ALBERT

Description: Experimental studies have shown that convergent-divergent nozzles, when run at low pressure ratios, often undergo a flow resonance accompanied by emission of acoustic tones. The phenomenon, different in characteristics from conventional 'screech' tones, is addressed in this paper. Unlike screech, the resonant frequency (fN) increases with increasing supply pressure. There is a 'staging' behaviour; odd-harmonic stages resonate at lower pressures while the fundamental occurs in a wide range of higher pressures corresponding to a 'fully expanded Mach number' (Mj) around unity. Within a stage, fN varies approximately linearly with Mj; the slope of the variation steepens when the angle of divergence of the nozzle is decreased. Based on the data, correlation equations are provided for the prediction of fN. A companion computational study captures the phenomenon and predicts the frequencies, including the stage jump, quite well. While the underlying mechanisms are not completely understood yet, it is clear that the unsteadiness of a shock occurring within the divergent section plays a direct role. The shock drives the flow downstream like a vibrating diaphragm, and resonance takes place similarly to the (no-flow) acoustic resonance of a conical section having one end closed and the other end open. Thus, the fundamental is accompanied by a standing one-quarter wave within the divergent section, the next stage by a standing three-quarter wave, and so on. The distance from the foot of the shock to the nozzle exit imposes the pertinent length scale. The principal trends in the frequency variation are explained qualitatively from the characteristic variation of that length scale. A striking feature is that tripping of the nozzle's internal boundary layer tends to suppress the resonance. It is likely that the trip effect occurs due to a break in the azimuthal coherence of the unsteady flow.

Description: We present new laboratory data on long wave forcing over a barred beach profile under random wave breaking conditions. The data include incident and radiated wave amplitudes, wave set-up, and detailed measurements of the cross-shore variation in long wave amplitude, including shoreline (swash) amplitudes. The total surf zone width was varied via changes in both wave height and the water level over the bar crest. The data obtained from the barred beach are also compared with previous data obtained from a plane beach under essentially identical short wave forcing conditions. The presence of the bar induces a frequency downshift in the spectral peak of the radiated long waves, a consequence of the increased surf zone width on the barred beach and a clear signature of long wave forcing by a time-varying breakpoint. Further comparisons of the two data sets suggest that the bar leads to resonant trapping and amplification (or suppression) of the shoreline motion at discrete long wave frequencies. Well-defined standing long wave motion occurs at discrete frequencies inside the bar and the resonant response is consistent with a simple seiche between the bar crest and shoreline, in agreement with previous numerical model studies. The long wave structure offshore of the breakpoint depends on the relative positions of the bar, shoreline and breakpoint, and is inconsistent with a numerical solution for a free standing long wave over the barred beach profile. © 2004 Cambridge University Press.

Description: Steady and unsteady numerical simulations of two-dimensional flow in a collapsible channel were carried out to study the flow limitation which typically occurs when the upstream transmural pressure is held constant while flow rate and pressure gradient along the collapsible channel can vary independently. Multiple steady solutions are found for a range of upstream transmural pressures and Reynolds number using an arclength control method. The stability of these steady solutions is tested in order to check the correlation between flow limitation and self-excited oscillations (the latter being a consequence of unstable steady solutions). Both stable and unstable solutions are found when flow is limited. Self-excited oscillations and divergence instabilities are observed in certain solution branches. The instability of the steady solutions seems to depend on the unsteady boundary conditions used, i.e. on which parameters are allowed to vary. However, steady solutions associated with the solution branch before flow limitation where the membrane wall bulges are found to be stable for each of the three different boundary conditions employed. We conclude that there is no one to one correlation between the two phenomena in this two dimensional channel model.

