Typical properties of dynamic systems and the instability of hydrodynamic flows

Summary Based on Peixot's theorem of topological dynamics, the unstable behaviour of hydrodynamic flows on a two-dimensional annuloid T ² is analysed. The generating property is the curvature of the group of S ₀ Diff T ² diffeomorphisms of the (Riemannian) flow region T ² . This group is the configuration space of the ideal fluid flowing on T ² .

---

a m ma u mn u ¶rt;uauu ¶rt;am mu n¶rt;uu¶rt;¶rt;uauu nm a ¶rt; m T ² u¶rt; mu. ¶rt;au m m a m uuann S ₀ Diff T ² ¶rt;uu amu mu ( uaa) T ² . manna m uau nmam ¶rt; u¶rt;a u¶rt;mu a T ² .

     

Heat flow in the upper-silesian coal basin: Re-evaluation of data with special attention to the lithology

Summary The area of the Upper Silesian Coal Basin was characterized by generally high heat flow ranging from 60 to 120 mWm^–2, mean 82±16 mWm^–2, which has been difficult to explain. Therefore all published data on the heat flow in this region (n=37) were summarized and re-evaluated. Special attention was paid to the detailed assessment of the lithological structure and the contribution of the individual rock types to the characteristic in-situ thermal conductivity. Also the thermal conductivity of the coal bearing layers was estimated and its effect on the temperature-depth distribution was investigated. The application of the data obtained for the representative thermal conductivity profiles of the whole drilled section considerably reduced the mean heat flow to 70±8 mWm^–2. The latter value is fully compatible with the tectonic structure of the northern part of the Carpathian Frontal Foredeep. Slightly increased geothermal activity compared with the heat flow field of the adjacent part of the Bohemian Massif corresponds to certain deep geological rejuvenation during the creation of the Western Carpathians.

---

a -uu aa aamum nu uuau mn nma (m 60 ¶rt; 120 m.^–2 nu ¶rt; 82±16 m. ^–2), m ¶rt;a ¶rt u. m u u nm a nua ¶rt;a mn nma (n=37) ¶rt; ¶rt;a ua. ua ¶rt; ¶rt;ma aau umuu aa u u mnn¶rt;mu in situ ¶rt; a¶rt; muna n¶rt;. a a mnn¶rt;m m, a ma, a ma u¶rt;aa an¶rt;u mnam nu. nau n mam ¶rt; nuau mnn¶rt;mu m u amu aa nu am uum ¶rt;u mn nm ¶rt; 70±8 m.^–2. a uua n mam mmu u amu anam a nua. m uumu amumu n au mn n nuaa amu aua mmmmuuau amuuauu nu uauu um ana¶rdt; anam.

     

Spherical harmonic analysis and Fourier transformation

Summary The paper deals with the computation of spherical harmonic coefficients from surface measurements of the magnetic or gravity field of the Earth when the measurements are distributed regularly. The Fourier representation of associated Legendre functions which this procedure makes use of, then enables the harmonic analysis to be transformed to Fourier analysis which has better numerical properties.

---

ama na ama uu uu uum n nm uu aum uuaumau n u a, ¶rt;a mu uu an ammu ma. ¶rt;mau n a¶rt; , m unm mm n¶rt;¶rt;, nm nmauu aau naam aau , m a¶rt;am uu uumu mau.

     

Determination of the geopotential scale factor from satellite altimetry

Summary The geopotential scale factor R ₀ =GM/W ₀ has been determined on the basis of satellite altimetry as R _{0=(6 363 672·5±0·3) m} and/or the geopotential value on the geoid W ₀ =(62 636 256·5±3) m ² s ^–2 . It has been stated that R ₀ and/or W ₀ is independent of the tidal distortion of surface W=W ₀ due to the zero frequency tide.

---

¶rt;a nmu amumuu u ama amnmuaa R ₀ =GM/W ₀ =(6 363 672,5±0,3) m u/uu aunmuaa a nmuu¶rt;a W ₀ =(62 636 256,5±3) m² s^–2. m, m R ₀ u/uu W ₀ auum m nm amu a a nuu ¶rt;au nmu W=W ₀ .

     

Velocities of seismic waves propagating through the Bohemian massif from foci in Poland

mam mm ua a na Pn, Pg, Sn u Sg nu¶rt;u u au -ma. aa, m ¶rt; amu 5° m numa ua¶rt;a ¶rt;am mu a na n au ma¶rt;amu u mu anmau , uu m n u ma¶rt;am¶rt;a. am nmau a uu m anmau mmu aua.     

