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1.
The approach of two water drops in the absence of air flow around them is theoretically investigated. By assuming deformation criteria it is possible to solve the equation of motion of the drops under the influence of a variety of forces. These forces include the viscous force exerted by the air between the two deformed surfaces, the London-Van Der Waals forces and the force of gravity. It is found that the viscous forces dominate over the whole distance of the interaction. The equations have analytical solutions when a head-on approach is considered and when the deformation of the drops is assumed constant during the interaction. The equations were solved numerically for other deformation criteria and for non head-on approaches.The results of the present model are used in the following paper to compute the coalescence efficiencies of water drops. The model is primarily applicable to situations in which the large drop is stationary and the small one approaches it from below. However, it could also be used for interaction between freely falling drops as long as their relative velocities exceed about 13 cm/sec.Appendix: List of symbols C constant of the motion - D distance between the deformed surfaces of the drops - D o initial value ofD - D m the value at which the viscous force is maximum - D N normalized distance - D s the distance at which the velocity of approach vanishes - F c centrifugal force - F g force due to gravity - F N normalized viscous force - F LV force due to London-Van der Waals effect - F R radial component of the force - F V viscous force - F t tangential component of the force - g acceleration due to gravity - M L mass of large drop - m s mass of small drop - p ratio of radii of interacting drops - R radius of an arbitrary drop - r distance between the centers of mass of the two drops - R D radius of deformation - R L radius of larger drop - R s radius of smaller drop - t time - u defined in equation 20 — has the meaning of kinetic energy - v relative velocity of the deformed surfaces - v 0 initial value ofv - V 0 initial relative velocity of the centers of the drops - V c critical impact velocity - V i impact velocity - V N ,v n normalized velocity - V t tangential component of the velocity - W i velocity of the small drop at infinity for it to reach the pointD 0 at velocityV 0 - x instantaneous impact distance -  average critical impact distance for coalescence - x 0 initial value of the impact distance - x c critical impact distance for coalescence - coefficient of deformation - i impact angle according toWhelpdale andList (1971) - coefficient of deformation - viscosity - surface tension - F s sum of forces acting on the small drop - F L sum of forces acting on the large drop - time constant - R Rayleigh's oscillation period On sabbatical leave (1976–77) from the Department of Geophysics and Planetary Sciences, Tel Aviv University, Ramat Aviv, Israel.The National Center for Atmospheric Research is sponsored by the National Science Foundation.  相似文献   

2.
The coalescence of water drops of sizes comparable to rain drops (200–2500 m diameter) was investigated. The method used provided a good separation between collision and coalescence effects. The result suggests a dependence of the coalescence efficiency on both the size of the large drop and the ratio of the radii of the interacting drops (p-ratio). The coalescence was observed to rapidly decrease due to bouncing and partial coalescence as the angle of impact increased from head-on to grazing angle. However, some bouncing was observed at very low impact angles.The results of the coalescence efficiency were fitted with an empirical equation for use in numerical models of cloud growth and precipitation development.On sabbatical leave (1976–77) from the Department of Geophysics and Planetary Sciences, Tel Aviv University, Ramat Aviv, Israel.The National Center for Atmospheric Research is sponsored by the National Science Foundation.  相似文献   

3.
New equations and techniques for dealing with drop breakups are developed and applied to the modelling of the evolution of raindrop spectra in rainshafts. Breakup experiments byMcTaggart-Cowan andList (1975) served as data base.No matter what the original size distribution, the spectrum evolution will always lead to a Marshall-Palmer type equilibrium di tributionN=N 0e–D, with =constant andN 0 proportional to the rainfall rateR. (D stands for raindrop diameter.) ForR29 mm h–1 and an original Marshall-Palmer distribution, the required fall height to reach equilibrium is 2 km.The equilibrium distributions are characterized by linear relationships betweenR, the radar reflectivity factorZ, the liquid water content LWC and theN 0 of the Marshall-Palmer distribution. Possible explanations for the discrepancy with observations are given.The fact that the all-water processes cannot produce drops withD2.5 mm (as confirmed by observations) leads to the conclusion that observed large raindrops withD5 mm represent melted hailstones and have not yet reached an equilibrium distribution. These latter conclusions were reached within the original assumption of videspread, steady state precipitation.  相似文献   

