Towards a realistic theory of the geodynamo

Abstract

The physics of the geodynamo is discussed. The main processes relevant for the buoyancy driven geodynamo are isolated. The successive stages of development of geodynamo theory are briefly described. The mechanism of local turbulence in the Earth's core is explained, and an estimate is presented of the turbulent transport of density inhomogeneities in the Earth's core. The significance of this turbulent transport to the geodynamo mechanism is stressed. The general scheme of the complete geodynamo theory of the future is outlined.     

Theoretical analyses of acidization dissolution front instability in fluid‐saturated carbonate rocks

This paper presents an instability theory that can be used to understand the fundamental behavior of an acidization dissolution front when it propagates in fluid‐saturated carbonate rocks. The proposed theory includes two fundamental concepts, namely the intrinsic time and length of an acidization dissolution system, and a theoretical criterion that involves the comparison of the Zhao number and its critical value of the acidization dissolution system. The intrinsic time is used to determine the time scale at which the acidization dissolution front is formed, while the intrinsic length is used to determine the length scale at which the instability of the acidization dissolution front can be initiated. Under the assumption that the acidization dissolution reaction is a fast process, the critical Zhao number, which is used to assess the instability likelihood of an acidization dissolution front propagating in fluid‐saturated carbonate rocks, has been derived in a strictly mathematical manner. Based on the proposed instability theory of a propagating acidization dissolution front, it has been theoretically recognized that: (i) the increase of the mineral dissolution ratio can stabilize the acidization dissolution front in fluid‐saturated carbonate rocks; (ii) the increase of the final porosity of the carbonate rock can destabilize the acidization dissolution front, while the increase of the initial porosity can stabilize the acidization dissolution front in fluid‐saturated carbonate rocks; (iii) the increase of the mineral dissolution ratio can cause an increase in the dimensionless propagation speed of the acidization dissolution front; (iv) the increase of the initial porosity can enable the acidization dissolution front to propagate faster, while the increase of the final porosity can enable the acidization dissolution front to propagate slower in the acidization dissolution system. Copyright © 2012 John Wiley & Sons, Ltd.     

我国工程地质现状与发展方向

本文回顾了我国工程地质及其分支学科的发展和现状,指出了我国工程地质工作中存在的主要问题以及今后的发展趋向。     

地震拓扑预测

本文对地震参数建立了地震拓扑空间并把灰色系统理论中的拓扑预测方法引入地震预测之中,研究地震长趋势的预测问题。     

输水管网模糊地震可靠性的 Monte Carlo 法分析程序

本文详细介绍了笔者所建议的运用模糊图理论和方法进行城市输水管网的地震可靠性分析途径和计算程序。对于输水管网中每段管道的震害预测,建立了相应的专家系统。在此基础上,定义了管网系统的模糊可靠性,更好地反映了人们对于管道损坏状态估计的模糊性和对可靠性要求上的模糊性。以模糊矩阵来描述输水管网的状态是十分方便的。通过计算模糊矩阵的传递闭包,极易找出最短路、关键段等。由于地震作用和管道抗震能力都是随机的,因此整个管网系统的可靠性分析是藉助Monle Carlo法进行的。以Monle Carlo法对模糊图进行分析,从而得到管网的地震可靠性,这还是首次。用PASCAL和PROLOG编制了在微机上实用的计算机程序,特别是以智能语言PROLOG编制的程序,更有许多特色。由于采用了一些技巧,使在微机上可以分析相当大的系统,为城市抗震防灾工作提供了一个有力的工具。     

Body force circulations in a compressible atmosphere: Key concepts

The body force circulation problem of Eliassen is extended to spherical geometry and a quasi-compressible atmosphere using the zonally symmetric tidal theory. The concept of body force circulation is generalized to include the effects of mechanical friction and Newtonian cooling. This viewpoint is conceptually advantageous when the circulation is driven by body forces against radiative relaxation. The resulting linear theory is qualitatively useful in middle atmosphere applications, including the equatorial momentum source for which an analytic solution has not been given previously. Further generalizations of the theory are possible by including dynamical and photochemical feedback effects.     

Dimension and entropy in the soil-covered landscape

Both the Hausdorff dimension and the K-entropy supply a measure of the irregularity of the landspace surface. The relationship between the two measures is investigated over a variety of terrains in Britain and a method of calculating the entropy is checked against an independent estimate of the dimension with reasonable agreement. The calculation of the K-entropy requires that the landscape surface be represented by an homogenous ergodic random field. This condition is satisfied by the tendency of soil-covered terrains to progressively approximate to a form well represented by a Gaussian field. Gaussian random fields can either be very smooth, possessing derivatives of all orders at every point or they are highly irregular and non-differentiable everywhere. Within the regular conceptualization the Rice-Kac theory is used to predict the numbers of crossing points and the extent of excursion sets. These predictions are tested against an example terrain from the High Weald of East Sussex with very good agreement, apart from predictions of local maxima. A worked example of the calculation of the K-entropy is given as an appendix. The potential role of information theory in geomorphology extends beyond the use made of entropy in this investigation. In particular ergodic theory has important practical and theoretical implications.     

Explorations into the formal structure of drainage basins

Every basin of higher than first order is drained by a channel network composed of two subnetworks. Their basins are separated by a drainage divide line, called the basin divider, which is the primary organizing feature of the main basin. Each basin of magnitude n contains n – 1 subnetworks of higher order, and is therefore organized by a set of n – 1 dividers. The dividers and the basin boundary are interconnected in a graph called the divider network of the basin; in graph-theoretic terms this network forms a tree and has the same magnitude and link numbers as the channel network draining the basin. While the subbasins and subnetworks of a drainage basin form a nesting hierarchy, the corresponding dividers do not; indeed, any two dividers share at most one node in common, and whether they do so is independent of whether the corresponding subbasins are nesting or disjoint. However, the dividers of nesting basins are linked by recursive relationships which permit the derivation of a set of algebraic equations; these equations relate the dividers of a basin to other basin components; for example, their combined length is equal to half the length of all first-order basin boundaries minus the length of the main basin boundary. The second part of the paper explores the dependence of the divider length on other basin parameters. The expected length, as predicted by the assumption of topological randomness, is clearly rejected by the data. An alternative approach (regression) is based on the observed magnitudes of the subbasins separated by each divider, and is reasonably successful in estimating divider length. The last section introduces the concept of the standardized basin defined by a boundary length of unity; the estimated lengths of the basin divider and the basin boundary permit an approximate reconstruction of the idealized basin shape and the location of the divider in it.