Forecast of abnormally high solar activity in the next century and of its possible negative effects on the earth

Summary Based on the relation between the relative sunspot number R, the number of sunspot groups f ₀ generated per unit time on the Sun as a whole and their average lifetime T ₀ , and on the extrapolation of time behaviour of f ₀ and T ₀ , it is proved that abnormally high solar activity may be expected in the first half of the 21st century. At this time, the maximum annual relative sunspot numbers R_M of the 11-year cycles should reach values of about 300 units. This abnormally high solar activity in the next century can be understood as the antipole of the Maunderean minimum. This forecast is used to discuss some of the possible consequences of this abnormally high solar activity for the processes on the Earth: changes of climate (heat waves and draughts in Central Europe), in the higher layers of the Earth's atmosphere (anomalous propagation of radio waves, increased effect of the density of the upper atmosphere on the orbits of man-made satellites), in seismicity (increased seismic activity in Europe and Southeast Asia), for technical devices (induced electric currents), in the biosphere. etc.

---

a mu ¶rt; uau a R nm, unn nm f ₀ uu ¶rt;uu u a ë u u ¶rt; n¶rt;ummu uu ₀ , u a manuu ¶rt;a f ₀ u ₀ , naa, m n nu ¶rt; 21 a u¶rt;am uum amum. aua¶rt;u ua a R m¶rt; 11-mu ua m u ¶rt;muam au 300 ¶rt;uu. m uum amum ¶rt; nuam a amun¶rt; a¶rt; uua. a m na ¶rt;am m n¶rt;mu m uum amumu a n nmau a : a uu uama (aa u a n¶rt;a ¶rt; n), a u u am u (aa anmau a¶rt;u, uu n nmmu u am a ¶rt;uu um m), a um (na ua amum n u -m uu), a muu mma (u¶rt;ua muu mu), a u u ma ¶rt;a.

     

On the role of vertical resolution in the analysis of shallow convective fields

Summary The present paper is an attempt to demonstrate the fact that misleading information about the thermodynamic structure of shallow cumulus fields is obtained when standard isobaric level (SIL) data input is used. The 1-D cumulus model serves as the main tool of examination and the reference input data are those of significant levels (SL) in soundings. The computed cloud tops (SIL) exceeded (SL) tops in nearly 80% of the cases and the excesses are more than 1 kilometre in 25% of the cases. Some discrepancies were also found in potential stability analysis. The local changes in equivalent potential temperature may be seriously affected and even falsified. The important role of high resolution in studies of mesoscale phenomena was again accentuated.

---

mam mum ¶rt;aam, m u am u¶rt; ¶rt;a unam ¶rt;a ma¶rt;am uauu (SIL), m num uauu m¶rt;uau mm mu n. ¶rt;m, una nu u¶rt;auu, m ¶rt;a ¶rt; aa, a am n ¶rt; au unm ¶rt;a au ¶rt;aa. auma u a ¶rt; SIL n¶rt;m n au 80% a, a 25% a ¶rt;a a 1 . au ma ma nu aau nmua mumu. aQj uu uam nmua mnam m m aum ua. n¶rt;uam aa aua nmu nu uuu u a.

     

L'ordre du coefficient de récombinaison dans la coucheE

Résumé On propose une méthode de détermination de l'ordre du coefficient équivalent de récombinaison en n'utilisant que les données ionosphériques. A cette fin on évalue l'apport de la vitesse des changements passagersdN _m E/dt dans la densité électroniqueN _m E. L'évaluation se fait en présence d'une série de valeurs choisies de , on observe laquelle des courbes définis _m (t) dans cette étude coïncidera de plus près avec _m (t) mesurée. Les changements de montrés sur la figure 4 sont obtenus de cette manière. La valeur diurne de varie de (0.5÷1) 10^–7 cm³ sec^–1; peu après le lever et peu avant le coucher du soleil devient >10^–7 cm³ sec^–1. Lorsque cos>0, d'après la règle décrcit et devient 10^–8 cm³ sec^–1. Les explications des changements de obtenus de cette manière sont données en rendant compte des changements par rapport aux ions atomiques et moléculaires, à la disparition rapide des ions positifs pendant le coucher du soleil en présence d'un coefficient de récombinaison plus grand et des changements de température eventuels. La symétrie ou l'asymétrie des fréquences critiquesf ₀ E quand cos sont égaux permettent dans la marche diurne de juger de l'ordre de . Toutes ces évaluations indiquent également des valeurs de environ 10^–7 cm³ sec^–1. En précisant des mesures def ₀ E il est possible de définir non seulement l'ordre, mais aussi la valeur de elle-même.

