Modeling axisymmetric flow and transport

Unmodified versions of common computer programs such as MODFLOW, MT3DMS, and SEAWAT that use Cartesian geometry can accurately simulate axially symmetric ground water flow and solute transport. Axisymmetric flow and transport are simulated by adjusting several input parameters to account for the increase in flow area with radial distance from the injection or extraction well. Logarithmic weighting of interblock transmissivity, a standard option in MODFLOW, can be used for axisymmetric models to represent the linear change in hydraulic conductance within a single finite-difference cell. Results from three test problems (ground water extraction, an aquifer push-pull test, and upconing of saline water into an extraction well) show good agreement with analytical solutions or with results from other numerical models designed specifically to simulate the axisymmetric geometry. Axisymmetric models are not commonly used but can offer an efficient alternative to full three-dimensional models, provided the assumption of axial symmetry can be justified. For the upconing problem, the axisymmetric model was more than 1000 times faster than an equivalent three-dimensional model. Computational gains with the axisymmetric models may be useful for quickly determining appropriate levels of grid resolution for three-dimensional models and for estimating aquifer parameters from field tests.     

Similarity solution of axisymmetric flow in porous media

Applications of the axisymmetric Boussinesq equation to groundwater hydrology and reservoir engineering have long been recognised. An archetypal example is invasion by drilling fluid into a permeable bed where there is initially no such fluid present, a circumstance of some importance in the oil industry. It is well known that the governing Boussinesq model can be reduced to a nonlinear ordinary differential equation using a similarity variable, a transformation that is valid for a certain time-dependent flux at the origin. Here, a new analytical approximation is obtained for this case. The new solution,, which has a simple form, is demonstrated to be highly accurate.     

On sea-salt nuclei in the atmosphere

Summary The residues of cloud droplets collected at the summit of a mountain were examined with an electron microscope and their materials were identified with the aid of micro-electron-diffraction method. About 30% of nuclei of cloud droplets larger than 5 in radius were mainly composed of sodium chloride and their masses were 10^–1210^–13 gr. We also found salt particles in snow crystals. Some discussions are made about the process of the capture of these particles by snow crystals.     

On convection in atmosphere

Summary In order to throw light on the mechanics of the cellular patterns of clouds observed from satellites we have applied classical methods to a new class of convection problems, namely a system consisting of two superposed layers with different properties heated from below, and have considered specially the case in which fluid may pass from one layer to the other and change its properties as it does so. A means is provided for computing the critical Rayleigh number and cell width to height ratio when the physical properties of the two layers are given.     

On the energy content of the atmosphere

Summary Vertical profiles of the content of sensible heat, potential energy, and latent heat in the atmosphere between 1000 and 100 mb, during January and July, are derived for the latitude circles 0, 10, 20, 30, 40, 50, and 60°N. Contrasts between oceans and continents are found to vary significantly with latitude and season.

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Zusammenfassung Vertikalprofile des Gehalts an fühlbarer Wärme, potentieller Energie und latenter Wärme in der Atmosphäre zwischen 1000 and 100 mb werden für Januar und Juli und die Breitenkreise 0, 10, 20, 30, 40, 50, und 60°N abgeleitet. Gegensätze zwischen Land und See ändern sich mit geographischer Breite und Jahreszeit.

     

Effect of the anomalous part of the atmosphere on the observed acceleration of gravity

Summary With the aid of a simplified model, the gravitational effect of the anomalous part of the atmosphere was analysed theoretically and formulae were derived for numerical computation. It was found that under extreme meteorological conditions this effect is of the same order as the present accuracy of absolute gravity observations, i.e. ±100–150 nm s^–2. It is, therefore, recommended to reduce these observations to some model of the normal atmosphere by introducing computational corrections.     

