On the robustness of the toroidal velocity theorem

In dynamo theory the toroidal velocity theorem in its classical version (Elsasser, Phys. Rev. 1946, vol. 69, pp. 106–116, Bullard and Gellman, Phil. Trans. R. Soc. Lond. 1954, vol. A247, pp. 213–278) rules out dynamo action in a spherical conducting volume provided that the fluid is incompressible, the conductivity is uniform, and the velocity field is purely toroidal. We prove in this note that this result is robust in the sense that slight compressibility of the fluid, small non-radial variations and even large radial variations in conductivity, and the presence of a small non-toroidal velocity component do not invalidate the theorem. Moreover, by proper choice of the conductivity distribution modelling the conducting volume, small deviations from spherical symmetry of the conductor can also be taken into account.     

On one generalization of trochoidal waves

Summary The concept of the generalized trochoidal waves discussed in[1] is revised and modified. A new formula defining the auxiliary function (b, c) was found with the aid of the results derived in[3] and some physical considerations.     

The application of a shift theorem analysis technique to multipoint measurements

A Fourier domain technique has been proposed previously which, in principle, quantifies the extent to which multipoint in-situ measurements can identify whether or not an observed structure is time stationary in its rest frame. Once a structure, sampled for example by four spacecraft, is shown to be quasi-stationary in its rest frame, the structure’s velocity vector can be determined with respect to the sampling spacecraft. We investigate the properties of this technique, which we will refer to as a stationarity test, by applying it to two point measurements of a simulated boundary layer. The boundary layer was evolved using a PIC (particle in cell) electromagnetic code. Initial and boundary conditions were chosen such, that two cases could be considered, i.e. a spacecraft pair moving through (1) a time stationary boundary structure and (2) a boundary structure which is evolving (expanding) in time. The code also introduces noise in the simulated data time series which is uncorrelated between the two spacecraft. We demonstrate that, provided that the time series is Hanning windowed, the test is effective in determining the relative velocity between the boundary layer and spacecraft and in determining the range of frequencies over which the data can be treated as time stationary or time evolving. This work presents a first step towards understanding the effectiveness of this technique, as required in order for it to be applied to multispacecraft data.     

On one possible type of upper cyclogenesis

Summary Based on model considerations it is shown that, under certain assumptions, upper cyclogenesis may be expected in the region of the auroral oval as a result of heat released at the time energetic particles of extraterrestrial origin penetrate into the lower stratosphere or even troposphere.

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Book Review: Ertel's Potential Vorticity. (Ertel's Collected Papers,Vol. III). Edited by W. Schröder,Interdivisional Commission on History of IAGA and History Commission of the German Geophysical Society,Bremen - Roennebeck 1997

Studia Geophysica et Geodaetica -     

On one formulation of the frontal wave problem

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On one method of solving the direct gravimetric problem

Summary The general solution of the direct gravimetric problem for homogeneous and inhomogeneous bodies was derived in[1] in the form of Green-type integrals. In the present paper it is proved that this solution simplifies considerably, if the solution of the external Dirichlet problem, defined by conditions(2), is known for a closed surface bounding the attracting body.Dedicated to RNDr Jan Pícha, CSc., on his 60th Birthday     

On forced torsional oscillation of a cylindrical shell of non-homogeneous material by the application of a periodic shearing force at one end

Summary In the present note the author has considered the torsional vibration of a cylindrical shell of non-homogeneous material whose rigidity and density vary linearly with distance from the axis of the shell. It is assumed that one end of the shell is fixed while the other end is acted on by a periodic shearing force, both the inner and the outer curved surface being free from stress at all times.     

Archaeogeophysical-Based Approach for Inca Archaeology: Overview and one operational application

Even if, in recent decades, the use of remote sensing technologies (from satellite, aerial and ground) for archaeology is stepping into its golden age, in Southern America geophysics for preventive archaeology is more recent and less used than in Europe, Central America and Middle East. In this paper, we provide a brief overview and show the preliminary results obtained from the investigations conducted in Chachabamba (Peru). The archaeological area is located on a strategic terrace overlooking three Inca roads, which served the most important ceremonial centres (including Machu Picchu) of the Urubamba Valley also known as the Sacred Valley. In particular, Chachabamba investigations were conducted with two principal aims: (1) to give new impetus to archaeological research with targeted investigations aimed at improving and completing the site’s knowledge framework; (2) to experiment and validate an archaeogeophysical approach to be reapplied in other sites of the Urubamba valley, including Machu Picchu, having similar characteristics as those found in Chachabamba.     