---

Summary A method for the determination of the order of the equivalent recombination coefficient is suggested, by using ionospheric data only. The increase in the speed of temporary changes indN _m /dt in the electronic densityN _m E is estimated for this purpose. The estimation is done with series of selected for the sake of expediency values of , following at the same time which curves _m (t), determined in the course of work, will coincide most closely with the _m (t) measured. The changes in , shown in figure 4, have been obtained in this way. The diurnal value of is in the range of (0.5 to 1) 10^–7 cm³ sec, being >10^–7 cm³ sec a little after sunrise and a little prior to sunset. At cos<0, by rule decreases and becomes 10^–8 cm³ sec. Explanations of the changes thus obtained in are indicated, taking into consideration the relation of atomic and molecular ions, the rapid disappearance of positive ions at sunset with a higher recombination coefficient and eventual temperature changes. From the symmetry or asymmetry of the critical frequencies off ₀ E at equal cos in the course of the day it can also be judged for the order of . All those estimates show values of in the range of 10^–7 cm³ sec. In the case of precise measurements off ₀ E, not only the determination of the order but also the real value of is possible.

     

A new dissipation model based on memory mechanism

Summary The model of dissipation based on memory introduced by Caputo is generalized and checked with experimental dissipation curves of various materials.List of symbols unidimensional stress - unidimensional strain - Q ^–1 specific dissipation function - c(t) creep compliance - m(t) relaxation modulus - c ₀ instantaneous compliance - m equilibrium modulus - (t) creep function - relaxation function - () spectral distribution of retardation times - spectral distribution of relaxation times - c ^*() complex compliance - m ^*() complex modulus - tang loss-tangent     

A numerical study of the heat transfer through a fluid layer with recirculating flow between concentric and eccentric spheres

A numerical study has been made of the heat transfer through a fluid layer with recirculating flow. The outer fluid surface was assumed to be spherical, while the inner surface consisted of a sphere concentrically or eccentrically located with respect to the outer spherical surface. The recirculating flow was assumed to be driven by a gas flow creating stress on the fluid's outer surface so that creeping (low Reynolds number) flow developed in its interior. The present study solves the Stokes equation of motion and the convective diffusion equation in bispherical coordinates and presents the streamline and isotherm patterns.Nomenclature a _i inner sphere radius - a _d outer sphere radius - A ₁ defined by equation (5) - A ₂ defined by equation (6) - B ₁ defined by equation (7) - B ₂ defined by equation (8) - c dimensional factor for bispherical coordinates - C constant in equation (4) - d narrowest distance between the two eccentric spheres - E ² operator defined by equation (1) in spherical coordinates and by equation (21) in bispherical coordinates - G modified vorticity, defined in equation (22) - G ^* non-dimensional modified vorticity, defined in equation (28) - h metric coefficient of bispherical coordinate system, defined in equation (18) - k _w thermal conductivity of water - K ₁ defined by equation (9) - K ₂ defined by equation (10) - N _Re Reynolds number=2a _dU/gn - N _Pe,h Peclet number=2a _dU/ - n integer counter - q heat flux - r radius - r ^* non-dimensional radius=r/a _d - S surface area - t time - t ^* non-dimensional time=t/a _d ² - T temperature - T _o temperature at inner sphere surface - T _a temperature at outer sphere surface - T ^* non-dimensional temperature;=(T–T _o)/(T_a–T_o) - u velocity - u _r radial velocity in spherical coordinates - u angular velocity in spherical coordinates - u radial velocity in bispherical coordinates - u angular velocity in bispherical coordinates - U free stream velocity - u _r ^* =u _r/U - u ^* =u /U - u ^* =u /U - u ^* =u /U Greek symbols a ₁ small displacement - vorticity, defined in equation (17) - ^* non-dimensional vorticity, defined in equation (27) - radial bispherical coordinates - _o bispherical coordinate of inner sphere - _a bispherical coordinate of outer sphere - angular coordinate in spherical coordinates - thermal diffusivity - _w thermal diffusivity of water - kinematic viscosity - angular bispherical coordinate - spherical coordinate - streamfunction - non-dimensional streamfunction for spherical coordinates, = /(U a _d ² ) - ^* non-dimensional streamfunction for bispherical coordinates, defined in equation (26)     

