A nonlinear stability analysis of convection in a generalized incompressible fluid

Abstract

We establish a nonlinear stability result for convection in a generalized incompressible fluid. Both numerical calculations and an asymptotic analysis are carried out. The linear and nonlinear results are shown to be very close in both cases, implying that the region of possible subcritical instabilities is very small.

During this work I was supported by a research studentship awarded by the Science and Engineering Council of the United Kingdom.     

Bioconcentration factors for petroleum hydrocarbons, PAHs, LABs and biogenic hydrocarbons in the blue mussel

Bioconcentration factors (K_bc) for petroleum hydrocarbons, PAHs, LABs and biogenic hydrocarbons in Mytilus edulis were measured in field experiments using time-integrating water samplers. Seven deployments at five sites gave lipid weight K_bcs for total hydrocarbons ranging from 0.99 × 10⁶ to 3.1 × 10⁶ (mean 1.6 × 10⁶)—a narrower range than has been obtained previously. Bioconcentration factors for the PAHs were similar to those for total hydrocarbons where the major hydrocarbon source was oil. However, at other sites the factors for PAHs were an order of magnitude lower than those for petroleum and for hydrocarbons originating from algae. Compositional profiles for the linear alkyl benzenes (LABs) suggested that these compounds were assimilated primarily from the dissolved phase, despite their greater abundance on particles.     

Seafloor hydrothermal activity and spreading rates: the eocene carbon dioxide greenhouse revisited

A suggestion has been made that enhanced rates of hydrothermal activity during the Eocene could have caused a global warming by adding calcium to the ocean and pumping CO₂ into the atmosphere (Owen and Rea, 1984). This phenomenon was purported to be consistent with the predictions of the CO₂ geochemical cycle model of Berner, Lasaga and Garrels (1983) (henceforth BLAG). In fact, however, the BLAG model predicts only a weak connection between hydrothermal activity and atmospheric CO₂ levels. By contrast, it predicts a strong correlation between seafloor spreading rates and pCO₂, since the release rate of CO₂ from carbonate metamorphism is assumed to be proportional to the mean spreading rate. The Eocene warming can be conveniently explained if the BLAG model is extended by assuming that the rate of carbonate metamorphism is also proportional to the total length of the midocean ridges from which the spreading originates.     

Correlated Nd,Sr and Pb isotope variation in Walvis Ridge basalts and implications for the evolution of their mantle source

Basement intersected in DSDP holes 525A, 528 and 527 on the Walvis Ridge consists of submarine basalt flows and pillows with minor intercalated sediments. These holes are situated on the crest and mid and lower northwest flank of a NNW-SSE-trending ridge block which would have closely paralleled the paleo mid-ocean ridge [13, 14]. The basalts were erupted approximately 70 m.y. ago, an age equivalent to that of immediately adjacent oceanic crust in the Angola Basin and consistent with formation at the paleo mid-ocean ridge [14]. The basalt types vary from aphyric quartz tholeiites on the ridge crest to highly plagioclase phyric olivine tholeiites on the ridge flank. These show systematic differences in incompatible trace element and isotopic composition. Many element and isotope ratio pairs form systematic trends with the ridge crest basalts at one end and the highly phyric ridge flank basalts at the other.The low ¹⁴³Nd/¹⁴⁴Nd (0.51238), ²⁰⁶Pb/²⁰⁴Pb (17.54), ²⁰⁸Pb/²⁰⁴Pb (15.47), ²⁰⁸Pb/²⁰⁴Pb (38.14) and high⁸⁷Sr/⁸⁶Sr (0.70512) ratios of the ridge crest basalts suggest derivation from an old Nd/Sm-, Rb/Sr- and Pb/U-enriched mantle source. This isotopic signature is similar to that of alkaline basalts on Tristan de Cunha but offset to significantly lower Nd and Pb isotopic ratios. The isotopic ratio trends may be extrapolated beyond the ridge flank basalts with higher¹⁴³Nd/¹⁴⁴Nd (0.51270), ²⁰⁶Pb/²⁰⁴Pb (18.32), ²⁰⁷Pb/²⁰⁴Pb (15.52), ²⁰⁸Pb/²⁰⁴Pb (38.77) and lower ⁸⁷Sr/⁸⁶Sr (0.70417) ratios in the direction of increasingly Nd/Sm-, Rb/Sr- and Pb/U-depleted source compositions. These isotopic correlations are equally consistent with mixing od depleted and enriched end member melts or partial melting of an inhomogenous, variably enriched mantle source. However, observe ZrBaNbY interelement relationships are inconsistent with any simple two-component model of magma mixing, as might result from the rise of a lower mantle plume through the upper mantle. Incompatible element and Pb isotopic systematics also preclude extensive involvement of depleted (N-type) MORB material or its mantle sources. In our preferred petrogenetic model the Walvis Ridge basalts were derived by partial melting of mantle similar to an enriched (E-type) MORB source which had become heterogeneous on a small scale due to the introduction of small-volume melts and metasomatic fluids.     

