ALBERT

Description: The laminar viscous flow in the gap between two concentric spheres is investigated for a rotating inner sphere. The solution is obtained by solving the Navier-Stokes equations by means of finite-difference techniques, where the equations are restricted to axially symmetric flows. The flow field is hydrodynamically unstable above a critical Reynolds number. This investigation indicates that the critical Reynolds number beyond which Taylor vortices appear is slightly higher in a spherical gap than for the flow between concentric cylinders. The formation of Taylor vortices could be observed only for small gap widths s ≦ 0·17. The final state of the flow field depends on the initial conditions and the acceleration of the inner sphere. Steady and unsteady flow modes are predicted for various Reynolds numbers and gap widths. The results are in agreement with experiment if certain accuracy conditions of the finite-difference methods are satisfied. It is seen that the equatorial symmetry is of great importance for the development of the Taylor vortices in the gap. © 1982, Cambridge University Press. All rights reserved.

Description: New radiocarbon dates, carbon and oxygen isotope analyses of mollusks and marl, and palynologic analysis have clarified age relationships at the Corry kettle bog in northwestern Pennsylvania. A 4000-yr difference in radiocarbon dates between basal peat and marl top, previously interpreted as caused by the presence of an unconformity, is reinterpreted as due to “hard-water effects” from carbonate bedrock and glacial deposits. A radiocarbon date of 14,000 yr from basal marl, previously used as a minimum age for glacial deposition, is also likely too old; instead a similar age is estimated for the base of the underlying lake clay. Radiocarbon dates on marl should be used with caution and supported by isotopic and pollen analyses.

Description: Movement of pack ice in Smith Sound in northern Baffin Bay was observed for April 1975 using the satellite imagery obtained by Landsat. Mean velocity was found to be directed to the south with a magnitude of 4 km d−1. The influence of the wind is discussed and the amount of ice transported from Smith Sound evaluated. The findings show that on a daily average 600 km2 of pack ice was carried out of the area.

Description: In this article the distribution of stress and velocities in glaciers and ice sheets is reinvestigated. We first derive the general equations governing non-linear viscous flow under plane deformations and formulate the relevant boundary conditions, including, in particular, a proper treatment of the accumulation–ablation mechanism. It is then shown how the emerging set of non-linear equations for the established boundary-value problem can be separated into a system covering steady-state problems on the one hand, and transient, time-dependent processes on the other hand. This separation is performed under the assumption that steady-state stresses are larger than the corresponding transient counterparts, suggesting a linearization of the transient equations with regard to the stresses. The steady-state equations are then analysed for the special case of an infinitely long, nearly parallel-sided slab. With the assumption that bottom undulations are small as compared to the glacier thickness it is shown that the original non-linear boundary-value problem can be decomposed into an infinite hierarchy of boundary-value problems defined on the simpler domain of the exactly parallel-sided slab, all of which are linear except for the lowest order one. Since its solution is readily available, the determination of the velocities and stresses due to bedrock protuberances is basically a linear problem, even though the constitutive response may be non-linear.Assuming harmonic bedrock undulations we show for a Navier–Stokes fluid that the transfer of the bedrock undulations to the surface strongly depends on the mean inclination of the slab, but, more importantly, does now show a maximum when plotted as a function of wavelength λ. This result is contradictory to the corresponding results of Budd (1970[a]) and implies serious drawbacks to his calculations of longitudinal stresses and strain-rates in his subsequent article (Budd, 1970[b]). Yet, it is not true that for maximal transfer of bottom protuberances to the surface a distinct wavelength would not exist. The calculations of Budd must rather be extended to include non-linear constitutive behaviour, variations of temperature with depth, and sliding at the bed. It then turns out that under certain circumstances maximal transfer of bottom undulations to the surface in a distinct wavelength domain (3 〈 λ 〈 5) may indeed exist. Sliding at the bed and vertical temperature variation thereby play a decisive role.Equally important is the stress distribution at the base, in particular the influence of the longitudinal strain effects on the latter. Rheological non-linearities, vertical temperature variations, and the sliding law at the bed play an important role and are investigated in detail.For non-linear constitutive behaviour and spatially dependent temperature-variation solutions must be sought numerically. The finite-difference scheme used suggests a generalization of Glen’s flow law so as to account for a nearly linear behaviour at low strain-rates.We conclude with a perspective of possible extensions of the general theory to various other time-dependent and time-independent problems.

