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1.
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)/(Ta–To) - 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)  相似文献   

2.
Radial velocity anomalies in the lower mantle that give rise to triplications in the travel-time curve for short-periodP waves will produce arrivals havingdT/d values that differe by roughly 0.2–0.5 s/deg. The first two arrivals associated with such triplications will be separated by less than one second over a distance range of 4°–10° they may not, therefore, be separable visually on single seismograms, so that their presence can only be inferred from some measurable property that depends on their mutual interference. If there are lateral variations in the regions of anomalous velocity gradients, the interfering signals will also have different azimuths of arrival. Using two synthetic wavelets we have investigated the effect of interference on bothdT/d and azimuth measurements at the Yellowknife Array. We found that if the interfering pulses have a dominant frequencyv, there is a range of time separations (0.30/v0.55/v) over which the measureddT/d and azimuth values may fluctuate by much more than the differences indT/d and azimuth between the interfering signals. We have evaluated the following empirically defined functions for three different primary signals, and for three different relative amplitudes of the interfering signals:f (t), the drift function, which expresses how the measured slownesses,p, and azimuths, , differ from the slownesses and azimuths of the primary wavelets; f(), the range function, which describes the behaviour of the upper and lower bounds ofp and as a function of the difference in arrival times of the signals, andf , studied the properties of these functions, and have outlined how these properties provide criteria based on the numerical and statistical characteristics of the arrival vectors, and on the waveform of the signal that will enable small radial velocity anomalies to be more clearly delineated.Contribution No. 863 from the Earth Physics Branch.  相似文献   

3.
Summary Measuring, with the aid of two filters, the instantaneous intensity of the solar radiation in two wave lengths ( B = 0.44 , R = 0.64 ) by means of a sun photometer designed byVolz, we carried out determinations of the decadic turbidity coefficientB (=0.5 ) and the wave length exponent of the haze extinction for Mexico City. Observations were made for almost two and a half years (1960 to 1962 period). A seasonal size distribution in both parameters was found. Although the data thus obtained are provenient of a contaminated atmosphere, comparison of our data is made with those found for higher latitudes ofÅngström, Schüepp andVolz. The height of the homogeneous haze layerH D was calculated showing pronounced variations for a given wind direction. The maximum and minimum values ofB enable us to get, by the first approximation, the aerosol size distribution ofJunge for our latitudes. However, for exceptional very clear days having maximum actinometric intensity of the solar radiation the sensitivity of the microamperimeter in theVolz sun photometer fails.  相似文献   

4.
Summary This paper is an attempt towards determination of station adjustments for Shillong and Delly Observatories from considerations of a large number ofP n residuals. Station adjustments toJeffreys-Bullen travel time tables for Shillong comes to about 4 seconds and for Delhi 2 seconds respectively for 20°.  相似文献   

5.
To account for elastic and attenuating effects in the elastic wave equation, the stress-strain relationship can be defined through a general, anisotropic, causal relaxation function ijkl (x, ). Then, the wave equation operator is not necessarily symmetric (self-adjoint), but the reciprocity property is still satisfied. The representation theorem contains a term proportional to the history of strain. The dual problem consists of solving the wave equation withfinal time conditions and an anti-causal relaxation function. The problem of interpretation of seismic waveforms can be set as the nonlinear inverse problem of estimating the matter density (x) and all the functions ijkl (x, ). This inverse problem can be solved using iterative gradient methods, each iteration consisting of the propagation of the actual source in the current medium, with causal attenuation, the propagation of the residuals—acting as if they were sources—backwards in time, with anti-causal attenuation, and the correlation of the two wavefields thus obtained.  相似文献   

6.
We consider the second-order differential equations ofP-SV motion in an isotropic elastic medium with spherical coordinates. We assume that in the medium Lamé's parameters , r p and compressional and shear-wave velocities , r, wherer is radial distance. With this regular heterogeneity both the radial functions appearing in displacement components satisfy a fourth-order differential equation which provides solutions in terms of exponential functions. We then consider a layered spherical earth in which each layer has heterogeneity as specified above. The dispersion equation of the Rayleigh wave is obtained using the Thomson-Haskel method. Due to exponential function solutions in each layer, the dispersion equation has similar simplicity, as in a flat-layered earth. The dispersion equation is further simplified, whenp=–2. We obtain numerical results which agree with results obtained by other methods.  相似文献   