4.
A formula to determine the local magnitude (ML) following Richters original definition was empirically derived for the Korean Peninsula. A total of 1,644 digital seismograms from 142 Korean earthquakes that occurred from 1997 to 2000 were corrected for instrument response and convolved with the nominal Wood-Anderson torsion seismograph response to be appropriate for the original definition of ML. Then, the zero-to-peak amplitude was measured in millimeters on the synthetic Wood-Anderson seismogram. Multiple regression analysis was conducted to determine distance and station correction terms for the measured peak amplitudes. The best-fit solution for ML yielded the following formula for the Korean Peninsula:where A() and S denote the peak amplitude on the synthetic Wood-Anderson seismogram at distance and the station correction term, respectively. Note that the second term, distance correction, was adjusted with Richters ML, taking into consideration attenuation differences between the Korean Peninsula and southern California, where Richter originally introduced ML. On average, the magnitudes determined in this study are nearly the same as those determined by the Korea Institute of Geoscience and Mineral Resources (KIGAM), but are larger than those of the Korea Meteorological Administration (KMA) by as much as 0.36.  相似文献   

5.
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   

6.
Considering the blocking problem as a baroclinic instability problem in a dispersive wave system with diabatic heating effects, it is of great interest to investigate the role of wavegroup velocityv gr in blocking processes, becausev gr controls the energy transfer in the wave field. Using a Newtonian Cooling —type of forcing with a phase differencek to the main field and taking the linearized version of a two-level model, the phase speedc r, the group velocityv gr and the growth ratekc i have been obtained as analytical functions of the mean zonal windU, the thermal windU T, the coefficient of diabatic heating x, the phase differencek and the wavelengthL. Now the hypothesis is introduced, that a blocking should be expected, ifv gr has a maximum value in the vicinity ofL o, for whichc r vanishes and thee-folding timet=1/kc i (kc i>0) is smaller than 6 days (see condition (20) in the text). One finds, that for special parameter combinations (U T, U, ), where 15 m/secU T25m/sec,U=10m/sec, 0.8·10–51.5·10–5 [sec–1], certain valuesL o with an appropriate phase differencek exist, which satisfy the conditions mentioned above (for values see Table 2). TherebyL o varies within the range 8500 km <L o<11000 km corresponding to the preferred planetary blocking wavenumber 2 in middle latitudes 50°<<70° N.  相似文献   

7.
Scattering of seismic waves can be shown to have a frequency dependenceQ –1 3–v if scattering is produced by arrays of inhomogeneities with a 3D power spectrumW 3D(k) k –v. In the earth's crust and upper mantle the total attenuation is often dominated by scattering rather than intrinsic absorption, and is found to be frequency dependent according toQ –1 , where –1<–0.5. IfD 1 is the fractal dimension of the surface of the 3D inhomogeneities measured on a 2D section, then this corresponds respectively to 1.5<D 11.75, since it can be shown that =2(D 1–2). Laboratory results show that such a distribution of inhomogeneities, if due to microcracking, can be produced only at low stress intensities and slow crack velocities controlled by stress corrosion reactions. Thus it is likely that the earth's brittle crust is pervaded by tensile microcracks, at least partially filled by a chemically active fluid, and preferentially aligned parallel to the maximum principal compressive stress. The possibility of stress corrosion implies that microcracks may grow under conditions which are very sensitive to pre-existing heterogeneities in material constants, and hence it may be difficult in practice to separate the relative contribution of crack-induced heterogeneity from more permanent geological heterogeneities.By constrast, shear faults formed by dynamic rupture at critical stress intensities produceD 1=1, consistent with a dynamic rupture criterion for a power law distribution of fault lengths with negative exponentD. The results presented here suggest empirically thatD 1-1/2(D+1), thereby providing the basis for a possible framework to unify the interpretation of temporal variations in seismicb-value (b-D/2) and the frequency dependence of scattering attenuation ().This is PRIS contribution 046.  相似文献   