Description: The effect of rotation on the flow around an obstacle in a Hele Shaw cell is considered. For the flow outside the strip-shaped boundary layer near the obstacle, it is shown that the rotating and non-rotating cases are related by a simple transformation. The flow in the boundary layer near the obstacle is computed numerically and its relation to the Stewartson E¼ and [Formula Omitted] layers is briefly discussed. © 1981, Cambridge University Press. All rights reserved.

Description: The linear stability properties of the Ekman layer in a rapidly rotating gas have been computed numerically. The two types of instability present in an Ekman layer of a homogeneous fluid, which are usually called classes A and B, respectively, are significantly modified by the compressibility. The critical Reynolds number for the class A instability is found to first increase and then decrease for increasing values of the Mach number. The instability waves of class B are monotonically destabilized as the value of the Mach number increases. In addition, a new class of unstable waves appears for a finite value of the Mach number. © 1984, Cambridge University Press. All rights reserved.

Description: Movement of pack ice in Smith Sound in northern Baffin Bay was observed for April 1975 using the satellite imagery obtained by Landsat. Mean velocity was found to be directed to the south with a magnitude of 4 km d−1. The influence of the wind is discussed and the amount of ice transported from Smith Sound evaluated. The findings show that on a daily average 600 km2of pack ice was carried out of the area.

Description: In this article the distribution of stress and velocities in glaciers and ice sheets is reinvestigated. We first derive the general equations governing non-linear viscous flow under plane deformations and formulate the relevant boundary conditions, including, in particular, a proper treatment of the accumulation–ablation mechanism. It is then shown how the emerging set of non-linear equations for the established boundary-value problem can be separated into a system covering steady-state problems on the one hand, and transient, time-dependent processes on the other hand. This separation is performed under the assumption that steady-state stresses are larger than the corresponding transient counterparts, suggesting a linearization of the transient equations with regard to the stresses. The steady-state equations are then analysed for the special case of an infinitely long, nearly parallel-sided slab. With the assumption that bottom undulations are small as compared to the glacier thickness it is shown that the original non-linear boundary-value problem can be decomposed into an infinite hierarchy of boundary-value problems defined on the simpler domain of the exactly parallel-sided slab, all of which are linear except for the lowest order one. Since its solution is readily available, the determination of the velocities and stresses due to bedrock protuberances is basically a linear problem, even though the constitutive response may be non-linear. Assuming harmonic bedrock undulations we show for a Navier–Stokes fluid that the transfer of the bedrock undulations to the surface strongly depends on the mean inclination of the slab, but, more importantly, does now show a maximum when plotted as a function of wavelength λ. This result is contradictory to the corresponding results of Budd (1970[a]) and implies serious drawbacks to his calculations of longitudinal stresses and strain-rates in his subsequent article (Budd, 1970[b]). Yet, it is not true that for maximal transfer of bottom protuberances to the surface a distinct wavelength would not exist. The calculations of Budd must rather be extended to include non-linear constitutive behaviour, variations of temperature with depth, and sliding at the bed. It then turns out that under certain circumstances maximal transfer of bottom undulations to the surface in a distinct wavelength domain (3 〈 λ 〈 5) may indeed exist. Sliding at the bed and vertical temperature variation thereby play a decisive role. Equally important is the stress distribution at the base, in particular the influence of the longitudinal strain effects on the latter. Rheological non-linearities, vertical temperature variations, and the sliding law at the bed play an important role and are investigated in detail. For non-linear constitutive behaviour and spatially dependent temperature-variation solutions must be sought numerically. The finite-difference scheme used suggests a generalization of Glen’s flow law so as to account for a nearly linear behaviour at low strain-rates. We conclude with a perspective of possible extensions of the general theory to various other time-dependent and time-independent problems.