ALBERT

Description: A Fourier-integral method is developed to obtain transient solutions to potential wavemaker problems. This method yields solutions for wavemaker velocities which need not be given as powers of time. The results are compared with known small-time and local solutions. Examples considered include ramp, step, and harmonic wavemaker velocities. As time becomes large, the behaviour near the wave front is derived for the impulsive wavemaker, and for the harmonic wavemaker it is shown that the steady-state solution is recovered. The solution for a wavemaker velocity given as a Fourier cosine series compares favourably with available experimental results. Capillary effects are included and nonlinear effects are discussed. © 1990, Cambridge University Press. All rights reserved.

Description: A formal derivation of evolution equations is given for viscous gravity waves and viscous capillary—gravity waves with surfactants in water of infinite depth. Multiple scales are used to describe the slow modulation of a wave packet, and matched asymptotic expansions are introduced to represent the viscous boundary layer at the free surface. The resulting dissipative nonlinear Schrödinger equations show that the largest terms in the damping coefficients are unaltered from previous linear results up to third order in the amplitude expansions. The modulational instability of infinite wavetrains of small but finite amplitude is studied numerically. The results show the effect of viscosity and surfactants on the Benjamin-Feir instability and subsequent nonlinear evolution. In an inviscid limit for capillary-gravity waves, a small-amplitude recurrence is observed that is not directly related to the Benjamin—Feir instability. © 1991, Cambridge University Press. All rights reserved.

Description: We report on the present status of the Lawrence Livermore AMS spectrometer, including sample throughput and progress towards routine 1% measurement capability for 14C, first results on other isotopes and experience with a multisample high-intensity ion source.

Description: A phenomenological study of the processes occurring when a shock wave interacts with porous polyester and polyether foams has been undertaken. Plane shock waves generated in a shock tube were reflected off a slab of foam mounted against the back wall of the tube. Tests were conducted with an initial shock wave Mach number of 1.4 and a 70 mm thick slab of foam. The reduction in reflected shock wave strength and substantial increase in the back wall pressure over that for rigid wall reflection, found by other workers, were confirmed. Piezoelectric pressure transducers were used to record the pressure before, alongside and behind the foam specimen. Schlieren photographs of the flow were made and showed some features not previously reported. In particular it is shown that there is a flow of gas across the face of the foam at some point of the process. Previous investigations of this interaction process have assumed that the face of the foam is a contact surface. Short duration photographs of the distortion of the foam were taken, enabling the wave propagation in the foam material itself to be studied. It is established that the front of this compaction wave in the foam material moves at considerably lower velocity (∼ 90 m/s) than the gas wave as detected by the pressure transducers (∼ 200 m/s). This result contrasts with the assumption made in previous work that the two-phase medium behaves essentially as a homogeneous substance. A simple physical model based on a zone of compacted material in the foam acting as a high-resistance flow barrier, is proposed to explain the observed phenomena. © 1993, Cambridge University Press. All rights reserved.

Description: An incompressible inviscid flow theory for single and two-element airfoils experiencing trailing-edge stall is presented. For the single airfoil the model requires a simple sequence of conformal transformations to map a Joukowsky airfoil, partially truncated on the upper surface, onto a circle over which the flow problem is solved. Source and doublet singularities are used to create free streamlines simulating shear layers bounding the near wake. The model's simplicity permits extension of the method to airfoil-flap configurations in which trailing-edge stall is assumed on the flap. Williams’ analytical method to calculate the potential flow about two lifting bodies is incorporated in the Joukowsky-arc wake-singularity model to allow for flow separation. The theoretical pressure distributions from these models show good agreement with wind-tunnel measurements. © 1993, Cambridge University Press

Description: Laminar vortex pairs with small Froude number were generated by a submerged delta wing at negative angle of attack or by a pair of vertically oriented, counter-rotating flaps. The vortex pairs thus generated rise and interact with the free surface. The surface and subsurface flow field was studied using flow visualization and particle image velocimetry. Initial surface deformations, striations, are shown to be caused by stretching and interaction of cross-stream vortices near the surface. With small amounts of surface contamination, contamination fronts (producing Reynolds ridges) form on the surface and secondary vorticity, generated beneath the surface beyond the fronts, rolls up to form vortices with opposite rotation outboard of the primary vortices. The circulation associated with the secondary vortices is as much as 1/3 that of the primary vortices. The secondary vortices cause the primary vortex pair to rebound from the surface. Slight surface deformations, scars, are caused by the primary and secondary vortices. © 1994, Cambridge University Press. All rights reserved.