Description: Transverse stability and instability of solitary waves correspond to a class of perturbations that are travelling in a direction transverse to the direction of the basic solitary wave. In this paper we consider the problem of transverse instability of solitary waves for the water-wave problem, from both the model equation point of view and the full water-wave equations. A new universal geometric condition for transverse instability forms the backbone of the analysis. The theory is first illustrated by application to model PDEs for water waves such as the KP equation, and then it is applied to the full water-wave problem. This is the first theory proposed for transverse instability of solitary waves of the full water-wave problem. The theory suggests the introduction of a new functional for water waves, whose importance is suggested by the mathematical structure. Without explicit calculation, the theory is used to argue that the basic class of solitary waves of the water-wave problem, which bifurcate at Froude number unity, are likely to be stable to transverse perturbations, even at large amplitude.

Description: The paper explores, using different levels of turbulence closure, the computed behavior of the three-dimensional turbulent wall jet in order to determine the cause of the remarkably high lateral rates of spread observed in experiments. Initially, to ensure accurate numerical solution, the equations are cast into the form appropriate to a self-similar shear flow thereby reducing the problem to one of two independent variables. Our computations confirm that the strong lateral spreading arises from the creation of streamwise vorticity, rather than from anisotropic diffusion. The predicted ratio of the normal to lateral spreading rates is, however, very sensitive to the approximation made for the pressure-strain correlation. The version that, in other flows, has led to the best agreement with experiments again comes closest in calculating the wall jet, although the computed rate of spread is still some 50% greater than in most of the measurements. Our subsequent calculations, using a forward-marching scheme show that, because of the strong coupling between axial and secondary flow, the flow takes much longer to reach its self-preserving state than in a two-dimensional wall jet. Thus, it appears very probable that none of the experimental data are fully developed.

Description: Turbulent flow in a rectangular channel is investigated to determine the scale and pattern of the eddies that contribute most to the total turbulent kinetic energy and the Reynolds shear stress. Instantaneous, two-dimensional particle image velocimeter measurements in the streamwise-wall-normal plane at Reynolds numbers Reh = 5378 and 29 935 are used to form two-point spatial correlation functions, from which the proper orthogonal modes are determined. Large-scale motions – having length scales of the order of the channel width and represented by a small set of low-order eigenmodes – contain a large fraction of the kinetic energy of the streamwise velocity component and a small fraction of the kinetic energy of the wall-normal velocities. Surprisingly, the set of large-scale modes that contains half of the total turbulent kinetic energy in the channel, also contains two-thirds to three-quarters of the total Reynolds shear stress in the outer region. Thus, it is the large-scale motions, rather than the main turbulent motions, that dominate turbulent transport in all parts of the channel except the buffer layer. Samples of the large-scale structures associated with the dominant eigenfunctions are found by projecting individual realizations onto the dominant modes. In the streamwise wall-normal plane their patterns often consist of an inclined region of second quadrant vectors separated from an upstream region of fourth quadrant vectors by a stagnation point/shear layer. The inclined Q4/shear layer/Q2 region of the largest motions extends beyond the centreline of the channel and lies under a region of fluid that rotates about the spanwise direction. This pattern is very similar to the signature of a hairpin vortex. Reynolds number similarity of the large structures is demonstrated, approximately, by comparing the two-dimensional correlation coefficients and the eigenvalues of the different modes at the two Reynolds numbers.

Description: Experiments by Kessler on bioconvection in laboratory suspensions of bacteria (Bacillus subtilis), contained in a deep chamber, reveal the development of a thin upper boundary layer of cell-rich fluid which becomes unstable, leading to the formation of falling plumes. We use the continuum description of such a suspension developed by Hillesdon et al. (1995) as the basis for a theoretical model of the boundary layer and an axisymmetric plume. If the boundary layer has dimensionless thickness λ [Lt ] 1, the plume has width λ1/2. A similarity solution is found for the plume in which the cell flux and volume flux can be matched to those in the boundary layer and in the bulk of the suspension outside both regions. The corresponding model for a two-dimensional plume fails to give a self-consistent solution.

