ALBERT

Description: The dissolution rates of spheres of two magnesian olivines, two plagioclases, and quartz in tholeiitic basalt have been determined at three super-liquidus temperatures and one-atmosphere pressure. There are considerable differences in the rates among the minerals, e.g. at 1210°, 12° above the liquidus temperature of the basalt, labradorite dissolves at 86 µm/h. and the magnesian olivines at 9 and 14 µm/h. The rates are not time dependent and this, coupled with the existence of concentration gradients in the composition of quenched melt adjacent to partially dissolved crystals, indicates that the dissolution rates are dictated by a combination of diffusion and convection of components to and from the crystal-liquid interface. Values for the activation enthalpy of dissolution are small for quartz and plagioclase (40–50 kcal mol−1) but large for olivine 73–118 kcal mol−1). Dissolution of plagioclase in rock melts seems to be a much more rapid process than crystal growth, whereas olivines apparently dissolve and grow at similar rates. Crystal dissolution is sufficiently slow that ascending, crystal-bearing magma may become superheated and yet fail to dissolve the crystal fraction before quenching; this may be the reason that olivine phenocrysts are often rounded.

Description: Cephalopods may be divided into five types according to their buoyancy. Members of several families such as the Octopodidae, Loliginidae and Ommastrephidae are negatively buoyant and must swim to stay in midwater and are therefore highly muscular animals. Others have mechanisms to make them neutrally buoyant so they can remain suspended in midwater without effort. Nautilus, Spirula and cuttlefishes have low pressure gas-filled chambers and their flesh is muscular and non-buoyant (Denton & Gilpin-Brown, 1973). Squids of one family, the Gonatidae, have a low density oil in their livers to give buoyancy but most of their body is muscular. Some oceanic octopods have very watery tissues in which lighter chloride ions replace sulphate ions (Denton & Shaw, 1961). In 12 of the 26 teuthoid families the buoyancy is provided by low-density ammonia-rich solution in their body and head tissues or in an expanded coelomic cavity (Clarke, Denton & Gilpin-Brown, 1979). These ammoniacal squids are extremely abundant in the oceans of the world and form a large part of the diet of birds, cetaceans, seals and fish (Clarke, 1977). When their biomass is estimated from their utilization by predators it is important to know their properties as food and, in particular, their calorific values. As pointed out by Croxall & Prince in a review of the calorific values of cephalopods (1982), all the known values are of muscular, negatively buoyant species because they are of value as food for humans but no measurements have been made on the ammoniacal or oily species which are probably as important, or even more important, in the economy of the ocean (Clarke, 1983).

Description: The Stewartson-Warn-Warn (SWW) solution for the time evolution of an inviscid, nonlinear Rossby-wave critical layer, which predicts that the critical layer will alternate between absorbing and over-reflecting states as time goes on, is shown to be hydrodynamically unstable. The instability is a two-dimensional shear instability, owing its existence to a local reversal of the cross-stream absolute vorticity gradient within the long, thin Kelvin cat's eyes of the SWW streamline pattern. The unstable condition first develops while the critical layer is still an absorber, well before the first over-reflecting stage is reached. The exponentially growingmodes have a two-scale cross-stream structure like that of the basic SWW solution. They are found analytically using themethod ofmatched asymptotic expansions, enabling the problem to be reduced to a transcendental equation for the complex eigenvalue. Growth rates are of the order of the inner vorticity scale δq, i.e. the initial absolute vorticity gradient dq0/dy times the critical-layer width scale. This ismuch faster than the time evolution of the SWW solution itself, albeitmuch slower than the shear rate du0/dy of the basic flow. Nonlinear saturation of the growing instability is expected to take place in a central region of width comparable to the width of the SWW cat's-eye pattern, probably leading to chaoticmotion there, with very large 'eddy-viscosity ' values. Those values correspond to critical-layer Reynolds numbers λ-1≪ 1, suggesting that formost initial conditions the time evolution of the critical layer will depart drastically from that predicted by the SWW solution. A companion paper (Haynes 1985) establishes that the instability can, indeed, grow to large enough amplitudes for this to happen. The simplest way in which the instability could affect the time evolution of the critical layer would be to prevent or reduce the oscillations between over-reflecting and absorbing states which, according to the SWW solution, follow the first onset of perfect reflection. The possibility that absorption (or over-reflection)might be prolonged indefinitely is ruled out, inmany cases of interest (even if the 'eddy viscosity' is large), by the existence of a rigorous, general upper bound on themagnitude of the time-integrated absorptivity α(t). The bound is uniformly valid for all time t. The absorptivity α(t) is defined as the integral over all past t of the jump in the wave-induced Reynolds stress across the critical layer. In typical cases the bound implies that, nomatter how large tmay become, | α(t)| cannot greatly exceed the rate of absorption predicted by linear theorymultiplied by the timescale on which linear theory breaks down, say the time for the cat's-eye flow to twist up the absolute vorticity contours by about half a turn. An alternative statement is that| α(t) | cannot greatly exceed the initial absolute vorticity gradient dq0/dy times the cube of the widthscale of the critical layer. In typical cases, therefore, a brief answer to the question posed in the title is that the critical layer absorbs at first, at a rate ∝ dq0/dy, whereas after linear theory breaks down the critical layer becomes a perfect reflector in the long-time average. If absolute vorticity gradients vanish throughout the critical layer then the bound is zero, implying perfect reflection for all t. The general conditions for the bound to apply are that the wave amplitude and critical-layer width are uniformly bounded for all t, themotion is two-dimensional, and vorticity is neither created nor destroyed within the critical layer, nor transported into or out of it by diffusion, by advection, or by othermeans. Vorticitymay, however, be diffused or turbulently transported within the critical layer, provided that the region within which the transport acts is of bounded width and the range of values of vorticity within that region remains bounded. There are no other restrictions on wave amplitude, none on wavelength, and no assumptions about flow details within the critical layer nor about the initial vorticity profile q0(y), apart from an assumption that q0(y) has singularities no worse than a finite number of jump discontinuities. The proof, in itsmost general form,makes use of a new finite-amplitude conservation theorem for disturbances to parallel shear flows, generalizing the classical results of Taylor, Eliassen & Palm, and others. © 1985, Cambridge University Press. All rights reserved.