Uncertainties in field-line tracing in the magnetosphere. Part I: the axisymmetric part of the internal geomagnetic field

The technique of tracing along magnetic field lines is widely used in magnetospheric physics to provide a magnetic frame of reference that facilitates both the planning of experiments and the interpretation of observations. The precision of any such magnetic frame of reference depends critically on the accurate representation of the various sources of magnetic field in the magnetosphere. In order to consider this important problem systematically, a study is initiated to estimate first the uncertainties in magnetic-field-line tracing in the magnetosphere that arise solely from the published (standard) errors in the specification of the geomagnetic field of internal origin. Because of the complexity in computing these uncertainties for the complete geomagnetic field of internal origin, attention is focused in this preliminary paper on the uncertainties in magnetic-field-line tracing that result from the standard errors in just the axisymmetric part of the internal geomagnetic field. An exact analytic equation exists for the magnetic field lines of an arbitrary linear combination of axisymmetric multipoles. This equation is used to derive numerical estimates of the uncertainties in magnetic-field-line tracing that are due to the published standard errors in the axisymmetric spherical harmonic coefficients (i.e. g_n⁰ ± g_n⁰). Numerical results determined from the analytic equation are compared with computational results based on stepwise numerical integration along magnetic field lines. Excellent agreement is obtained between the analytical and computational methods in the axisymmetric case, which provides great confidence in the accuracy of the computer program used for stepwise numerical integration along magnetic field lines. This computer program is then used in the following paper to estimate the uncertainties in magnetic-field-line tracing in the magnetosphere that arise from the published standard errors in the full set of spherical harmonic coefficients, which define the complete (non-axisymmetric) geomagnetic field of internal origin. Numerical estimates of the uncertainties in magnetic-field-line tracing in the magnetosphere, calculated here for the axisymmetric part of the internal geomagnetic filed, should be regarded as first approximations in the sense that such estimates are only as accurate as the published standard errors in the set of axisymmetric spherical harmonic coefficients. However, all procedures developed in this preliminary paper can be applied to the derivation of 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, Falmer, Brighton, BN1 9QH, UK     

On the vertical transport of angular momentum in the atmosphere

Summary The possible modes of vertical transport of angular momentum in the atmosphere are considered. Momentum balance calculations for both hemispheres show the possibility of countergradient transport by vertical eddies in the region of the mid-latitude jet. As a consequence, it is pointed out that the transport of momentum downward from the region of maximum westerlies would have to be accomplished by the mean meridional motions, through the action of Coriolis torques. The same mechanism may account for a large part of the upward transport in the tropics. The very approximate nature of the calculations must, however, be borne clearly in mind.     

On global short-periodic synchronous oscillations of the atmosphere

Summary The existence of global synchronous atmospheric oscillations with the period of about 1.4 hour is indicated in terms of a simple theoretical model of the circumpolar circulation.

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u nu nm mmu ¶rt;u un uuu naa maua au am nu¶rt; 1,4 .

     

On some of the relations for vertical velocity in the atmosphere

¶rt;aam n¶rt;amm mu ¶rt; mua m am. u mu ¶rt;am a mumu unmuu aau, m m anum¶rt;, a anuu aau.     

On the question of carbon dioxide heat radiation in the atmosphere

Summary The new, more reliable data on transmisson function of the atmosphere in the region of 12–18 carbon dioxide absorption band are obtained. The radiation chart for calculations of atmospheric heat radiation is built on the base of this data. The dependence of atmospheric heat radiation on CO₂ and H₂O contents and also on temperature vertical distribution is investigated with the help of the radiation chart. It is shown, that the heat radiation of the atmosphere almost doesn't depend on variations of carbon dioxide content in the atmosphere. The income of atmospheric heat radiation in the region of spectra from 12 to 18 in integrated atmospheric radiation is determined.

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, 12–18. . , . , . 12–18 .

     

On the problem of the production of kinetic energy in the atmosphere

Резюме В статье рассматривается возможньй путь синоптической интерпретации теоретических заклочений из [1]. Показывается что существует временная связь между развитием и увеличением областей антициклонов как источников кинетической знергни и послеидущей скорой циклогенетической деятельностью в их краях. Для иаложения нриведенного механизма необходима еще принципияльная синоптическая и теоретическая обработка.

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Dedicated to Univ. Prof. Dr Bedřich Šalamon on his 80th birthday

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Address: Boční II, Praha 13-Spořilov.     

Large scale vertical eddies in the atmosphere and the energy of the mean zonal flow

Summary The zonal eddy stress across horizontal surfaces due to large scale vertical motions was evaluated for two months from data for the northern hemisphere for a number of levels up to 50 mb. From this information and from the corresponding distributions for each of the two months of the mean zonal winds, the rate of transformation of kinetic energy from eddy to mean zonal form was calculated. The two sets of data gave rather small values for the hemisphere which were of opposite sign.     