7.
The Drude law (molecular refraction) for the temperature radiation in a monoatomic model of the Earth's mantle is derived. The considerations are based on the Lorentz electron theory of solids. The characteristic frequency (or eigenfrequency) of independent electron oscillators (in energy units, ) is identified with the band gapE G of a solid. The only assumption is that solid material related to the Earth's mantle has the mean atomic weight A21 g/mole, and its energy gap (E G) is about 9 eV. In this case the value of molecular refraction (in cm3/g) is (n 2–1)/=0.5160.52, where andn are the density and the refractive index at wavelength D=0.5893 m (sodium light), respectively. The average molecular refraction of important silicate and oxide minerals with A21, obtained byAnderson andSchreiber (1965) from laboratory data, is , where denotes the mean arithmetic value calculated from three principal refractive indices of crystal. For the rock-forming minerals with 19A<24 g/mole the new relation was found byAnderson (1975).  相似文献   

8.
Summary Regional variations have been indicated in the slope of theP travel-time curve in the shadow zone of the earth's core. Further study is needed since the uncertainties of the slope are large, especially for the observations from North American stations. There is no significant difference between themean slope of theP travel-time curve in the 95°102.9 range and those obtained byJeffreys, andJeffreys andBullen. However, there is a significant difference between themean slope in the 103° to 135° range as obtained in this study, and those obtained byJeffreys andBullen, and in a later revision byJeffreys. Themean travel-time curve ofP in the shadow zone of the earth's core should be lowered. A trial travel-time table is given with amean slope of 4.41 sec/deg. This table is in close agreement with the times obtained byGutenberg andRichter, and with the trial travel-times ofLehmann. Under the assumption of diffraction the longitudinal wave velocity has been determined to be 13.7 km/sec at the core-mantle boundary.This paper was presented at the Annual Meeting of the Seismological Society of America Reno, Nevada, 1966.  相似文献   

9.
Riassunto L'Autore dimostra che, nel sistema di coordinate polari , , , si possono determinare un numeros di funzioni della sola variabile :Q 1,Q 3, ....Q 2s–1 tali che la sommatoria delleQ 2i–1/2i–1 rappresenti il potenzialeV di un geoide di rotazione. La condizione di armonicità determina ciascunaQ (che si riduce a un polinomio nelle potenze di sen ) a meno di una costante arbitraria; si dispone pertanto dis costanti che servono per soddisfare la natura dellaV sulla superficie del geoide. Come esempio l'Autore ha determinato la gravità sul geoide sferico, confermando i risultati delSomigliana, e su uno sferoide generico dove ha ritrovato la relazione diClairaut.
Summary The Author proofs that, in the system of polar coordinates , , , it is possible to determine a numbers of functions only of the variable :Q 1,Q 3 ....Q 2s–1 in such a way as to make the summatory of theQ 2i–1/2i–1 represent the potential function of a rotational geoid. The condition of harmonicity determines, saving an arbitrary constant, each of theQ which is reduced to a polynom developed by the sin powers; therefore one disposes of a number of constants to make use for satisfing theV on the geoid. To illustrate his theory the Author determines the gravity on the spherical geoid, thus confirmingSomigliana's formulas and on a spheroidal on which he pointed outClairaut's relations.
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10.
Summary The frequency equation of Rayleigh waves propagating over the free surface of an isotropic, perfectly elastic, heterogeneous semi-infinite medium with material properties varying as = 0 e az , = 0 e az , = 0 e az (a>0) has been obtained. Solution of the frequency equation in closed form is obtained in two cases (i) =0, (ii) =, and the Rayleigh wave dispersion curves for phase and group velocities drawn. In both the cases the medium yields single Rayleigh modes which cannot propagate below certain cut-off frequencies. It is found that in case (i), <c<c 0 and 0.87500 <c g <c 0, and in case (ii), 1.03082 <c<c 1 and 0.90850 <c g <c 1, wherec andc g denote phase nad group velocities respectively, is the constant shear wave velocity of the mediumc 0 andc 1 are the corresponding Rayleigh wave velocities of the homogeneous medium of the same Poisson's ratio. The motion of the surface particles is found to be retrograde elliptical as in the homogeneous case, but the ratic of the major and minor axes now becomes frequency dependent and is plotted against frequency. In both the cases (i) and (ii), the ratio starts at a lower value at the cut-off frequency and approaches the corresponding value of the homogeneous medium at high frequencies.  相似文献   

