The statistics of a passive scalar in field-guided magnetohydrodynamic turbulence

A variety of studies of magnetised plasma turbulence invoke theories for the advection of a passive scalar by turbulent fluctuations. Examples include modelling the electron density fluctuations in the interstellar medium, understanding the chemical composition of galaxy clusters and the intergalactic medium, and testing the prevailing phenomenological theories of magnetohydrodynamic turbulence. While passive scalar turbulence has been extensively studied in the hydrodynamic case, its counterpart in MHD turbulence is significantly less well understood. Herein we conduct a series of high-resolution direct numerical simulations of incompressible, field-guided, MHD turbulence in order to establish the fundamental properties of passive scalar evolution. We study the scalar anisotropy, establish the scaling relation analogous to Yaglom’s law, and measure the intermittency of the passive scalar statistics. We also assess to what extent the pseudo Alfvén fluctuations in strong MHD turbulence can be modelled as a passive scalar. The results suggest that the dynamics of a passive scalar in MHD turbulence is considerably more complicated than in the hydrodynamic case.     

1) I. A. H. S. / A. I. H. S.

Abstract

A simple method is used to study the response of runoff in the Sahel to climate change. The statistical characteristics of rainfall are calculated over the western part of the Sahel for the period 1961–1990, using the BADOPLU network. Daily rainfall is simulated using a Markov process with Weibull distribution for rainfall depths. Runoff is modelled using a conceptual SCS model and the curve numbers are calculated for West Africa. Climate change is provided by simulations using the Arpège GCM (Scenario A1B), and a perturbation method is used on the parameters which describe the rainfall. Changes in rainfall are assumed to occur through increases in frequency, not intensity. Using Arpège, runoff is mainly found to increase, in depth and in number of events, by the end of the 21st century. Changes in evaporation and land use are not included in the analysis. The impact of this 21st century potential climate change (rainfall) on the runoff is found to be of the same magnitude as the impact of changes in land use.     

A detailed study of the duality relation for the least squares adjustment in euclidean spaces

The Euclidean spaces with their inner products are used to describe methods of least squares adjustment as orthogonal projections on finite-dimensional subspaces. A unified Euclidean space approach to the least squares adjustment methods “observation equations” and “condition equations” is suggested. Hence not only the two adjustment solutions are treated from the view-point of Euclidean space theory in a unified frame but also the existing duality relation between the methods of “observation equations” and “condition equations” is discussed in full detail. Another purpose of this paper is to contribute to the development of some familiarity with Euclidean and Hilbert space concepts. We are convinced that Euclidean and Hilbert space techniques in least squares adjustment are elegant and powerful geodetic methods.     

Morphology and structure of the Galapagos Rise

Geophysical data collected on three U.S. Naval Oceanographic Office cruises to the Galapagos Rise are presented. These data allow definition of the morphology and structure of the Galapagos Rise.A postulated “hot spot” beneath the Galapagos platform is suggested as the cause of: (1) decreased seismicity along the spreading center for a 400 km E—W distance from the islands; (2) distinctive petro-chemistry of tholeiites from the islands and adjacent oceanic crust generated by the Galapagos Rise; (3) high-amplitude magnetic anomalies in a 1,000 km E—W band including and just north of the Galapagos platform; and (4) morphologic shape and the regionally elevated sea floor of the Galapagos Rise as it approaches the insular platform.     

The geology of the Taparko gold deposit, Birimian greenstone belt, Burkina Faso, West Africa

The Taparko gold deposit, located in the eastern branch of the Proterozoic Birimian Bouroum-Yalogo greenstone belt (Burkina Faso) consists of a network of quartz veins developed in a N 170° trending shear zone (250 m wide, 4 km long) superimposed on the regional Birimian structural pattern. The quartz vein network is composed of: (a) a dominant array of quartz veins (type 1), parallel to the shear zone and comprising strongly deformed dark quartz exhibiting foliation, layering, ribbon, tension gashes, etc.; (b) oblique and subparallel related veins (type 2) of gray to white weakly deformed quartz crosscutting the dominant quartz veins resulting in breccia structures; and (c) shallow dipping veins (type 3), cross-cutting veins types 1 and 2 and filled by undeformed white buck structure quartz. Cross-cutting relationships and different quartz types in different veins and within individual veins imply a concomitant filling of the veins during the progressive deformation. Initial sinistral transcurrent shearing evolved with time to sinistral reverse shearing. Metallic minerals occur only in type 1 and 2 veins and were deposited in two stages, with native gold being related to second stage sulfides. Gold (and chalcopyrite) precipitated preferentially upon the surfaces of fractured pyrite grains in low-pressure sites (pressure shadow zones) around and/or within the sulfide grains (along subsequently annealed fractures). The formation of the South Taparko deposit can be divided into a succession of events: (a) during the first event, N 170°-directed sinistral transcurrent shearing resulted in a N 20° mylonitic foliation and fractured rock which allowed H₂O-, CO₂- and SiO₂-rich fluids to circulate and deposit quartz with buck texture; (b) during the second event, type 1 quartz was strongly deformed and type 2 veins formed with sigmoidal shapes as viewed on a horizontal plane; and (c) during the third event, the sinistral transcurrent shearing evolved to sinistral reverse shearing and the deformation style evolved correspondingly from ductile to brittle-ductile. During the last phase of deformation gold nucleated and deposited in low-pressure zones. Received: 9 July 1997 / Accepted: 23 March 1998     

Analysis of the weightiness of site effects on reinforced concrete (RC) building seismic behaviour: The Adra town example (SE Spain)

The damage distribution in Adra town (south‐eastern Spain) during the 1993 and 1994 Adra earthquakes (5.0 magnitude), that reached a maximum intensity degree of VII (European Macroseismic Scale (EMS scale)), was concentrated mainly in the south‐east zone of the town and the most relevant damage occurred in reinforced concrete (RC) buildings with four or five storeys. In order to evaluate the influence of ground condition on RC building behaviour, geological, geomorphological and geophysical surveys were carried out, and a detailed map of ground surface structure was obtained. Short‐period microtremor observations were performed in 160 sites on a 100m × 100m dimension grid and Nakamura's method was applied in order to determine a distribution map of soil predominant periods. Shorter predominant periods (0.1–0.3 s) were found in mountainous and neighbouring zones and larger periods (greater than 0.5 s) in thicker Holocene alluvial fans. A relationship T = (0.049 ± 0.001)N, where T is the natural period of swaying motion and N is the number of storeys, has been empirically obtained by using microtremor measurements at the top of 38 RC buildings (ranging from 2 to 9 storeys). 1‐D simulation of strong motion on different soil conditions and for several typical RC buildings were computed, using the acceleration record in Adra town of the 1993 earthquake. It is noteworthy that all the aforementioned results show the influence of site effects in the degree and distribution of observed building damage. Copyright © 2007 John Wiley & Sons, Ltd.