Description: The dispersion of passive scalars by the steady viscous flow through a twisted pipe is both a simple example of chaotic advection and an elaboration of Taylor's classic shear dispersion problem. In this article we study the statistics of the axial dispersion of both diffusive and perfect (non-diffusive) tracer in this system. For diffusive tracer chaotic advection assists molecular diffusion in transverse mixing and so diminishes the axial dispersion below that of integrable advection. As in many other studies of shear dispersion the axial distribution ultimately becomes Gaussian as. Thus there is a diffusive regime, but with an effective diffusivity that is enhanced above molecular values. In contrast to the classic case, the effective diffusivity is not necessarily inversely proportional to the molecular diffusivity. For instance, in the irregular regime the effective diffusivity is proportional to the logarithm of the molecular diffusivity. For perfect tracer chaotic advection does not result in a diffusive process, even in the irregular regime in which streamlines wander throughout the cross-section of the pipe. Instead the variance of the axial position is proportional to t In t so that the measured diffusion coefflcent diverges like ln t. This faster than linear growth of variance is attributed to the trapping of tracer for long times near the solid boundary, where the no-slip condition ensures that the fluid moves slowly. Analogous logarithmic effects associated with the no-slip condition are well known in the context of porous media. A simple argument, based on Lagrangian statistics and a local analysis of the trajectories near the pipe wall, is used to calculate the constants of proportionality before the logarithmic terms in both the large- and infinite-Peclet-number limits. © 1994, Cambridge University Press. All rights reserved.

Description: We examine the stability characteristics of a two-dimensional flow which consists initially of an inflexionally unstable shear layer on an f-plane. Under the action of the primary instability, the vorticity in the shear-layer initially coalesces into two Kelvin-Helmholtz vortices which subsequently merge to form a single coherent vortex. At a sequence of times during this process, we test the stability of the two-dimensional flow to fully three-dimensional perturbations. A somewhat novel approach is developed which removes inconsistencies in the secondary stability analyses which might otherwise arise owing to the time-dependence of the two-dimensional flow. In the non-rotating case, and before the onset of pairing, we obtain a spectrum of unstable longitudinal modes which is similar to that obtained previously by Pierrehumbert & Widnall (1982) for the Stuart vortex, and by Klaassen & Peltier (1985, 1989, 1991) for more realistic flows. In addition, we demonstrate the existence of a new sequence of three-dimensional subharmonic (and therefore ‘helical’) instabilities. After pairing is complete, the secondary instability spectrum is essentially unaltered except for a doubling of length- and timescales that is consistent with the notion of spatial and temporal self-similarity. Once pairing begins, the spectrum quickly becomes dominated by the unstable modes of the emerging subharmonic Kelvin-Helmholtz vortex, and is therefore similar to that which is characteristic of the post-pairing regime. Also in the context of non-rotating flow, we demonstrate that the direct transfer of energy into the dissipative subrange via secondary instability is possible only if the background flow is stationary, since even slow time-dependence acts to decorrelate small-scale modes and thereby to impose a short-wave cutoff on the spectrum. The stability of the merged vortex state is assessed for various values of the planetary vorticity f. Slow rotation may either stabilize or destabilize the columnar vortices, depending upon the sign of f while fast rotation of either sign tends to be stabilizing. When f has opposite sign to the relative vorticity of the two-dimensional basic state, the flow becomes unstable to a new mode of instability that has not been previously identified. Modes whose energy is concentrated in the vortex cores are shown to be associated, even at non-zero f with Pierrehumbert’s (1986) elliptical instability. Through detailed consideration of the vortex interaction mechanisms which drive instability, we are able to provide physical explanations for many aspects of the three-dimensionalization process. © 1994, Cambridge University Press

Description: An experimental investigation of the sedimentation of monodisperse colloidal silica spheres with grafted octadecyl chains with three different interaction potentials is presented. Small particles (0.27 µm) behaved as hard spheres in cyclohexane, but larger ones (0.60 and 0.94 µm) are weakly flocculated by van der Waals attractions. The smallest particles (0.08 µm) in hexadecane are strongly flocculated by attractions between the octadecyl layers. A medical computer tomography (CT) scanner provided an accurate and absolute density measurement without disrupting the process. For the hard spheres and the weakly flocculated systems, the kinetics of sedimentation for the dispersed phase could readily be predicted utilizing the flux curve. For flocculated networks, we found a power–law relationship between compressive yield stresses and solids fractions comparable with other experimental systems. © 1990, Cambridge University Press. All rights reserved.

Description: Experimental studies of low-Reynolds number, pressure-driven core—annular flow in a straight capillary tube are reported. The annular film is thin compared with the radius of the tube, and the viscosity of the film fluid is much larger than the viscosity of the core fluid. Photographs show that the film is unstable under all conditions investigated in the experiment. The film fluid collects in axisymmetric lobes that are spaced periodically along the capillary wall. The spacing of the lobes and their translational velocity correspond closely with the wavelength of the most unstable disturbance and phase velocity calculated from linear stability theory. Eventually, the continued growth of the lobes results in the formation of a fluid lens that breaks the inner core. © 1990, Cambridge University Press. All rights reserved.