11.
Summary The external field due to plasma within the magnetosphere has been computed as a function ofA p, which is a measure of solar wind velocity, for very quiet to slightly disturbed conditions using mean daily horizontal intensity from 1932 to 1968 at Alibag. The intensity, corrected for secular change and reduced to a common epoch, showed initially a small increase withA p followed by a steady depression with further increase in the index. ForA p7.5, which is representative of conditions over the 33-hour interval during which data relating to low-energy protons were acquired and used byHoffman andBracken [4]2) to compute current distributions, the decrease, computed here from surface data, is 6 . This is in goodagreement with the southward directed field of the quiet-time proton belt 9±5 obtained byHoffman andBracken.  相似文献   

12.
Summary The problem of the propagation of finite Love Waves in a heterogeneous elastic half space lying over a homogeneous elastic half space, using the quasilinear stress-strain relation due toS. Ferhst [4] is considered in detail. The variations of the parameter in the layer assumed to be of the form 1= 0e z, 0e z where is a constant andz is distance measured from the surface into the layer.  相似文献   

13.
Zusammenfassung Das Gebiet um die Ostsee ist als erdmagnetisch stark gestört bekannt. Die Karte zeigt die Verteilung der intensiven Anomalien, wo Z 2000 and 5000 überschreitet. Der Gruppierung dieser Anomalien kann man eine ung.N Richtung zuschreiben.
Summary The area around the Baltic Sea is known as magnetically intensely disturbed. The map shows the distribution of most intensive anomalies, where Z is more than 2000 and 5000 . The direction of the group of these intensive anomalies can be as appr.N supposed.
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14.
The Rayleigh wave phase and group velocities in the period range of 24–39 sec, obtained from two earthquakes which occurred in northeastern brazil and which were recorded by the Brazilian seismological station RDJ (Rio de Janeiro), have been used to study crustal and upper mantle structures of the Brazilian coastal region. Three crustal and upper mantle models have been tried out to explain crustal and upper mantle structures of the region. The upper crust has not been resolved, due basically to the narrow period range of the phase and group velocities data. The phase velocity inversions have exhibited good resolutions for both lower crust and upper mantle, with shear wave velocities characteristic of these regions. The group velocity data inversions for these models have showed good results only for the lower crust. The shear wave velocities of the lower crust (3.86 and 3.89 km/sec), obtained with phase velocity inversions, are similar to that (=3.89 km/sec) found byHwang (1985) to the eastern South American region, while group velocity inversions have presented shear velocity (=3.75 km/sec) similar to that (=3.78 km/sec) found byLazcano (1972) to the Brazilian shield. It was not possible to define sharply the crust-mantle transition, but an analysis of the phase and group velocity inversions results has indicated that the total thickness of the crust should be between 30 and 39 km. The crustal and upper mantle model, obtained with phase velocity inversion, can be used as a preliminary model for the Brazilian coast.  相似文献   

15.
Summary Utilising two years data collected at two tropical coastal stations, Madras (13°04N, 80°15E) and Waltair (17°42N, 83°18E) and for one tropical continental station, Nagpur (21°09N, 79°07E), the authors have re-evaluated the constants ofBrunt's regression equation. Analyses of the observations for Waltair and Nagpur show good correlation coefficients (r) between the values of the effective emissivity of the atmosphere (the effective emissivity is the ratio of incoming long-wave sky radiation at the surfaceR s , to black body radiation T 4) and the square root values of surface vapour pressuree (mb). The value ofr for Waltair from radiometer observations is 0.98. It is also determined for Waltair and Nagpur from Ångström compensation pyrgeometer observations as 0.83 and 0.91 respectively. A low correlation co-efficient 0.56 is obtained for Madras. It might be due to higher surface vapour pressure values at Madras than at Waltair and Nagpur. The applicability of the reduced regression equations are examined for different years for the different stations. The agreement between the computed values with the new regression equations and the observed long-wave sky radiation at the surface seems to be quite good.  相似文献   

16.
The concept of planetary wave breaking (McIntyre andPalmer, 1983; 1984) is critically reviewed. It is concluded that the wave breaking signature is not unique to any particular dynamic event in the stratosphere. Therefore, the classification of stratospheric transport events, such as wave breaking, groups fundamentally different events together. Better qualification of the wave breaking signature and a more solid theoretical basis of planetary wave breaking must be presented if the concept is to be of significant utility in describing stratospheric tracer transport.  相似文献   

