Stability of power-law discs — II. The global spiral modes

This paper reports on the in-plane normal modes in the self-consistent and the cut-out power-law discs. Although the cut-out discs are remarkably stable to bisymmetric perturbations, they are very susceptible to one-armed modes. For this harmonic, there is no inner Lindblad resonance, thus removing a powerful stabilizing influence. A physical mechanism for the generation of the one-armed instabilities is put forward. Incoming trailing waves are reflected as leading waves at the inner cut-out, thus completing the feedback for the swing-amplifier. Growing three-armed and four-armed modes occur only at very low temperatures. However, neutral m  = 3 and m  = 4 modes are possible at higher temperatures for some discs. The rotation curve index β has a marked effect on stability. For all azimuthal wavenumbers, any unstable modes persist to higher temperatures and grow more vigorously if the rotation curve is rising (β < 0) than if the rotation curve is falling (β > 0). If the central regions or outer parts of the disc are carved out more abruptly, any instabilities become more virulent. The self-consistent power-law discs possess a number of unusual stability properties. There is no natural time-scale in the self-consistent disc. If a mode is admitted at some pattern speed and growth rate, then it must be present at all pattern speeds and growth rates. Our analysis — although falling short of a complete proof — suggests that such a two-dimensional continuum of non-axisymmetric modes does not occur and that the self-consistent power-law discs admit no global non-axisymmetric normal modes whatsoever. Without reflecting boundaries or cut-outs, there is no resonant cavity and no possibility of unstable growing modes. The self-consistent power-law discs certainly admit equi-angular spirals as neutral modes, together with a one-dimensional continuum of growing axisymmetric modes.     

Geochemistry of high-grade eclogites and metarodingites from the Central Alps

Analyses for major, minor, and trace element contents of metamorphosed, variably rodingitized mafic rocks demonstrate substantial removal of Na and as much as three-fold gains in Ca as a consequence of rodingitization. Modest declines in Si and Fe can be explained in terms of dilution effects. Losses in K and Ba do not correlate with Ca% and may have been caused by an alteration process not related to the rodingitization. The Ca-metasomatism was not accompanied by a gain in Sr. The relative contents of Ti, Zr, Hf, Y, Co, Sc, and heavy REE show no readily detectable changes, despite the rodingitization (±other alteration) and subsequent metamorphisms, namely, eclogite facies (T800° C, P 20kbar) followed by amphibolite facies, sillimanite zone. Protoliths were tholeiitic basalt or diabase, and gabbro, with trace element contents indicative of a spreading center origin. Trace element and REE patterns indicate low-pressure fractionation of this magma, with plagioclase stable. This petrogenesis is consistent with prior conclusions on the shallow crustal origin of the protolith of the eclogite-metarodingite-garnet lherzolite suite in the Cima Lunga-Adula nappe, Central Alps. Based on their bulk chemical composition, the mafic rocks in this suite could be the equivalent of Mesozoic ophiolitic rocks in the more external parts of the Alps.     

57Fe NCR of Fe phases in “magnetic cassiterites”

A pyralspite garnet from an anomalously magnetic concentrate of a pegmatitic cassiterite ore has been investigated using ⁵⁷Fe nuclear gamma-ray resonance spectroscopy. The quadrupole splitting and isomer shift values of 3.6 mm/s and 1.4 mm/s, respectively, are among the largest observed for Fe²⁺ ions and indicate a very low covalency of the dodecahedral Fe²⁺ — O²-bonds. These data support the more recent and lower value (10.2–10.1 kcal/ mole) of White and Moore (1972) for the CFSE of the dodecahedral Fe²⁺ ion and suggest that the CFSE should be a useful approximation to the site preference energy of Fe²⁺ for this site.     

Long base line tilt and strain measurement

Two types of noise afflict strain and tilt measurement. They may be categorized as “active” noise, which is due to atmospheric pressure variations, temperature variations, water-table variations and so forth; and “passive” or signal-generated noise which is a consequence of the interaction of the strain field of interest with inhomogeneities of material properties local to the measurement site.The reason why both types of noise are normally reduced by the use of long base line instruments is explained and a simple, practical long base line tiltmeter is described.     

