ALBERT

Description: Composite curvature averages for 14C age depth profiles of deep ocean sediment, continental sediment, and soil each indicate a global trend for 14C age increment per cm depth to increase with 14C age over the range for which a definitive statistical sample is available. The global trend indicated for peat profiles is constant 14C age increment per cm depth over the past 10,000 14C yr. Correlation coefficients between changes in 14C yr/cm and maximum profile thickness contradict compaction as an adequate explanation for the global trend indicated by sediment and soil profiles. This trend must be explained by additional factors such as progressively decreasing contamination from older carbon, increasing cosmic ray intensity, decreasing geomagnetic intensity, diminishing 12C in the active biosphere during profile accumulation, and climate factors affecting the rate of accumulation. The diverse trend of peat profiles may indicate climatic conditions more favorable to peat growth during the earlier portion of the past 10,000 yr.

Description: The stability of the viscometric motion of a viscoelastic fluid held between rotating parallel disks with large radii to small-amplitude perturbations is studied for the Oldroyd-B constitutive model. The disturbances are assumed to be radially localized and are expressed in Fourier form so that a separable eigenvalue problem results; these disturbances describe either axisymmetric or spiral vortices, depending on whether the most dangerous disturbance has zero or non-zero azimuthal wavenumber, respectively. The critical value of the dimensionless radius R* for the onset of the instability is computed as a function of the Deborah number De, a dimensionless time constant of the fluid, the azimuthal and radial wavenumbers, and the ratio of the viscosities of the solvent to the polymer solution. Calculations meant to match the experiments of McKinley et al. (1991) for a Boger fluid show that the most dangerous instabilities are spiral vortices with positive and negative angle that start at the same critical radius and travel outward and inward toward the centre of the disk; the axisymmetric mode also becomes unstable at only slightly greater values of R*, or De for fixed R*. The predicted dependence of the value of De for a fixed R* on the gap between the disks agrees quantitatively with the measurements of McKinley et al., when the longest relaxation time for the fluid at the shear rate corresponding to the maximum value of R* is used to define the time constant in the Oldroyd-B model. © 1993, Cambridge University Press. All rights reserved.

Description: The three-dimensional nonlinear oscillations of an isolated, inviscid drop with surface tension are studied by a multiple timescale analysis and pre-averaging applied to the variational principle for the appropriate Lagrangian. Amplitude equations are derived which describe the generic cubic resonance caused by the spatial degeneracy of the eigenfrequencies of the linear normal modes. This resonant coupling leads to the instability of the finite amplitude axisymmetric oscillations to small non-axisymmetric perturbations, as is demonstrated here for the three and four-lobed normal modes. Solutions to the interaction equations that describe finite amplitude, non-axisymmetric travelling-wave solutions are also obtained and their stability is investigated. A non-generic cubic resonance between the two-lobed and four-lobed oscillatory modes leads to quasi-periodic motions. © 1987, Cambridge University Press. All rights reserved.

Description: Moderate-amplitude axisymmetric oscillations of charged inviscid drops held together by surface tension are calculated by a multiple-timescale expansion. The corrections to the drop shape and velocity caused by mode coupling at second order in amplitude are predicted for two-, three-and four-lobed motions of drops with net charge up to the Rayleigh limit Qc= 4π1/2. Resonant oscillations between four-and six-lobed motions occur for total charge values near Qr= (32/3π)1/2and are analysed. Both frequency and amplitude modulation of the oscillation are predicted for drop motions starting from general initial deformations. © 1984, Cambridge University Press. All rights reserved.

Description: Experimental observations and linear stability calculations are presented for the stability of torsional flows of viscoelastic fluids between two parallel coaxial disks, one of which is held stationary while the other is rotated at a constant angular velocity. Beyond a critical value of the dimensionless rotation rate, or Deborah number, the purely circumferential, viscometric base flow becomes unstable with respect to a nonaxisymmetric, time-dependent motion consisting of spiral vortices which travel radially outwards across the disks. Video-imaging measurements in two highly elastic polyisobutylene solutions are used to determine the radial wavelength, wavespeed and azimuthal structure of the spiral disturbance. The spatial characteristics of this purely elastic instability scale with the rotation rate and axial separation between the disks; however, the observed spiral structure of the secondary motion is a sensitive function of the fluid rheology and the aspect ratio of the finite disks. Very near the centre of the disk the flow remains stable at all rotation rates, and the unsteady secondary motion is only observed in an annular region beyond a critical radius, denoted R*1. The spiral vortices initially increase in intensity as they propagate radially outwards across the disk; however, at larger radii they are damped and the spiral structure disappears beyond a second critical radius, R*2. This restabilization of the base viscometric flow is described quantitatively by considering a viscoelastic constitutive equation that captures the nonlinear rheology of the polymeric test fluids in steady shearing flows. A radially localized, linear stability analysis of torsional motions between infinite parallel coaxial disks for this model predicts an instability to non-axisymmetric disturbances for a finite range of radii, which depends on the Deborah number and on the rheological parameters in the model. The most dangerous instability mode varies with the Deborah number; however, at low rotation rates the steady viscometric flow is stable to all localized disturbances, at any radial position. Experimental values for the wavespeed, wavelength and azimuthal structure of this flow instability are described well by the analysis; however, the critical radii calculated for growth of infinitesimal disturbances are smaller than the values obtained from experimental observations of secondary motions. Calculation of the time rate of change in the additional viscous energy created or dissipated by the disturbance shows that the mechanism of instability for both axisymmetric and non-axisymmetric perturbations is the same, and arises from a coupling between the kinematics of the steady curvilinear base flow and the polymeric stresses in the disturbance flow. For finitely extensible dumb-bells, the magnitude of this coupling is reduced and an additional dissipative contribution to the mechanical energy balance arises, so that the disturbance is damped at large radial positions where the mean shear rate is large. Hysteresis experiments demonstrate that the instability is subcritical in the rotation rate, and, at long times, the initially well-defined spiral flow develops into a more complex three-dimensional aperiodic motion. Experimental observations indicate that this nonlinear evolution proceeds via a rapid splitting of the spiral vortices into vortices of approximately half the initial radial wavelength, and ultimately results in a state consisting of both inwardly and outwardly travelling spiral vortices with a range of radial wavenumbers. © 1994, Cambridge University Press. All rights reserved.