17.
A predictive equation to estimate the next interoccurrence time () for the next earthquake (M6) in the Ometepec segment is presented, based on Bayes' theorem and the Gaussian process.Bayes' theorem is used to relate the Gaussian process to both a log-normal distribution of recurrence times () and a log-normal distribution of magnitudes (M) (Nishenko andBuland, 1987;Lomnitz, 1964). We constructed two new random variablesX=InM andY=In with normal marginal densities, and based on the Gaussian process model we assume that their joint density is normal. Using this information, we determine the Bayesian conditional probability. Finally, a predictive equation is derived, based on the criterion of maximization of the Bayesian conditional probability. The model forecasts the next interoccurrence time, conditional on the magnitude of the last event.Realistic estimates of future damaging earthquakes are based on relocated historical earthquakes. However, at the present time there is a controversy between Nishenko-Singh and Gonzalez-Ruiz-Mc-Nally concerning the rupturing process of the 1907 earthquake. We use our Bayesian analysis to examine and discuss this very important controversy. To clarify to the full significance of the analysis, we put forward the results using two catalogues: (1) The Ometepec catalogue without the 1907 earthquake (González-Ruíz-McNally), and (2) the Ometepec catalogue including the 1907 earthquake (Nishenko-Singh).The comparison of the prediction error reveals that in the Nishenko-Singh catalogue, the errors are considerably smaller than the average error for the González-Ruíz-McNally catalogue of relocated events.Finally, using the Nishenko-Singh catalogue which locates the 1907 event inside the Ometepec segment, we conclude that the next expected damaging earthquake (M6.0) will occur approximately within the next time interval =11.82 years from the last event (which occurred on July 2, 1984), or equivalently will probably occur in April, 1996.  相似文献   

18.
Long-period recordings of dispersive Rayleigh waves along numerous station lines, or profiles, in Europe have for the first time permitted a uniform inversion of these observations based on a new method of phase velocity regionalization.Regional dispersion relations obtained by this method have then been subjected to a complete inversion procedure commonly known as the hedgehog method. The results are presented in a map outlining the thickness of the lower lithosphere (lid) and the shear (S) velocities in both the lid and the asthenosphere channel.A comparison of these results with the minimum compressional (P) wave velocities in the asthenosphere and their corresponding depths provides an estimate of theV p /V s ratio for the asthenosphere in the European area.Contribution No. 314, Institute of Geophysics, ETH-Zürich, Switzerland.  相似文献   

