Problems connected with the tangential metric coefficient in the Schwarzschild metric: A possible solution

Four situations are shown where the Schwarzschild metric cannot be used or is subject to unsurmountable problems. The first is the question of a metric useful for PPN-formalism checking different gravitational theories. The second problem occurs in connection with Mach's principle, when the flatness of the spacetime inside a massive hollow sphere is a generally accepted solution. The metrical discontinuity on the same spherical shell is a third problem. The fourth one is the anisotropy of the mass-energy of a test particle in the gravitational field. Three principles for solution are proposed:

1. The space is not dilated, but rather contracted, in the gravitational field; then the measurement-rods are shorter and measured distances have greater magnitudes.
2. The potential energy is to be related to a potential level where a stationary observer is placed and the general relativistic potential must be used.
3. A new metric must be introduced which is distinct from the Schwarzschild metric, so that the space in the gravitational field is warped isotropically.

Then the problems stated are shown to be easily solvable.     

The equatorial photospheric rotation rate

The equatorial photospheric rotation rate has been observed on 14 days in 1978–1980. The resulting rotation rate, = 14.14±0.04°/day, is 2% slower than the rate as observed for long-lived sunspots.Stationed at Kitt Peak National Observatory.Operated by the Association of Universities for Research in Astronomy, Inc. under contract with the National Science Foundation.     

Solar limb brightening at the extreme limb from photoelectric eclipse observations

Photoelectric observations of the light intensity from the solar crescent before and after totality were made during the eclipses of 7 March, 1970 and 26 February, 1979. Effective wavelengths were determined by interference filters of 20 nm bandwidth. To obtain the limb darkening function, the resulting intensity curves were analyzed by an extension of the method of Julius in which we take into account the actual lunar limb profile. The limb darkening function at 433 nm was obtained for the region 0.937 < sin < 0.9999. Our results are in good agreement with existing center-to-limb measurements in the region of overlap which extends to sin = 0.99. Additional data were obtained at 600 nm for 0.994 < sin < 0.9999. The curves at both wavelengths show a distinctive limb brightening effect at sin = 0.999.     

Theorie generale planetaire etendue au cas de la resonance et application au systeme des satellites galileens de Jupiter

We consider a system of planets defined by a given distribution of mean mean motions and masses: we represent the osculating elliptic elements of their heliocentric orbits by quasi-periodic functions of time, through a method adapted to the commensurability case; these functions are the sum of the general solution of a critical system, expressed in long-period terms, and of a particular solution. As in the B. Brown's method (applied to the galilean satellites), the critical system contains the secular terms, the longperiod terms (great inequalities), and the resonant terms; the particular solution consists of short-period terms only, whose amplitude is an explicit function of the solution of the critical system.If all the long-period terms in the critical system are harmonic of one fundamental term, we can perform a simple change of variables which transforms the critical system in an autonomous one, and thus we reduce the resolution to an eigenvalue problem. Applying that to the galilean satellites of Jupiter and neglecting the solar perturbations, we obtain a differential system with constant coefficients, whose linear part concerns all the variables (including the major-axes and the mean longitudes) and gives, as a first approximation, the great inequalities, the free oscillations and the libration; nevertheless this solution agrees already with known results, but should be improved by taking into account the non-linear parts and the solar terms in a new approximation.

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Proceedings of the Conference on Analytical Methods and Ephemerides: Theory and Observations of the Moon and Planets. Facultés universitaires Notre Dame de la Paix, Namur, Belgium, 28–31 July, 1980     

A comparative study of the performance of various vertical discretization schemes