Description: Experimental observations and linear stability analysis are used to quantitatively describe a purely elastic flow instability in the inertialess motion of a viscoelastic fluid confined between a rotating cone and a stationary circular disk. Beyond a critical value of the dimensionless rotation rate, or Deborah number, the spatially homogeneous azimuthal base flow that is stable in the limit of small Reynolds numbers and small cone angles becomes unstable with respect to non-axisymmetric disturbances in the form of spiral vortices that extend throughout the fluid sample. Digital video-imaging measurements of the spatial and temporal dynamics of the instability in a highly elastic, constant-viscosity fluid show that the resulting secondary flow is composed of logarithmically spaced spiral roll cells that extend across the disk in the self-similar form of a Bernoulli Spiral. Linear stability analyses are reported for the quasi-linear Oldroyd-B constitutive equation and the nonlinear dumbbell model proposed by Chilcott & Rallison. Introduction of a radial coordinate transformation yields an accurate description of the logarithmic spiral instabilities observed experimentally, and substitution into the linearized disturbance equations leads to a separable eigenvalue problem. Experiments and calculations for two different elastic fluids and for a range of cone angles and Deborah numbers are presented to systematically explore the effects of geometric and rheological variations on the spiral instability. Excellent quantitative agreement is obtained between the predicted and measured wavenumber, wave speed and spiral mode of the elastic instability. The Oldroyd-B model correctly predicts the non-axisymmetric form of the spiral instability; however, incorporation of a shear-rate-dependent first normal stress difference via the nonlinear Chilcott-Rallison model is shown to be essential in describing the variation of the stability boundaries with increasing shear rate. © 1995, Cambridge University Press. All rights reserved.

Description: The steady-state and time-dependent flow transitions observed in a well-characterized viscoelastic fluid flowing through an abrupt axisymmetric contraction are characterized in terms of the Deborah number and contraction ratio by laser-Doppler velocimetry and flow visualization measurements. A sequence of flow transitions are identified that lead to time-periodic, quasi-periodic and aperiodic dynamics near the lip of the contraction and to the formation of an elastic vortex at the lip entrance. This lip vortex increases in intensity and expands outwards into the upstream tube as the Deborah number is increased, until a further flow instability leads to unsteady oscillations of the large elastic vortex. The values of the critical Deborah number for the onset of each of these transitions depends on the contraction ratio B, defined as the ratio of the radii of the large and small tubes. Time-dependent, three-dimensional flow near the contraction lip is observed only for contraction ratios 2 〈 b〈 5, and the flow remains steady for higher contraction ratios. Rounding the corner of the 4:1 abrupt contraction leads to increased values of Deborah number for the onset of these flow transitions, but does not change the general structure of the transitions. © 1991, Cambridge University Press. All rights reserved.

Description: Galerkin finite element approximations are combined with computer implemented perturbation methods for tracking families of solutions to calculate the steady axisymmetric flows in a differentially rotated cylindrical drop as a function of Reynolds number Re, drop aspect ratio and the rotation ratio between the two end disks. The flows for Reynolds numbers below 100 are primarily viscous and reasonably described by an asymptotic analysis. When the disks are exactly counter-rotated, multiple steady flows are calculated that bifurcate to higher values of Re from the expected solution with two identical secondary cells stacked symmetrically about the axial midplane. The new flows have two cells of different size and are stable beyond the critical value Rec. The slope of the locus of Recfor drops with aspect ratio up to 3 disagrees with the result for two disks of infinite radius computed assuming the similarity form of the velocity field. Changing the rotation ratio from exact counter rotation ruptures the junction of the multiple flow fields into two separated flow families. © 1984, Cambridge University Press. All rights reserved.