ALBERT

Description: It has been observed by Walters & Davidson (1963) that release of a mass of gas in water sometimes produces a rising toroidal bubble. This paper is concerned with the history of such a bubble, given that at the initial instant the motion is irrotational everywhere in the water. The variation of its overall radius a with time may be predicted from the vertical impulse equation, and it should be possible to make the same prediction by equating the rate of loss of combined kinetic and potential energy to the rate of viscous dissipation. This is indeed seen to be the case, but not before it is recognized that in a viscous fluid vorticity will continually diffuse out from the bubble surface, destroying the irrotationality of the motion, and necessitating an examination of the distribution of vorticity. The impulse equation takes the same form as in an inviscid fluid, but the energy equation is severely modified. Other results include an evaluation of the effect of a hydrostatic variation in bubble volume, and a prediction of the time which will have elapsed before the bubble becomes unstable under the action of surface tension.

Description: The stability is considered of the flow with velocity components [ {0,Omega r[1+O(epsilon^2)],;2epsilonOmega r_0f(r/r_0)} ] (where f(x) is a function of order one) in cylindrical polar co-ordinates (r, ϕ, z), bounded by the rigid cylinders r/r0 = x1 and r/r0 = 1 (0 [les ] x1 〈 1). When ε [Lt ] 1, the flow is shown to be unstable to non-axisymmetric inviscid disturbances of sufficiently large axial wavelength. The case of Poiseuille flow in a rotating pipe is considered in more detail, and the growth rate of the most rapidly growing disturbance is found to be 2εΩ.

Description: When pure solvent is separated from a solution of non-zero concentration Cb by a semi-permeable membrane, permeable to solvent (water) but not to solute, water flows osmotically across the membrane towards the solution. Its velocity J is given by J = PΔC, where P is a constant and ΔC is the concentration difference across the membrane. Because the osmotic flow advects solute away from the membrane, ΔC is usually less than Cb, by a factor γ which depends on the thickness of and flow in a concentration boundary layer. In this paper the layer is analysed on the assumption that the stirring motions in the bulk solution, which counter the osmotic advection, can be represented as two-dimensional stagnation-point flow. The steady-state results are compared with those of the standard physiological model in which the layer has a given thickness δ and the osmotic advection is countered only by diffusion. It turns out that the standard theory, although mechanistically inadequate, accurately predicts the value of γ over a wide range of values of the governing parameter β = PCbδ/D (where D is the solute diffusivity) if δ is given by where ν is the kinematic viscosity of the fluid and α is the stirring parameter. The final approach to the steady state is also analysed, and it is shown to be achieved in a time scale (D/ν)1/3/αk′ where k′ is a dimensionless number whose dependence on β is computed. Moreover, if β exceeds a certain critical value (≈ 10), the approach to the steady state is not monotonic but takes the form of a damped oscillation (in practice, however, β is unlikely to rise significantly above 1). The theory is extended to the case where the solute concentration is non-zero on both sides of the membrane and in that case it is shown that J is bounded as β → ∞. © 1980, Cambridge University Press. All rights reserved.

Description: Experiments are performed on steady and impulsively started flow in an approximately two-dimensional closed channel, with one wall locally indented. In plan the indentation is a long trapezium which halves the channel width; the inclination of the sloping walls is approximately 5.7°, and these tapered sections merge smoothly into the narrowest section via rounded corners. The Reynolds number Re = a0u0/v (ao= unindented channel width, u0= steady mean velocity in the unindented channel) lies in the range 300 ^ Re ^ 1800. In steady flow, flow visualization reveals that separation occurs on the lee slope of the indentation, at a distance downstream of the convex corner which decreases (tending to a non-zero value) as Re increases. There is no upstream separation, and there is some evidence of three-dimensionality of the flow in the downstream separated eddy. Pressure measurements agree qualitatively but not quantitatively with theoretical predictions. Unsteady flow visualization reveals that, as in external flow, wall-shear reversal occurs over much of the lee slope (at dimensionless time τ = ū0t/a0≈ 4) before there is any evidence of severe boundary-layer thickening and breakaway. Then, at τ ≈ 5.5, a separated eddy develops, and its nose moves gradually upstream from the downstream end of the indentation to its eventual (τ ≈ 75) steady-state position on the lee slope. At about the same time as the wall-shear reversal, wavy vortices appear at the edge of the boundary layer on both walls of the channel, and (for Re 〈 750) subsequently disappear again; these are interpreted as manifestations of inflection-point instability and not as intrinsic aspects of boundary-layer separation. Pressure measurements are made to investigate the discrepancy between the actual pressure drop across the lee slope and that predicted on the assumption that energy dissipation is quasi-steady. This discrepancy has a maximum value of approximately 1.5ρū20 (ρ = fluid density), and decays to zero by the time τ ≈ 7. © 1983, Cambridge University Press. All rights reserved.

Description: Three characteristics of the output of a forest-stand simulation model were matched to pollen records of actual vegetation in central Tennessee. Temporal shifts of individual pollen taxon frequencies were compared to shifts of individual plant species frequencies in simulated biomass for the last 16,000 yr. Individual pollen profiles (temporally ordered species frequencies) were also compared to simulated biomass profiles during that period. Modern ratios of pollen to vegetation composition (R values) were compared with those calculated from simulated biomass percentages and fossil pollen percentages. The model output was similar to the comparable characteristics of the pollen record. The model output is therefore a plausible description of vegetation characteristics at the site of pollen deposition in central Tennessee. The model produced information unavailable from other sets of prehistoric data. This information describes the invasion and growth of the yellow-poplar which produces no windborne pollen, and of palynologically indistinguishable oak and pine species. These results suggest that many paleoecological questions can be answered through appropriate simulation modeling studies.

Description: Pollen was collected from modern alluvium and from the atmosphere to document the nature and amount of paleoenvironmental information reflected by alluvial pollen chronologies. Results indicate that pollen in alluvium is a homogeneous mixture derived almost entirely from the floodplain itself. The few pollen grains derived from nonfloodplain plant communities and preserved in alluvial sediments are so well mixed that their frequencies no longer reflect the geographic distribution of the specific plant communities in which they originated. In contrast, the abundance of alluvial pollen grains, derived from the major floodplain taxa (Chenopodiineae, Ambrosia type), varies with summer and winter climate. This annual variation is preserved in alluvial pollen assemblages through a combination of processes within sedimentation basins involving discontinuous deposition events and mechanical pollen degradation. The high-frequency, wide-amplitude pollen variance in alluvial pollen assemblages contrasts with the low-frequency, narrow-amplitude pollen variance in sediments of lakes and ponds. The slight geographic variance in alluvial pollen assemblages, in contrast to the large variance in soil pollen, allows use of alluvial pollen to infer climate throughout the watershed in which pollen is sampled.