Gravitational potential inside 3-D inhomogeneous earth: A boundary — Value problem for the Poisson equation

Summary The problem of determining the gravitational potential inside the Earth is discussed under assumptions that the 3-D density distribution is known, that the external gravity field is described by known Stokes parameters and, finally, that the smoothed Earth surface is defined by a set of topography coefficients. The spectral method was used to separate the angular and radial parts. The solution of Poisson's equation for the internal gravitational potential was reduced to a system of ordinary differential equations with homogeneous boundary conditions and to a system of linear algebraic equations.

---

¶rt;am na uuaumau nmuaa mu u n¶rt;naa, m um nmam an¶rt;u nmm, m aumau n nua umu mu naamau u, a, m au mnaua nm u a¶rt;am ¶rt; mnauu uum. a¶rt;u u a¶rt;ua am num nma m¶rt;. u au aa ¶rt; maumau nmuaa ¶rt;um u um ¶rt;uua au ¶rt;¶rt;u au uu u um u aauu au.

     

Uncertainties in field-line tracing in the magnetosphere. Part II: the complete internal geomagnetic field

The discussion in the preceding paper is restricted to the uncertainties in magnetic-field-iine tracing in the magnetosphere resulting from published standard errors in the spherical harmonic coefficients that define the axisymmetric part of the internal geomagnetic field (i.e. g_n⁰ ± g_n⁰). Numerical estimates of these uncertainties based on an analytic equation for axisymmetric field lines are in excellent agreement with independent computational estimates based on stepwise numerical integration along magnetic field lines. This comparison confirms the accuracy of the computer program used in the present paper to estimate the uncertainties in magnetic-field-line tracing that arise from published standard errors in the full set of spherical harmonic coefficients, which define the complete (non-axisymmetric) internal geomagnetic field (i.e. g_n^m ± g_n^m and h_n^m ± h_n^m). An algorithm is formulated that greatly reduces the computing time required to estimate these uncertainties in magnetic-field-line tracing. The validity of this algorithm is checked numerically for both the axisymmetric part of the internal geomagnetic field in the general case (1 n 10) and the complete internal geomagnetic field in a restrictive case (0 m n, 1 n 3). On this basis it is assumed that the algorithm can be used with confidence in those cases for which the computing time would otherwise be prohibitively long. For the complete internal geomagnetic field, the maximum characteristic uncertainty in the geocentric distance of a field line that crosses the geomagnetic equator at a nominal dipolar distance of 2 R_E is typically 100 km. The corresponding characteristic uncertainty for a field line that crosses the geomagnetic equator at a nominal dipolar distance of 6 R_E is typically 500 km. Histograms and scatter plots showing the characteristic uncertainties associated with magnetic-field-line tracing in the magnetosphere are presented for a range of illustrative examples. Finally, estimates are given for the maximum uncertainties in the locations of the conjugate points of selected geophysical observatories. Numerical estimates of the uncertainties in magnetic-field-line tracing in the magnetosphere, including the associated uncertainties in thelocations of the conjugate points of geophysical observatories, should be regarded as first approximations in the sense that these estimates are only as accurate as the published standard errors in the full set of spherical harmomic coefficients. As in the preceding paper, howerver, all computational techniques developed in this paper can be used to derive more realistic estimates of the uncertainties in magnetic-field-line tracing in the magnetosphere, following further progress in the determination of more accurate standard errors in the spherical harmonic coefficients.Also Visiting Reader in Physics, University of Sussex, Palmer, Brighton, BN1 9QH, UK     

Long term variation in the secular love number

Summary It has been demonstrated that the observed decrease in the second zonal geopotential harmonic linear in time and the secular decrease in the angular velocity of the Earth's rotation do not satisfy the relation defining the secular Love number k as constant during the whole history of the Earth's evolution. The discrepancy disappears if it is assumed thatdk/dt=–2.4×10^–6 cy^–1 .