Evidence for zonally-trapped propagating waves in the eastern atlantic from satellite sea surface temperature observations

It has been hypothesized (Moore et al., 1978; O'Brien et al., 1978), that equatorial upwelling and subsequent coastal upwelling on the eastern boundary of the Atlantic Ocean are the result of eastward propagating equatorially trapped Kelvin waves in the Atlantic. Concurrent satellite and ship sea surface temperature observations taken during the GATE experiment permit validation of the satellite data as well as relating sea surface temperature (SST) variability to the local current dynamics. A method based on cross-correlations and cross-spectra of the SST field at various locations is utilized to test the Kelvin wave hypothesis. Significant periodic variation of time lags in the SST variability in the eastern Atlantic is observed by the spectral techniques. Satellite data for the 1974 summer show periodic variability which fits either eastward or westward propagating waves with 1 m s^-1 phase speed, i.e., SST supports the quasi-continuous presence of Kelvin or Yanai waves. We find no evidence for a seasonally solitary eastward propagating signal in the eastern Atlantic from SST.     

Petrogenesis of garnet lherzolite, Cima di Gagnone, Lepontine Alps

Garnet lherzolite at Cima di Gagnone has chemical and mineralogical properties similar to those of other garnet lherzolites in the lower Pennine Adula/Cima Lunga Nappe (Alpe Arami, Monte Duria). The Cima di Gagnone occurrence encloses mafic boudins that belong to an eclogite-metarodingite suite common in the numerous neighboring ultramafic lenses. The ultramafic rocks at Cima di Gagnone, including the garnet lherzolite, are interpreted as tectonic fragments of an originally larger lherzolite body that underwent at least partial serpentinization prior to regional metamorphism. This lherzolite body cycled through at least three metamorphic facies: greenschist or blue-schist (as antigorite serpentinite) → eclogite (as garnet lherzolite), pre-Alpine or early Alpine → amphibolite facies (as chlorite-enstatite-tremolite peridotite), Lepontine metamorphism. Relics of titanoclinohumite in the garnet peridotite, as also recorded by Möckel near Alpe Arami, are consistent with this metamorphic history, since they indicate a possible connection with Pennine antigorite serpentinites, e.g., Liguria, Piedmont, Zermatt-Saas, Malenco, Pustertal, all of which have widespread titanoclinohumite belonging to the antigorite paragenesis. Estimated pressures in excess of 20 kbar and temperatures of 800°±50°C for the garnet lherzolite assemblage are not inconsistent with conditions inferred for Gagnone and Arami eclogites. These conditions could have been reached during deep subduction zone metamorphism. It is shown by calculation that the effects of Fe and Cr on the location of the garnet lherzolite/spinel lherzolite phase boundary largely counter-balance each other.     

Heavy metal release by peat erosion in the Peak District,southern Pennines,UK

Upper North Grain (UNG) is a heavily eroding blanket peat catchment in the Peak District, southern Pennines, UK. Concentrations of lead in the near‐surface peat layer at UNG are in excess of 1000 mg kg⁻¹. For peatland environments, these lead concentrations are some of the highest globally. High concentrations of industrially derived, atmospherically transported magnetic spherules are also stored in the near‐surface peat layer. Samples of suspended sediment taken during a storm event that occurred on 1 November 2002 at UNG, and of the potential catchment sources for suspended sediments, were analysed for lead content and the environmental magnetic properties of anhysteretic remanent magnetization (ARM) and saturation isothermal remanent magnetization (SIRM). At the beginning of the storm event, there is a peak in both suspended sediment and associated lead concentration. SIRM/ARM values for suspended sediment samples throughout the storm reveal that the initial ‘lead flush’ is associated with a specific sediment source, namely that of organic sediment eroded from the upper peat layer. Using the magnetic ‘fingerprinting’ approach to discrimination of sediment sources, this study reveals that erosion of the upper peat layer at UNG is releasing high concentrations of industrially derived lead (and, by inference, other toxic heavy metals associated with industrial particulates) into the fluvial systems of the southern Pennines. Climate‐change scenarios for the UK, involving higher summer temperatures and stormier winters, may result in an increased flux both of sediment‐associated and dissolved heavy metals from eroding peatland catchments in the southern Pennines, adversely affecting the quality of sediment and water entering reservoirs of the region. Copyright © 2005 John Wiley & Sons, Ltd.     

