple necessary and sufficient a priori criteria of instability and to find instability characteristics analytically through an asymptotic procedure avoiding a number of additional assumptions that other authors were forced to accept. A comparison of the two approaches is carried out. Surprisingly, the analytical results were found to hold their validity for rather steep waves (up to steepness 0.4) for a wide range of wave patterns. We have generalized the classical Phillips concept of weakly nonlinear wave instabilities by describing the interaction between the elementary classes of instabilities and have provided an understanding of when this interaction is essential. The mechanisms of the relatively high stability of short-crested waves are revealed and explained in terms of the interaction between different classes of instabilities. A helpful interpretation of the problem in terms of an infinite chain of interacting linear oscillators was developed. © 1995, Cambridge University Press. All rights reserved.

Description: We examine the effects of compressiblity on the structure of a single row of hollow-core, constant-pressure vortices. The problem is formulated and solved in the hodograph plane. The transformation from the physical plane to the hodograph plane results in a linear problem that is solved numerically. The numerical solution is checked via a Rayleigh-Janzen expansion. It is observed that for an appropriate choice of the parameters Mco = qoo/cx〉, and the speed ratio, a = q∞/qʋ where qʋ is the speed on the vortex boundary, transonic shock-free flow exists. Also, for a given fixed speed ratio, a, the vortices shrink in size and get closer as the Mach number at infinity, M∞, is increased. In the limit of an evacuated vortex core, we find that all such solutions exhibit cuspidal behaviour corresponding to the onset of limit lines. © 1995, Cambridge University Press. All rights reserved.

Description: The effects of the intensity and frequency of a time-periodic external field on the rotary motion of a dipolar spherical particle suspended in homogeneous shear are studied with the goal of providing insight into problems concerning the motion of swimming microorganisms and the macroscopic behaviour of ferrofluids. The analysis reveals two modes of motion: convergence of the particle to a global time-periodic attractor, and quasi-periodic motion. The former mode of particle rotation generally appears for sufficiently strong fields. However, asymptotic analysis clarifies that it may occur even for very weak fields as a cumulative result of appropriate resonance interactions.A sufficient condition for the occurrence of a global time-periodic attractor is established for an external field acting in the plane of shear. Asymptotic results together with numerical evidence indicate that this condition is in fact a necessary condition as well. Making use of this condition we obtain the division of the plane of parameters into domains respectively corresponding to quasi-periodic motion and global time-periodic attractors. The latter domain has the structure of non-intersecting Arnold's tongues. Throughout each, the average frequency of dipole rotation about the vorticity vector is a constant (integral) multiple of the forcing frequency (frequency locking). In the case of quasi-periodic motion, there simultaneously coexist separate domains in orientation space where the rotary motion is locally characterized by different constant rotation numbers. These may assume both rational and irrational values. Potential implications of the distinction between these modes of rotary motion on the characterization of effective (macroscale) ferrofluid properties are briefly discussed.

Description: The work suggests a simple qualitative model of the wind wave ‘horse-shoe’ patterns often seen on the sea surface. The model is aimed at explaining the persistent character of the patterns and their specific asymmetric shape. It is based on the idea that the dominant physical processes are quintet resonant interactions, input due to wind and dissipation, which balance each other. These processes are described at the lowest order in nonlinearity. The consideration is confined to the most essential modes: the central (basic) harmonic and two symmetric oblique satellites, the most rapidly growing ones due to the class II instability. The chosen harmonics are phase locked, i.e. all the waves have equal phase velocities in the direction of the basic wave. This fact along with the symmetry of the satellites ensures the quasi-stationary character of the resulting patterns. Mathematically the model is a set of three coupled ordinary differential equations for the wave amplitudes. It is derived starting with the integro-differential formulation of water wave equations (Zakharov's equation) modified by taking into account small (of order of quartic nonlinearity) non-conservative effects. In the derivation the symmetry properties of the unperturbed Hamiltonian system were used by taking special canonical transformations, which allow one exactly to reduce the Zakharov equation to the model. The study of system dynamics is focused on its qualitative aspects. It is shown that if the non-conservative effects are neglected one cannot obtain solutions describing persistent asymmetric patterns, but the presence of small non-conservative effects changes drastically the system dynamics at large times. The main new feature is attractive equilibria, which are essentially distinct from the conservative ones. For the existence of the attractors a balance between nonlinearity and non-conservative effects is necessary. A wide class of initial configurations evolves to the attractors of the system, providing a likely scenario for the emergence of the long-lived three-dimensional wind wave patterns. The resulting structures reproduce all the main features of the experimentally observed horse-shoe patterns. In particular, the model provides the characteristic ‘crescent’ shape of the wave fronts oriented forward and the front-back asymmetry of the wave profiles. © 1996, Cambridge University Press. All rights reserved.

