The role of the helicity spectrum function in turbulent dynamo theory

Abstract

It is shown that, for general homogeneous turbulence, the anti-symmetric part of the spectrum tensor can be expressed in terms of a single scalar function H(k,ω) (the helicity spectrum function). Under the first-order smoothing approximation, the coefficients α _ij β _ijk in the expansion of the mean electromotive force in terms of the mean magnetic field are determined; α _ij is a weighted integral of H(k,ω), and β _ijk contains a part β(a)ijk which is likewise a weighted integral of H(k, ω). When the turbulence is axisymmetric, β(a)ijk contains Rädler's (1969a) “Ω ∧ J-effect”. It is shown that when the turbulence is statistically symmetric about a plane perpendicular to the axis of symmetry, then βij = O but the Rädler effect is non-zero. Explicit expressions for αij and βijk are given when the velocity field is generated by random forcing in a rotating medium. Finally, it is shown by means of a local analysis that the Rädler effect, in conjunction with uniform mean shear, can give rise to non-oscillatory dynamo action, and it is argued that this effect may be significant in the well-mixed interior of a stellar convection zone, where by symmetry the α-effect may be weak.     

Reflection of hydrostatic mountain waves from spatially nonuniform layers

Abstract

The steady, hydrostatic, inviscid, Boussinesq flow of a stably stratified fluid over a bell-shaped ridge is investigated within the framework of a linear model. The three layer model atmosphere introduced is such that the Brunt-Väisälä frequency is constant in each layer but the interfaces of the middle layer are allowed to vary gently in the cross-ridge direction. In essence, the model can be tuned in both vertical and horizontal directions. These cross-ridge variations can produce significant differences in both the cross-ridge surface wind and the surface drag compared to the response obtained by use of a horizontally uniform reflecting layer. These changes are sensitive to both the vertical location of the middle layer and to the slope of its lower interface at the ridge crest. Many of these features are explained by means of a conventional layered-model analysis.     

Three-dimensional primary instabilities of a stratified,dissipative, parallel flow

Abstract

We demonstrate the existence of a class of dissipative, stratified, parallel shear flows which, as a consequence of linear supercritical instability, evolve directly into three-dimensional flows without the requirement for an intermediate two-dimensional finite-amplitude state. This represents a counter-example to a common misinterpretation of Squire's theorm, namely that the fastest-growing unstable mode of a dissipative parallel shear flow must be two-dimensional.     

A Comparison of Design-Based and Model-Based Analysis of Sample Surveys in Geography

Sample surveys are routinely used to gather primary data in human geography research. We highlight the difference between design-based analysis and model-based analysis of sample surveys and emphasize the advantages of using the design-based approach with these data. As an example, we demonstrate differences in results from model-based and design-based analyses of cancer prevalence in a population of predominantly minority women in North Carolina and South Carolina. The results from the two approaches reveal differences in population estimates of numerous variables and a different conclusion regarding the significance of an explanatory variable in a logistic regression model to explain colon cancer prevalence.     

ANNUAL BUSINESS MEETING,SEATTLE April 30, 1974

Samples used to estimate discrete choice models in geography and regional science are typically assumed to be simple random samples. This assumption is not always met with existing samples. Furthermore, data collection is usually less costly if a stratified sampling strategy is adopted. Existing sampling theory suggests that stratified sampling can affect the consistency of parameter estimates. This paper reviews the salient points of this theory and relates theory to practice by means of a simple example on housing choice by elderly.     

山地陡倾小交角层状岩体隧道围岩变形模拟

陡倾小交角层状岩体隧道围岩变形特征和一般的均质岩体隧道是不一样的。通过有限元计算和模型试验研究手段,以重庆涪南高速公路鸭江隧道工程为例,对陡倾小交角层状岩体隧道开挖过程中围岩的变形特征和机理进行了深入分析。研究结果表明:对于陡倾小交角层状岩体来说,层理面是主要控制结构面,隧道的开挖会导致一定范围内的岩层形成临空面,这部分岩层会向洞室产生滑移,从而引起地表的较大沉降;岩层倾角越大,地表沉降也会随之增大;与一般均质岩体隧道不同,陡倾小交角层状岩体隧道围岩变形具有非对称性,最大变形一般发生在顺层向。研究结论可供今后陡倾层状岩体隧道的施工设计参考。     

南海东北部深水海域大振幅内孤立波SAR遥感仿真研究

为了克服基于两层海洋的内孤立波SAR遥感仿真模型的缺陷,使用基于连续分层海洋模型的GK-dV方程,在南海东北部深水海域进行了大振幅内孤立波传播模拟,模拟输出内孤立波振幅91.0m,半波宽度262.0m。然后使用新建立的基于连续分层海洋模型的内孤立波SAR遥感仿真模型进行了内孤立波反演,反演出内孤立波半波宽度251.5m...     