---

aa, m a ¶rt;a au m aauunmuaa u u a ¶rt;a u mu au u ¶rt;mm mu, n¶rt; u a a nm mu umuu u. a uam, u ¶rt;nmumdk/dt=–2,4·10 ^–6 (mmu)^–1 .

     

Force function of two general spheroids

¶rt;um ua u ¶rt; u m, a u an¶rt;u nm m ¶rt;mam uu u¶rt;a ma, m ¶rt; uu u ¶rt; u nmua numu ¶rt;m a u ¶rt;mam m. mau ¶rt;u uu m: m nm u m; a, n¶rt;u au umu u unu¶rt; uuu; amu m u a; amua ¶rt;uam ma a ¶rt; u m um ¶rt;m ma. u ¶rt;a ¶rt; u¶rt;, nuu ¶rt; a, ¶rt;a ¶rt;a ¶rt;o 4- n¶rt;a um.     

Détermination des paramètres d'Ångström par des observations actionmétriques courantes

Summary By comparing the equalities expressing the solar flux within a wide spectral region on the assumption of an extintion within the atmospheric aerosol given by ^– and that of an extintion represented by ₁^–1, a relationship is established by means of which: 1) The error is discussed which is done when the air opacity is expressed by ₁, in the case when 1; 2) A simple and quick method is worked out for determining the parameters and from actinometric observations, carried out within the spectral regions <525 m and 525 m<<625 m.     

Single- and inter-station transfer functions for non-synchronous geomagnetic arrays — I. Theory of methods used in data analysis

Summary The theory of the multivariate coherence analysis(spectral domain approach) is developed for calculating single- and inter-station transfer functions and corresponding vector induction characteristics from time variations of the geomagnetic field components. An alternative approach of calculating similar induction characteristics using a time domain algorithm is shown.

---

aam mu m aaua(nma n¶rt;¶rt;) nuuu ama ¶rt;-u -mau n¶rt;am u u mmmu m aamumu u¶rt;uu n anua auau mau aum n u. u¶rt;um ma m¶rt; u aau aamumu u¶rt;uu nm ama amu un mua um. nuam aum na auu am u aamum ¶rt; n ama naam.

     

Modification of the Runcorn's equations on convection flows

Summary Runcorn's equations, which can be used to compute the stresses caused by convection flows from the outer gravity field, were transformed so that gravity anomalies or geoid heights can be employed as input data.

---

au aa, m n¶rt;m u n u mmu u anu, a uu nmau, u maua ma, m unam u¶rt; ¶rt; ¶rt;a, aauu u mmu uu mu¶rt;a.

     

Dynamical stability of convection cells in the upper mantle

Summary A two-dimensional flow model of an incompressible fluid with constant viscosity has been used to study the changes in the large-scale flow pattern (aspect ratio 4). Implications for convection in the Earth's mantle are discussed.

---

a ¶rt; mn uuu ua u¶rt;mu nm m unm ¶rt; uu uu mu ama¶rt;a. ¶rt;am mam ¶rt; uu amuu u.

     

Fracture surface energy of olivine

A relatively simple indentation technique for the rapid measurement of fracture surface energy, , of small samples is described. The reliability of this technique is assessed by testing soda-lime glass for which there are good independent fracture mechanics determinations of fracture surface energy. The indentation technique gives a value for of 4.33 J m^–2 which compares favourably with the accepted value of 3.8 J m^–2. Fracture surface energies of the {010} and {001} cleavage planes of single crystal olivine (modal composition Fo₈₈Fa₁₂) are then determined and compared with theoretical estimates of the thermodynamic surface energy, , calculated from atomistic parameters ( is equal to in the absence of dissipative processes during crack extension). The experimental values for _{010} and _{001} are respectively 0.98 J m^–2 and 1.26 J m^–2. The calculated values of _{010} and _{001} are respectively in the range from 0.37 J m^–2 to 8.63 J m^–2 and 12.06 J m^–2. The particular advantages of the indentation technique for the study of the fracture surface energies of geological materials are outlined.     

Expansions of the double product of the global gravity field

Summary Four fundamental forms of expansion of the double product of the gravity function into an infinite series are derived. Two isotropic parts are separated, one is expressed by Legendre polynomials and the other by invariants of Wigner's D-matrices.

---

¶rt; m n¶rt;mau ¶rt; au ¶rt; nu¶rt;uaumau uu ¶rt;. ¶rt; ¶rt; umn amu, na aam n nu a¶rt;a u ma n uauam amu ua.