Summary Most finite-difference numerical weather prediction models employ vertical discretizations that are staggered, and are low-order (usually second-order) approximations for the important terms such as the derivation of the geopotential from the hydrostatic equation, and the calculation of the vertically integrated divergence. In a sigma-coordinate model the latter is used for computing both the surface pressure change and the vertical velocity. All of the above-mentioned variables can diminish the accuracy of the forecast if they are not calculated accurately, and can have an impact on related quantities such as precipitation.In this study various discretization schemes in the vertical are compared both in theory and in practice. Four different vertical grids are tested: one unstaggered and three staggered (including the widely-used Lorenz grid). The comparison is carried out by assessing the accuracy of the grids using vertical numerics that range from second-order up to sixth-order.The theoretical part of the study examines how faithfully each vertical grid reproduces the vertical modes of the governing equations linearized with a basic state atmosphere. The performance of the grids is evaluated for 2nd, 4th and 6th-order numerical schemes based on Lagrange polynomials, and for a 6th-ordercompact scheme.Our interpretation of the results of the theoretical study is as follows. The most important result is that the order of accuracy employed in the numerics seems to be more significant than the choice of vertical grid. There are differences between the grids at second-order, but these differences effectively vanish as the order of accuracy increases. The sixth-order schemes all produce very accurate results with the grids performing equally well, and with the compact scheme significantly outperforming the Lagrange scheme. A second major result is that for the number of levels typically used in current operational forecast models, second-order schemes (which are used almost universally) all appear to be relatively poor, for other than the lowest modes.The theoretical claims were confirmed in practice using a large number (100) of forecasts with the Australian Bureau of Meteorology Research Centre's operational model. By comparing test model forecasts using the four grids and the different orders of numerics with very high resolution control model forecasts, the results of the theoretical study seem to be corroborated.With 8 Figures     

Interaction between atmospheric flows and obstacles: Experiments in a rotating channel

We performed an experimental study using scale models in a hydrodynamic rotating channel, concerning the interactions between fluid flows and obstacles of different shapes. The study was meant to analyze the characteristics of the wakes observed on the lee side of quasi-bidimensional obstacles, in a neutral atmosphere.The obstacles were half-cylinders (with aspect ratio 0.87), placed transversally on the channel bottom and totally submerged in the fluid. We call them quasi-bidimensional since their width was a little smaller than the channel width, thus allowing the flow to partially go round their edges.The simulations were performed in the rotating hydraulic channel of ICG-CNR in Turin, and included various conditions of rotation period and flow speed. An interesting behaviour of the wakes was found on the lee side of subsynoptic-scale obstacles, modelled in conditions of Reynolds-Rossby similitude. More precisely, if a given threshold of flow velocity is exceeded, wake size is constant and is fully determined by the height of the obstacle.     

Linear hydromagnetic stability of a differentially rotating non-uniformly stratified fluid layer

Summary Our discussion is concerned with the common effect of the non-uniformity of layer rotation and stratification. We have assumed a model of differential rotation with the upper part of the layer rotating more slowly, the bottom part more quickly. The upper part of the layer is stratified stably, the bottom part unstably.The thermal instabilities are preferred in the strong differential rotation case and they are the most easily excited by a strong magnetic field (10²–10³). The direction of its propagation is westward in the uniformly stratified layer and eastward in the non-uniformly stratified layer.     

Meso-beta scale numerical simulations of terrain drag-induced along-stream circulations. Part II: Concentration of potential vorticity within dryline bulges