Controlled moraines: origins,characteristics and palaeoglaciological implications

Controlled moraines are supraglacial debris concentrations that become hummocky moraine upon de-icing and possess clear linearity due to the inheritance of the former pattern of debris-rich folia in the parent ice. Linearity is most striking wherever glacier ice cores still exist but it increasingly deteriorates with progressive melt-out. As a result, moraine linearity has a low preservation potential in deglaciated terrains but hummocky moraine tracts previously interpreted as evidence of areal stagnation may instead record receding polythermal glacier margins in which debris-rich ice was concentrated in frozen toe zones. Recent applications of modern glaciological analogues to palaeoglaciological reconstructions have implied that: (a) controlled moraine development can be ascribed to a specific process (e.g. englacial thrusting or supercooling); and (b) controlled moraine preservation potential is good enough to imply the occurrence of the specific process in former glacier snouts (e.g. ancient polythermal or supercooled snouts). These assumptions are tested using case studies of controlled moraine construction in which a wide range of debris entrainment and debris-rich ice thickening mechanisms are seen to produce the same geomorphic features. Polythermal conditions are crucial to the concentration of supraglacial debris and controlled moraines in glacier snouts via processes that are most effective at the glacier–permafrost interface. End moraines lie on a process–form continuum constrained by basal thermal regime. The morphological expression of englacial structures in controlled moraine ridges is most striking while the moraines retain ice cores, but the final deposits/landforms tend to consist of discontinuous transverse ridges with intervening hummocks, preserving only a weak impression of the former englacial structure. These are arranged in arcuate zones of hummocky moraine up to 2 km wide containing ice-walled lake plains and lying down flow of streamlined landforms produced by warm-based ice. A variety of debris entrainment mechanisms can produce the same geomorphic signature. Spatial and temporal variability in process–form relationships will lead to the sequential development of different types of end moraines during the recession of a glacier or ice sheet margin.     

Catastrophic landslides,glacier behaviour and moraine formation – A view from an active plate margin

The influence of large bedrock landslides (“rock avalanches”) on the behaviour of glaciers is incompletely recognised. Here we present an example from an active tectonic margin in South Island, New Zealand where large earthquakes leave a significant imprint on glacial records. We demonstrate that terminal moraines on the western side of the Southern Alps record both ‘ordinary’ (i.e. climate-driven) and landslide-initiated glacial advances. Following consideration of the processes involved in rock avalanche-initiated moraine construction we suggest ways of determining the nature of the advance that built the terminal moraine. The implications of these observations are important in breaking the conventional linkage of individual terminal moraines with climate forcing.     

Computing near coastal tidal dynamics from observations and a numerical model

A two-dimensional vertically integrated model of the North Sea is used to compute the distribution of M₂ and M₄ tidal elevations and currents over the region. Comparison of computed and observed elevations and currents in the area shows that the model can accurately reproduce the M₂ tide in the North Sea, although there are difficulties with the M₄ tide particularly in the northern North Sea.Comparison between model and a large number of observations collected in a shallow water region off the east coast of England, revealed that the model can accurately reproduce the tides even in near coastal regions, where model resolution problems can occur. Comparisons of computed and observed M₂ tidal energy fluxes in this region, show that model and observations agree to within the order of 10% (the error associated with the necessary interpolation of the observations in order to compute the energy flux).The problem of computing energy dissipation in the area by subtracting the energy fluxes into and out of the region is shown to be ill-conditioned in that the energy dissipation in the area is comparable to the error in the energy flux. Consequently for the sea region considered here it is not meaningful to compare this energy budget with energy dissipation due to bottom friction.Energy dissipation for the whole of the North Sea is computed using the numerical model and the geographical distribution of dissipation due to bottom friction is given for the M₂ tide.