Description: laterally confined horizontal liquid layer is heated from below and cooled from above so that the single-component liquid is frozen in the upper part of the layer. When the imposed temperature difference is such that the Rayleigh number across the liquid is supercritical, there is Benard convection in the liquid layer coupled with the dynamics of the solidification interface. Experimental results are presented for quasi-steady temperature variations at the horizontal boundaries. When the solidified layer is thick compared with the liquid layer a hysteresis loop is found for the heights of the liquid layer in a range of subcritical Rayleigh numbers. The interfacial corrugations exhibit a polygonal structure in this case. At Rayleigh numbers far above the critical value 'bimodal patterns' are observed with two distinct length-scales. Finally a stability chart is given for the various interfacial patterns observed. © 1985, Cambridge University Press. All rights reserved.

Description: Numerical solutions of the Navier–Stokes equations for fully developed, sinusoidal and pulsatile flows in curved tubes are presented for conditions not accessible to analytical perturbation methods. Simulations of physiological pulsatile flows in the aortic arch reveal a wide variety of interesting flow phenomena, including: (1) complex secondary flows with up to seven vortices in the half-tube; (2) cascaded vortex structures with vortices embedded within vortices; (3) strong secondary flows with associated wall shear stress nearly as large as the axial component; (4) reversal of axial-flow direction at the inside wall; (5) peak axial wall shear stress at the inside wall; (6) highest r.m.s. wall shear stress at the inside wall; and (7) oscillatory impedance, which is accurately described by straight-tube theory. © 1985, Cambridge University Press. All rights reserved.

Description: As a uniformly coiled pipe is wound progressively tighter, centrifugal acceleration would be expected to drive the axial flow increasingly towards the outer wall of the pipe bend. Instead, the effect of bend curvature R is found experimentally to become fully expressed at small curvature ratios (a/R 〈 0.02), where a is the pipe radius. No further increase in the axial skew is observed inmore tightly coiled pipe sections (0.02 ≤ a/R ≤ 0.20). In this 'asymptotic' regime where pipe curvature is unimportant, the developing axial skew intensifies as ≈ [(Re— 100) L/a]¼, where Re = 2Wa/v and L is the entrance length. These results suggest that the action of centrifugal force remains balanced by swirl as flow develops in tightly coiled pipes, while in loosely coiled pipes the development of centrifugal effects lags the growth of swirl. © 1985, Cambridge University Press. All rights reserved.

Description: Measurements of rotating equilibrium bubble shapes in the low-gravity environment of a free-falling aircraft are presented. Emphasis is placed on bubbles which intersect the container boundaries. These data are compared with theoretical profiles derived from Laplace's formula and are in good agreement with themeasurements. The interface shape depends on the contact angle, the radius of intersection with the container, and the parameter F, which is ameasure of the relative importance of centrifugal force to surface tension. For isolated bubbles F has amaximum value of 1/2. A further increase in F causes the bubble to break contact with the axis of rotation. For large values of F the bubble becomesmore cylindrical and the capillary rise occurs over a thinner layer in order that the small radius of curvature can generate a sufficient pressure drop to account for the increased hydrostatic contribution. © 1985, Cambridge University Press. All rights reserved.

Description: The influence of a transverse sound wave on vortex shedding from a rigid circular cylinder in a duct has been explored at Reynolds numbers from 20000 to 40000. In the absence of sound, the vortex shedding is found to consist of strings of coherent cyclic events which have frequencies that wander randomly about the nominal vortex-shedding frequency. Application of sound at the vortex-shedding frequency eliminates this wander and correlates the shedding along the cylinder axis. The frequency of vortex shedding can be shifted by sound applied either above or below the nominal vortex-shedding frequency. This entrainment is produced by the velocity induced by the sound wave rather than by the sound pressure. These phenomena are also observed in tube rows. © 1985, Cambridge University Press. All rights reserved.

Description: Long axisymmetric liquid zones are subject to axial temperature gradients which induce steady viscous flows driven by thermocapillarity. The approximately parallel flow in a cylindrical zone is examined for linearized instabilities. Capillary, surface-wave and thermalmodes are found. Capillary breakup can be retarded or even suppressed for small Prandtl number and large Biot number B, whichmeasures heat transfer from the liquid to the surrounding atmosphere. In the limiting case B→∞ the zone becomes an isothermal jet subject to axial 'wind stress' on its interface. It is then possible to suppress capillary breakup entirely so that one canmaintain long coherent jets. © 1985, Cambridge University Press. All rights reserved.