On one method of solving the three-dimensional direct magnetic problem

Summary The solution of the direct magnetic problem is derived for three-dimensional bodies under the assumption that the components of the magnetization vector are analytical functions of the co-ordinates within the body being considered. The solution to the problem is given in the form of Green-type integrals and, much like with gravitational fields of inhomogeneous bodies, it may serve the purpose of solving the problem of the analytical continuation of the external field into the body.     

On one method of solving the two-dimensional direct magnetic problem

Summary In this paper the solution of the direct magnetic problem for two-dimensional bodies, founded on the application of Green's theorem is derived. This solution is derived under the assumption that the components of the magnetization vector have continuous derivatives with respect to the coordinates and that they are continuous within the body. The problem is solved in terms of Green-type integrals for the scalar and vector potential of the magnetostatic field and it may serve the purpose of solving the problem of the analytical continuation of the external field into the body.     

On one integral of equations of motion of relative horizontal flow

Резюме Бьул выведен интеграл уравнений двнженид Лагранжа, соответствующжа, соответствуюший чоступательниым, неустойчивым, тошоидальным волнам на границе раздела двух зональнух течений. Внд границы раздела в течение развития волны меняется, превращаясь из обычной трохоиды в циклоиду. Числовые оценки показывают, что рассматриваемые волны цхематичесски соответствуйт коротким воянам на квазистационарных атмосфернын фронтах.

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Dedicated to Professor Bedřich Ŝalamon on his 85th Birthday     

一种简易探地雷达天线的制作及其应用效果分析

由于商业探地雷达天线价格昂贵,又比较笨重,很多测量参数不能任意修改或修改起来比较困难,且在室内做实验又很不方便,所以,设计一种造价低,小巧方便且效果较好的天线显得很有意义.基于这样的考虑,本文从实用的角度出发,采用半定量化的方式较详细的介绍一种简易探地雷达天线的制作方法,并辅以网络分析仪对其实际应用效果进行分析研究.实验证明,对于常规的探地雷达实验研究,该天线在性能上已达了要求,是有效的,可行的.     

The cowling anti-dynamo theorem

Abstract

The Cowling anti-dynamo theorem is proved using the Bullard and Gellman spectral formulation of kinematic dynamo theory.     

On correct application of one-step inversion of gravity data

One of the main problems on the numerical solution of integral equations is the resolution of input data. Among the integral equations used in geodesy we have the “onestep inversion” based on the first derivative of the Poisson integral, which transforms gravity values on the Earth’s surface to the gravity potential on the reference ellipsoid. In this study, it is shown that the required spatial resolution of the input gravity data on the Earth’s surface for correct one-step inversion depends on the height of the computational region, the fact that if overlooked can cause totally wrong results. Consequently the following two major questions are posed: (i) How could one know whether the spatial resolution of the input gravity data for correct one-step inversion is sufficient? (ii) What should be done if the spatial resolution is not sufficient? By studying the behaviour of the integral kernel, an algorithm is presented which enables an appropriate answer to the former question. In order to address the latter question, a method is proposed to modify the integral kernel which overcomes the adverse effect of insufficient spatial resolution of the input gravity data. Our answers, which possess the novelty of the study, are numerically verified by means of real and simulated gravity data. The numerical results approve the efficiency of the proposed method in solving the problem of insufficient spatial resolution of the input gravity data for correct one-step inversion.     

On possible application of nepheline for alkaline rock dating

Suitability of unmetamorphosed nepheline for alkaline rock dating is examined. It is shown that only a considerable amount (more than 10%) of secondary minerals such as cancrinite, wischnewite, and sometime spreustein (¹) can falsily the results of age determination from nepheline. The possible presence of excess argon in secondary minerals, though rather infrequent, should also be taken into account.