Description: The formation of doubly-periodic patterns on the surface of a fluid layer with a uniform velocity field and constant depth is considered. The fluid is assumed to be inviscid and the flow irrotational. The problem of steady patterns is shown to have a novel variational formulation, which includes a new characterization of steady uniform mean flow, and steady uniform flow coupled with steady doubly periodic patterns. A central observation is that mean flow can be characterized geometrically by associating it with symmetries. The theory gives precise information about the role of the ten natural parameters in the problem which govern the wave-mean flow interaction for steady patterns in finite depth. The formulation is applied to the problem of interaction of capillary-gravity short-crested waves with oblique travelling waves, leading to several new observations for this class of waves. Moreover, by including oblique travelling waves and short-crested waves in the same analysis, new bifurcations of short-crested waves are found, which give rise to mixed waves which may have complicated spatial structure.

Description: 1. A total of forty-two Suffolk cross-bred and 230 stud Romney Marsh ewes were used in four experiments in which pregnant mare serum gonadotrophin (p.m.s.) was used in various combinations with progesterone and oestrogen in attempts to induce fertile mating in anoestrus.2. Groups of six Suffolk cross-bred ewes were injected with 1000 i.u. p.m.s. after pretreatment, commencing 4 days earlier, with 75 mg. progesterone administered in one of four different ways. Six twice-daily injections in oil resulted in oestrus in five ewes in each of two groups treated. Single injections in oil solution, aqueous suspension, and benzyl alcohol emulsion resulted in oestrus in two, nil, and four ewes, respectively. All were served within 48 hr. of injection of p.m.s.3. Ovulation was observed in five of six crossbred ewes which received six twice-daily injections of progesterone in oil, without subsequent injection of p.m.s. Three were served.4. Divided injections of progesterone commencing 4 days before 750–1000 i.u. p.m.s. failed to induce a satisfactory oestrous response in Romney Marsh ewes. An increase to 7 days in the duration of progesterone stimulation resulted in oestrus in all of eighteen ewes treated.5. The injection of a benzyl alcohol emulsion containing 75 or 150 mg. progesterone, given as a single dose 4 or 7 days before 750 i.u. p.m.s., failed to induce a satisfactory oestrous response. Of seventy-two ewes treated, only seven were served.6. Lambing results were most unsatisfactory when progesterone-p.m.s. treatment was followed by artificial insemination. Of 144 Romneys inseminated, only twelve lambed. Successful pregnancy appeared unrelated to the type of treatment or the occurrence of oestrus.7. On the basis of the oestrous responses observed after the injection of a variety of combinations of oestrogen, progesterone, and p.m.s., and by reference to quantitative data on progesterone-oestrogen relationships in oestrous behaviour in the spayed ewe, it is concluded that the developing follicle of the Romney Marsh ewe produces an amount of oestrogen approximately equivalent, in its physiological activity, to a single injection in oil of about 20 μg. oestradiol benzoate.

Description: The performance potentials of six perennial ryegrass varieties for conservation or grazing use were compared between 1994 and 1996 in N. Ireland. They were maintained, either under constant lax defoliation (conservation) or constant severe defoliation (simulated grazing) management for 3 years, or annually alternated between these two managements with the changeover taking place either in autumn or at the first cut of the following year. Starting one set with lax defoliation in the first year and the other with severe defoliation created duplicates of these two alternating treatments. The results showed that variety yield differed depending on the season and the management imposed and there were differential responses to the various treatments. Conducting an alternating management system that implemented the management change in autumn provided a valid estimate of yield performance potential for both simulated grazing and conservation use, compared to constant management systems. Although significant differences in variety ranking between lax defoliation and severe defoliation management yields were only observed in the third year, the study showed that if the management change was implemented in autumn, the yield potential of varieties in the following year was not affected by the preceding year's management regime. Leaving a longer sward (6 cm) to over-winter increased the spring performance of the varieties in some years, compared to a shorter sward (3 cm), which may have implications for grazing management. There were also indications that imposing an alternating management system might alter the absolute magnitude of the sward density ratings relative to a constantly managed system, though variety rankings would remain unaffected.It was concluded that the current alternating management testing system used to evaluate candidate varieties for UK National or regional recommended lists, does not cause any variety to be unfairly advantaged or disadvantaged.