Modelling the sustainability and productivity of pastoral systems in the communal areas of Namaqualand

We investigated the effects of rainfall and the number of animals on changes in vegetation and on the output of milk and meat from the communal areas of Namaqualand. Previously published short- and long-term models link processes that range from the levels of tissue (in, for example, the mammary gland), to the milk yields of individual animals, to the growth and survival of their young and to long-term changes in plant species populations at the ecosystem level. These models have been used to study how different factors and management strategies affect livestock productivity and vegetation composition on a 20,000 ha rangeland in Namaqualand. First, the inter-relations between rainfall, stocking rate and productivity were studied using the short-term model. This model shows that in addition to total rainfall and stocking rate, the timing of rainfall within a year also influences doe live weight and survival to the end of the year. When the long-term model is run, using recorded rainfall, predictions of small stock numbers agree closely with livestock data recorded over the same 30-year period. One thousand replicates of 100-year runs of the long-term model were then used to study the probable impact of different upper limits to stock numbers on animal performance. Off take (sales and slaughterings) are maximal when stock numbers are limited to 2000 adults. Animal numbers increase marginally as the limit is increased above this level, but the variability between years in numbers increases. Secondly, the long-term model was used to study the long-term effects of the stocking rate strategies on rangeland condition. The model predicts that although these effects are variable, when moderately degraded range is stocked with an upper limit at the recommended level it is unable to recover to less degraded states over 100 years. Thirdly, the model was used to examine the effects of reduction in stock numbers and slaughtering of kids in a drought year on goat numbers during the subsequent 5 years. Finally, the model predicts that a 10% reduction in mean annual rainfall will lead to a 35% reduction in animal numbers over 200 years.     

Use of a shared tuned mass damper (STMD) to reduce vibration and pounding in adjacent structures

The dynamic response of tall civil structures due to earthquakes is very important to civil engineers. Structures exposed to earthquakes experience vibrations that are detrimental to their structural components. Structural pounding is an additional problem that occurs when buildings experience earthquake excitation. This phenomena occurs when adjacent structures collide from their out‐of‐phase vibrations. Many energy dissipation devices are presently being used to reduce the system response. Tuned mass dampers (TMD) are commonly used to improve the response of structures. The stiffness and damping properties of the TMD are designed to be a function of the natural frequency of the building to which it is connected. This research involves attaching adjacent structures with a shared tuned mass damper (STMD) to reduce both the structures vibration and probability of pounding. Because the STMD is connected to both buildings, the problem of tuning the STMD stiffness and damping parameters becomes an issue. A design procedure utilizing a performance function is used to obtain the STMD parameters to result in the best overall system response. Copyright © 2001 John Wiley & Sons, Ltd.     

Calibration of diatoms along a nutrient gradient in Florida Everglades Water Conservation Area-2A, USA

The relationship between diatom taxa preserved in surface soils and environmental variables at 31 sites in Water Conservation Area 2A (WCA-2A) of the Florida Everglades was explored using multivariate analyses. Surface soils were collected along a phosphorus (P) gradient and analyzed for diatoms, total P, % nitrogen (N), %carbon (C), calcium (Ca), and biogenic silica (BSi). Phosphorus varied from 315-1781 g g^-1, and was not found to be correlated with the other geochemical variables. Canonical correspondence analysis (CCA) was used to examine which environmental variables correlated most closely with the distributions in diatom taxa. Canonical correspondence analysis with forward selection, constrained and partial CCA, and Monte Carlo permutation tests of significance show the most significant changes in diatom assemblages along the P gradient (p < 0.01), with additional species differences correlated with soil C, N, Ca, and BSi.Weighted-averaging (WA) regression and calibration models of diatom assemblages to P and BSi were developed. The diatom-based inference model for soil [P] had a high apparent r² (0.86) with RMSE_boot = 218 g g^-1. Indicator diatom species identified by assessing species WA optima and WA tolerance to [P], such as Nitzschia amphibia and N. palea for high [P] (~1300-1400 g^-1) and Achnanthes minutissima var. scotica and Mastogloia smithii for low [P] (~400-600 g g^-1), may be useful as monitoring tools for eutrophication in WCA-2A as well as other areas of the Everglades. Diatom assemblages analyzed by cluster analysis were related to location within WCA-2A, and dominant taxa within clusters are discussed in relation to the geochemical variables measured as well as hydrology and pH. Diversity of diatom assemblages and a Disturbance Index based on diatom data are discussed in relation to the historically P-limited Everglades ecosystem. Diatom assemblages should be very useful for reconstructions of [P] through time in the Florida Everglades, provided diatoms are well preserved in soil cores.     

Low energy ions in corotating interaction regions at 1 AU: Observations

The spacecraft ISEE-3 was launched in August 1978 and subsequently placed in orbit about the Sun-Earth L1 libration point where it continuously monitored the particles and fields in interplanetary space until mid-1982. The ISEE-3 Energetic Proton Anisotropy Spectrometer makes 3-dimensional intensity measurements of 35–1600 keV, Z ? 1 ions. This data is used in conjunction with simultaneous solar wind plasma and magnetic field data from the same spacecraft to study the properties of ions in interaction regions lying at the leading edges of nine corotating high speed solar wind streams observed during October 1978–July 1979. Seven streams have an enhancement of ? 300 keV ions in the compressed fast stream plasma between the stream interface and interaction region trailing edge. These enhancements are associated with plasma heating to above 3 × 10⁵ K, have soft spectra (spectral index ～ 4.5?6.0) and in five cases show anti-solar streaming in the solar wind frame.