19.
Zusammenfassung Die Gleichgewichtsfiguren lassen sich gänzlich unabhängig vom Dichtegesetz durch die Eingeschaft charakterisieren, daß der Absolutbetrag des Formparametersf0 ein Minimum sein muß. Diese merkwürdige Eigenschaft liefert eine Gleichung zwischen der geometrischen Abplattung und den beidenStokesschen Konstanten und , mit deren Hilfe aus den 4 Lösungen desHelmertschen Gleichungssystems für eine bestimmte Masse die 3 Gleichgewichtsfiguren ausgesiebt werden können. Jede beliebige heterogene sphäroidische Gleichgewichtsfigur ist entweder durch die Masse und die Gestalt ihrer freien Oberfläche oder durch die Masse und drei physikalische Parameter gänzlich eindeurig bestimmt; sie hat ein streng individuelles Dichtegesttz. Aus der dreifach unendlichen Mannigfaltigkeit der Gleichgewichtsfiguren können linear Reihen herausgegriffen werden, indem man entweder zwei physikalische Parameter festhält oder indem man die Figuren aufsucht, welche eine gegebene Fläche zur gemeinsamen äußeren Niveaufläche besitzen oder die Reihe jener Gleichgewichtsfiguren, die sich aus der Schar der äußeren Niveauflähen einer gegebenen Gleichgewichtsfigur bilden läßt.Obwohl das HauptträgheitsmomentC keineStockessche Konstante ist, kann das durch ,W 0 undC eindeutig definierte Normalsphäroid der Erde hypothesenfrei bestimmt werden, weil in der Reihe (,K) auch die Trägheitsmomente und damit die dynamische Abplattung konstant ist. Damit kann die empirisch bekannte dynamische Abplattung mittels des Rückganges auf die homogene Ausgangsfigur der Reihe (,K) durch die statische Abplattung ersetzt werden. Allerdings muß der Ableitung des Normalsphäroides an Stelle der primär unbekannten Werte für die Erdmasse und den Potentialwert des Geoides die Äquatorschwere und die Äquatorachse zugrunde gelegt werden.Abschließend werden noch die drei linearen Reihen (,W 0), (,K) und (W 0,K) diskutiert, welche sich im Normalsphäroid schneiden müssen. Auch kann in dem mit den Achsena, undh m gebildeten Koordinatensystem die Hüllfläche der Gleichgewichtsfiguren angegeben werden; sie ist durch den Formparameterf=–3a2/2 gekennzeichnet.
Summary The figures of equilibrium independant from the law of density in their interior can be characterized by the remarkable property that the absolute value of the «shape-parameter» must be a minimum. This gives an equation between the flattening and the twoStokes constant and , by which the 3 figures of equilibrium can be selected from the 4 solutions ofHelmert's equations for a given mass. Each inhomogeneous spheroidical figure of equilibrium is determined unequivocally by the mass and the shape of its free surface or by the mass and three physical parameters; the law of density is strictly individual. From the threefold infinite multiplicity of the figures of equilibrium linear series are to find out with two fixed physical parameters or you can compute a series of figures with a common level surface or the series built by all level surface of a given figure of equilibrium.Though the moments of inertia are notStokes constants the normal spheroid of earth unequivocally defined by ,W 0 andC can be determined without hypotheses, because in the series (,K) also the moments of inertia and the mechanical ellipticity are constant. Therefore the empirically known mechanical ellipticity can be substituted by the static flattening returning to the homogenous figure in the beginning of the series. Of course the determination of the normal spheroid of earth demands the knowledge of gravity in equator and of the equator-axis instead of the unknown mass of earch series (,W 0), (,K) and (K,W 0), which intersect in the normal spheroid, are discussed. Also the boundary surface of the figures of equilibrium in the Cartesian system of the coordinatesa, andh m is discussed; this surface is determined byf=–3a2/2.
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20.
Zusammenfassung In einer früheren Mitteilung wurde berichtet, daß in der astronomischen Navigation alle Höhendifferenzen (h) eines bestimmten Koppelortes einen Kreis beschreiben (Löhr, Dt. Hydrogr. Z. Bd. 11, Heft 1, 35, 1958).Im folgenden wird dieser geometrische Ort näher untersucht und h-Kreis benannt. Seine wesentliche Eigenschaft besteht darin, daß jede Sehne des Kreises, die vom Koppelort aus unter einem bestimmten Azimutwinkel gezogen wird, die Höhendifferenz des Gestirnes darstellt, das im Zeitpunkt der Beobachtung sich auf dem entsprechenden Azimutgroßkreis befand.Da die Längen- und Breitendifferenz ebenfalls Höhendifferenzen von Gestirnen — die einen Azimut von 90° (270°) und 0° (180°) nachweisen — darstellen, so ergibt sich daraus, daß die durch Konstruktion des h-Kreises entstandenen Schnittpunkte mit dem Meridian und Breitenparallel des Koppelortes die wahre Länge und Breite des Ortes des Beobachters angeben.
The h-circle and its practical use in determining the longitude and latitude of a point of observation
Summary An earlier report (Löhr, Dt. Hydrogr. Z., Vol. 11, Issue 1, p. 35, 1958) dealing with astronomical navigation, establishes that all altitude differences (h) from any given dead reckoning describe a circle.The following report examines this locus which is termed the h-Circle. The h-circle is characterized by the fact that any chord drawn from the dead reckoning at a certain azimuthal angle will represent the difference in altitude of that celestial body which at the time of observation was located in the corresponding azimuthal great circle.The longitude and latitude differences also represent the altitude differences of celestial bodies with azimuth 90° (270°) and 0° (180°). Hence, it follows that the true longitude and latitude of the observer's position are indicated by the points where the meridian and the latitude parallel of the dead reckoning are intersected by the h-circle.
Le h-cercle et sa mise en pratique pour la détermination de la longitude et de la latitude du lieu d'observation
Résumé Dans une communication précédente il a été rapporté qu'en navigation astronomique toutes les différences d'hauteur (h) d'un certain point estimé font un cercle (Löhr, Dt. Hydrogr. Z. Bd. 11, Heft 1, 35, 1958).Ci-après ce lieu géométrique sera examiné plus près et sera nommé le cercle h. Sa qualité essentielle réside dans le fait que chaque corde du cercle, tirée du point estimé sous un angle azimutal déterminé, constitue la différence d'hauteur de l'étoile, qui au moment de l'observation se trouva au grand cercle azimutal correspondant.Vu que des différences en longitude et en latitude forment également des différences d'hauteur des étoiles- qui indiquent un azimut de 90° (270°) et 0° (180°)-, il en ressort, que les points d'intersection entre les coordonnées géographiques du point estimé et le h-cercle, indiquent la vraie longitude et latitude du lieu de l'observateur.
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