Discussion on the calculation of the rights protection radius of the geothermal well for stratified thermal reservoir

In order to ensure the sustainable exploitation of geothermal resources and prevent the occurrence of thermal breakthrough during the process of geothermal water reinjection, the authors systematically summarized the calculation formulas of the rights protection radius of the geothermal well in this paper. Three shortcomings in the calculation method of the rights protection radius of the geothermal well were identified through theoretical derivation. (1) The parameter f, which is defined as the ratio of the specific heat of water to that of thermal reservoir rocks, is defective. (2) The value of the thermal reservoir recovery rate defined as 0.15 is relatively unilateral, which is not applicable for geothermal wells with different lithology. (3) The calculation time is fixed as 36 500 d, which is not appropriate for geothermal wells with interval development. Based on the problems above, the authors redefined the parameter f and used variables to replace the previous thermal reservoir recovery rate and exploitation time, which can be identified according to different thermal reservoirs and specific exploitation time. By comparison of the applicable conditions of different calculation formulas of the rights protection radius of the geothermal well, the authors proposed that different calaulation formuas should be chosen based on the relationship of the size between β^-1-α and 3λ. And by comparison of the rights protection radius calculation formulas for the mining well and the recharge well, it is found that the rights protection radius of the mining well is always bigger than that of the recharge well. Finally, Shuiwen residential area of Decheng district was taken as an example to verfity the theoretical results.     

Impressions of the turbulence variability in a weakly stratified,flat-bottom deep-sea ‘boundary layer’

The character of turbulent overturns in a weakly stratified deep-sea is investigated in some detail using 144 high-resolution temperature sensors at 0.7 m intervals, starting 5 m above the bottom. A 9-day, 1 Hz sampled record from the 912 m depth flat-bottom (<0.5% bottom-slope) mooring site in the central-north Alboran Sea (W-Mediterranean) demonstrates an overall conservative temperature range of only 0.05 °C, a typical mean buoyancy period as large as 3 h and a 1 Hz-profile-vertically-averaged turbulence dissipation rate maximum of only 10⁻⁸ m² s⁻³. Nonetheless, this ‘boundary layer’ varies in height between <6 and >104 m above the bottom and is thus not homogeneous throughout; the temperature variations are seldom quiescent and are generally turbulent in appearance, well exceeding noise levels. The turbulence character is associated with small-scale internal waves; examples are found of both shear- and convection-driven turbulence; particular association, although not phase-locked, is found between turbulence variations and tidal rather than with inertial motions; the mean buoyancy frequency of a few times the inertial frequency implies the importance of ‘slantwise convection’ in the direction of the earth rotational vector rather than in the direction of gravity. Such convection is observed both in near-homogeneous and weakly stratified form.     

Effects of anisotropic permeability on stabilization and pore water pressure distribution of poorly cemented stratified rock slopes

Slopes composed of stratified and poorly cemented rocks that fail during heavy rainfalls are typical in the outer zone of Taiwan's Western Foothills. This study investigates how hydraulic conductivity anisotropy influences pore water pressure (PWP) distributed in stratified, poorly cemented rock slopes and related slope stability through numerical simulation. The notion of representing thin alternating beds of stratified, poorly cemented rocks as an equivalent anisotropic medium for ground‐water flow analysis in finite slopes was validated. PWP was then derived in a modelled slope comprising an anisotropic medium with suitable boundary conditions. Simulation results indicate the significance of the principal directions of hydraulic conductivity tensor and the anisotropic ratio on PWP estimation for anisotropic finite slopes. For a stratified, poorly cemented rock slope, estimating PWP utilizing a phreatic surface with isotropic and hydrostatic assumptions will yield incorrect results. Stability analysis results demonstrate that hydraulic conductivity anisotropy affects the slope safety factor and slip surface pattern. Consequently, steady‐state groundwater flow analysis is essential for stratified, poorly cemented rock slopes when evaluating PWP distribution and slope stability. This study highlights the importance of hydraulic conductivity anisotropy on the stability of a stratified, poorly cemented rock slope. Copyright © 2006 John Wiley & Sons, Ltd.