On conversion between potential and kinetic energy in the atmosphere

Summary The basic concept of synoptic statistical methods for construction of prognostic charts was outlined by the author in a previous paper. As a result of these investigations it was found that a high correlation exists between time and space means of contourheights of an isobaric surface (850 mb surface). As it has been shown later byPichler this result may be interpreted by assuming that the geopotential fields obeys a numerical solution of the second order homogenous differential equation for wave propagation (hyperbolic equation) provided the phase velocity is given by . SinceReuter has used for s=666 km and for t=24 hours the conclusion may be drawn that the phase velocity of the wave propagation has an order of magnitude of 5 m/sec. Actually for long waves in the westerlies such a value can be found on an average. The same method can be used for extended forecast procedures if the wave equation is set down for 5 days mean values. Theoretical considerations lead then to a prognostic formula for a 5 days mean chart (8a). This formula can be applied for a sufficient number of grid points in order to construct prognostic charts. The underlying assumption, namely that the mean geopotential field satisfies also a solution of the wave equation turns out to be quite accurate even if only average values of the phase velocity were used for the computation. The usefullness of the method is illustrated for two cases.

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Vortrag gehalten am 7. April 1961 auf der 9. Allgemeinversammlung der «Società Italiana di Geofisica e Meteorologia» (Genova, 6.8. April 1961).     

On the properties of earthquake precursors in the electrostatic field of the surface atmosphere

The paper presents results of the analysis of occurrence times of earthquake precursors in a quasistatic electric field of the surface atmosphere on the Kamchatka Peninsula. The propagation velocity of the precursors and their occurrence time dependence on the earthquake source depth are estimated. A hypothesis on the possible correlation of the precursor propagation velocity with the diffusion rate of subsurface radon is proposed.     

Regionalization of daily flow characteristics in part of the Eastern Cape,South Africa

Abstract

A method is described that allows long-term 1-day annual and seasonal flow duration curves at any ungauged location in one of the drainage regions of South Africa to be established. The method is based on normalization of observed flow duration curves by a long-term mean daily flow and subsequent averaging of normalized ordinates of the curves. The estimate of mean daily discharge for an ungauged site is obtained using the information from the existing national data base of flow characteristics. The established set of flow duration curves at a site is further translated into actual daily streamflow time series using a simple nonlinear spatial interpolation technique.     

CTM-DI磁力仪的使用与维护

大连地震台“九五”期间配置的CDM-DI磁力仪（简称DI仪）由中国科学院地球物理研究所研制。该仪器经过2000年考核运行1年，观测精度较高。于2001年1月1日起正式作为我台绝对观测仪投入使用，2001年9月1日开始近零法观测。 1 DI仪在地磁台站模拟观测系统中的应用 1.1 DI仪在指零法观测中的应用 2001年我台应用DI仪作为绝对观测仪器，使用指零法完整观测1年，精度、稳定性良好，表1为2001年我台DI仪指零法模拟观测基线月剩余方差精度表。 2001年我台模拟记录仪运行稳定、状态良好。应用DI仪与其配合，所得基线精度良好，大大高于规范…     

On the theory of the axially-symmetric,time-average,state of the atmosphere

Summary A possible formal approach to a closed steady-state theory of the mean axially-symmetric variables is outlined. The approach involves alternating iterative solutions of the energy and momentum equations. In these equations the effects of transient eddy phenomena of all frequencies are assumed to be parameterized in terms of the mean symmetric variables.     

Hydrocarbons in the atmosphere

Trace concentrations of highly reactive hydrocarbons of biogenic origin have been proposed for some time as being important in aerosol formation processes in the atmosphere. More recently, assessments of potential photochemical reactions in the troposphere have proposed a role in the atmospheric ozone cycle for hydrocarbons, even for compounds such as methane that had previously been considered nonreactive. An assessment of the atmospheric hydrocarbon reaction system has been limited by a lack of observational information on the nature of conditions in the remote or non-urban atmosphere. Recent data on terpene concentrations and other biogenic hydrocarbon compounds are presented. Data on ethane and acetylene from aircraft samples taken over the north and south Pacific Ocean show concentrations in the 0.5 to 1 /m³ range for ethane and in the 0.05 to 0.3 g/m³ range for acetylene. A concentration gradient is present for these compounds between the northern and southern hemisphere. A rudimentary global concentration pattern for these C₂ compounds has been developed on the basis of recent data.