Summary Hydrostatic and nonhydrostatic simulation models are employed to study the intensification of a terrain drag-induced dryline. The study develops a multi-stage theory for the evolution of the dryline including the concentration of potential vorticity accompanying meso-gamma scale dryline bulges.The numerical simulations indicate three fundamental stages of dryline intensification all of which are either directly or indirectly a result of the terrain-drag on the mid/upper-tropospheric jet stream by the Front Range of the Colorado Rocky Mountains. The first stage involves the downward momentum flux accompanying a large amplitude hydrostatic mountain wave which induces a downslope windstorm along the lee slopes. The surge of momentum (i.e., the dry, warm air associated with the downslope windstorm) propagates down the leeslope and modifies an existing weak dryline boundary. As the downslope windstorm initiates an undular bore along the lee slopes, the high momentum gradient which propagates downstream accompanying the bore, as well as the strong lower tropospheric sinking motions ahead of the bore, contract the scale of the surface moisture boundary between the dry air from above the leeslope and the moist air over the High Plains. This process further strengthens the dryline.The second stage involves the coupling of the terrain drag-induced along-stream ageostrophic front within the midtroposphere to the boundary layer through a thermally-indirect circulation. As the along-stream ageostrophic circulation intensifies within the middle troposphere down-stream from the mountain wave, sinking air parcels originating above 40 kPa descend to below 60 kPa over the High Plains where surface pressures are, only 85 kPa. These descending air parcels within the upstream branch of the along-stream ageostrophic thermally-indirect circulation contain high values of momentum and very low dewpoint values. As the planetary boundary layer (PBL) deepens due to surface warming during the morning hours, momentum and dry air from the midtropospheric along-stream ageostrophic front are entrained into the PBL. This process amplifies the bore-induced hydrostatic dryline bulge via low-level ageostrophic confluence.Finally, regions of low Richardson number (arising from strong vertical shears) within the amplifying midtropospheric along-stream ageostrophic thermally-indirect circulation become preferred regions for the development of non-hydrostatic evanescent internal gravity waves. These waves are embedded within the hydrostatic along-stream front above the low-level dryline and are accomapanied by very significant values of vertical momentum flux which act to focus the meso-gamma scale structure of the dryline into smaller scale bulges where low-level winds and vorticities are very high. This meso-gamma scale process follows the hydrostatic tilting and vortex tube stretching which creates meso-beta scale maxima of mid-lower tropospheric vorticity. The turbulent momentum fluxes accompanying wavebreaking within the nonhydrostatic dryline bulge create very large (i.e., stratospheric values of) potential vorticity near 70 kPa due to the nonconservation of potential vorticity on isentropic surfaces.With 30 Figures     

Fossil-pollen evidence for abrupt climate changes during the past 18 000 years in eastern North America

A quantitative measure of the rate at which fossil-pollen abundances changed over the last 18 000 years at 18 sites spread across eastern North America distinguishes local from regionally synchronous changes. Abrupt regional changes occurred at most sites in late-glacial time (at 13700, 12 300, and 10000 radiocarbon yr BP) and during the last 1000 years. The record of abrupt late-glacial vegetation changes in eastern North America correlates well with abrupt global changes in ice-sheet volume, mountain snow-lines, North Atlantic deep-water production, atmospheric CO₂, and atmospheric dust, although the palynological signal varies from site to site. Changes in vegetation during most of the Holocene, although locally significant, were not regionally synchronous. The analysis reveals non-alpine evidence for Neoglacial/Little Ice Age climate change during the last 1000 years, which was the only time during the Holocene when climate change was of sufficient magnitude to cause a synchronous vegetational response throughout the subcontinent. During the two millennia preceding this widespread synchronous change, the rate of change at all sites was low and the average rate of change was the lowest of the Holocene.Contribution to Clima Locarno Past and Present Climate Dynamics; Conference September 1990, Swiss Academy of Sciences — National Climate Program     

Window technique for climate trend analysis

Climatic characteristics are affected by various systematic and occasional impacts: besides the changes in the observing system (locations of the stations of the meteorological network, instruments, observing procedures), the possible local-scale and global natural and antropogenic impacts on climatic conditions should be taken into account. Apart from the predictability problems, the phenomenological analysis of the climatic variability and the determination of past persistent climatic anomalies are significant problems, among other aspects, as evidence of the possible anomalous behavior of climate or for climate impact studies. In this paper, a special technique for the identification of such shifts in the observational series is presented. The existence of these significant shorter or longer term changes in the mean characteristics for the properly selected adjoining periods of time is the necessary condition for the formation of any more or less unidirectional climatic trends. Actually, the window technique is based on a complete set of orthogonal functions. The sensitivity of the proposed model on its main parameters is also investigated. This method is applied for hemispheric and Hungarian data series of the mean annual surface temperature.Contribution to Clima Locarno — Past and Present Climate Dynamics; Conference September 1990, Swiss Academy of Sciences — National Climate Program