Description: This study deals with the first 2 years of grazing trials on improved pastures of tropical grasses and legumes at Ibadan in Nigeria. The mixtures consisted of (i) Cynodon plectostachyus and Centrosema pubescens (legume), (ii) (i)+Chloris gayana and Digitaria decumbens, (iii) (ii) +Stylosanthes gracilis (legume). The mixtures were sown and planted in four blocks, the treatments being repeated four times, and were grazed rotationally by N'Dama cattle. During the first year's trial a uniform stocking rate of 1·7 steers/acre was adopted and a recovery period of 11 weeks was allowed. In the second year's trial the stocking rate was increased to 2·7 beasts/acre by the addition of nine yearling heifers and the recovery period was reduced to 5 weeks. Herbage yield and intake were measured by the clipping technique.

Description: SUMMARYA field experiment was conducted at nine sites in England (1991–94) to compare six sown species of cover crop and natural regeneration in terms of nitrogen uptake and effect on response to applied N by a subsequent spring barley crop. The success and extent of cover crop establishment varied among sites and was insignificant in two. This may be associated with the relatively late sowing of the cover crops, the earliest site being sown on 27 August and the latest on 19 October. Dry matter (DM) yield of the sown cover crop at time of incorporation was related to sowing date, earlier sowing giving the higher yields. Maximum total DM yield and N uptake by the above-ground portion of cover crops were 1280kgDM/ha and 38 kg N/ha respectively. The extent of N uptake by the cover crops appeared to be related to the success of establishment rather than to the level of soil nitrate-N at the time of their sowing. Effects of cover crop incorporation on the subsequent spring barley were small. There was no evidence for any positive effect of the cover crop on N supply to the barley. In one trial, incorporation of forage rye significantly reduced grain yield of the barley by 0·7–1·2 t/ha compared to other cover crop species.

Description: SUMMARYGroups of Awassi lambs, aged 7–13 months at start of the trial, were fed for 100 days on four different rations. A ‘control’ ration contained ground barley: the others contained different proportions of dried sugar-beet pulp, and no barley.Male lambs were initially heavier, and gave better weight gains than the females. Groups on beet pulp grew better than the ‘control’. The most economical weight gains were obtained in the group in which beet pulp constituted 40 % of the ‘concentrate’ portion of the diet.

Description: Seasonal haul-out patterns and diet of individually marked leopard seals (Hydrurga leptonyx) were investigated at Bird Island, South Georgia during the 1983–96 winters. A total of 2956 leopard seal sightings were made, and 121 seals were tagged during the study, mainly between 1993 and 1996. Photographs of scars and pelage patterns were also used to identify a subset of these individuals across years, which provided no evidence of tag loss between or within years. Leopard seals were observed between April and November; the mean time between the first and last sightings in each year was 208 d (s d ± 48). Between 1993–96, eight seals were resident around the island for more than 100 d, and the longest recorded residence was 130 d. The proportion of tagged seals resighted was 0.35 and 0.17 in 1995 and 1996 respectively. Based on estimates of body length, 70% were not sexually mature. There was considerable inter-annual variation in abundance, with a maximum of 502 sightings during 1994, compared with a minimum of 21 during 1986 and 1989. Antarctic fur seals (Arctocephalus gazella) were the main prey item (58% of kills observed and 53% of scats). Other items included penguins (28% of kills observed and 20% of scats) and fish (24% of scats). Antarctic krill (Euphausia superba), southern elephant seals (Mirounga leonina) and seabirds other than penguins were also present in the diet in small quantities.

Description: We present a radiocarbon chronology of key Sayan-Altai monuments from the Scythian period, based on a statistical analysis of dates produced in the 1980s and now supplemented with new dates. These new 14C dates were produced for samples from the Tuekta-1 barrows (burial mounds) and were measured both in St. Petersburg and Groningen. These tree-ring samples were fitted to the calibration curve. Chronologies were established for the Arzhan, Tuekta-1 and Pazyryk-5 barrows. The time of the construction of the Arzhan and Pazyryk-5 barrows is the 9th and late 5th–4th centuries bc, respectively, and agrees with archaeology. According to new data obtained, the time of the Tuekta-1 barrow construction is some years older than has been accepted thus far by archaeologists.