8.
Multifractal measures,especially for the geophysicist   总被引：9，自引：0，他引：9  
This text is addressed to both the beginner and the seasoned professional, geology being used as the main but not the sole illustration. The goal is to present an alternative approach to multifractals, extending and streamlining the original approach inMandelbrot (1974). The generalization from fractalsets to multifractalmeasures involves the passage from geometric objects that are characterized primarily by one number, namely a fractal dimension, to geometric objects that are characterized primarily by a function. The best is to choose the function (), which is a limit probability distribution that has been plotted suitably, on double logarithmic scales. The quantity is called Hölder exponent. In terms of the alternative functionf() used in the approach of Frisch-Parisi and of Halseyet al., one has ()=f()–E for measures supported by the Euclidean space of dimensionE. Whenf()0,f() is a fractal dimension. However, one may havef()<0, in which case is called latent. One may even have <0, in which case is called virtual. These anomalies' implications are explored, and experiments are suggested. Of central concern in this paper is the study of low-dimensional cuts through high-dimensional multifractals. This introduces a quantityD q, which is shown forq>1 to be a critical dimension for the cuts. An enhanced multifractal diagram is drawn, includingf(), a function called (q) andD q.This text incorporatesand supersedes Mandelbrot (1988). A more detailed treatment, in preparation, will incorporateMandelbrot (1989).  相似文献   

9.
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   

10.
Summary The partial differential equations of electromagnetic induction in a 3-D Earth of inhomogeneous conductivity are reduced to a system of ordinary differential equations of the 2nd order for the spectral coefficients of the field.
au am nu¶rt; ¶rt; maum u¶rt;uu u m ¶rt;¶rt; n n¶rt;umu n¶rt; um ¶rt;uua au m n¶rt;a ¶rt; nma uum n.
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11.
Summary In this paper the quasi-static temperature and stress distributions set up in an elastic sphere by radiation from a point source at a finite distance from the centre of the sphere and out-side it, have been discussed. The temperature boundary condition has been taken in the general form involving an arbitrary function of time. The final solutions have been obtained in terms of series involving Legendre polynomials. Numerical calculations have been done on IBM 1620 Computer and a desk calculator. The results have been represented in graphs.Notation the del operator - u the displacement vector - T the excess of temperature over that at state of zero stress and strain - , Lamé's constants - /2(+) Poisson's ratio - coefficient of linear expansion - 2(1+) - a radius of the sphere - d distance of the point source from the centre of the sphere - d o a/d - K coefficient of thermal conductivity - h heat transfer coefficient of the surface  相似文献   

12.
Summary In this paper the problem of a point source of stress moving over the surface of a thick aelotropic plate resting of a rigid foundation has been considered. Following the method ofAleksandrov & Vorovich (1960) the stress componentsZ x andZ z have been expanded in series of ascending powers of 1/h when the source velocity is less than (c 44/)1/2. When the velocity exceeds (c 44/)1/2 it has been shown that two cracks are produced in different directions and their successive reflections at the upper and lower surface are also obtained.  相似文献   

13.
Zusammenfassung Für ein schmelzendes Schneefeld im Gebirge bei Tromsö wird die Energieaufnahme abgeschätzt. Stichprobenhafte Beobachtungen von Strahlung, Temperatur, Feuchtigkeit und Wind im Gelände werden auf Registrierungen in Tromsö bezogen und aus stochastischen Zusammenhängen die tägliche Schmelzwassermenge während zwei Monaten überschlagsmässig bestimmt. Sie wird mit dem beobachteten Abfluss verglichen.
Summary For a melting snow field in the mountains near Tromsö the energy input is estimated. Samplelike observations of radiation, temperature, humidity and wind in the field are referred to registrations of these variables at Tromsö. From the stochastic relations the daily snow melt is approximately calculated through two months, and is compared with observed runoff.
Symbole A atmosphärische Gegenstrahlung - a Konstante - Albedo - b Konstante - c Konstante - D Richtung - Differenz - E effektive Entfernung (Korrelation) - e Dampfdruck - F relative Feuchte - G Globalstrahlung - H spezifische Feuchte - K kurzwelliger Strahlungssaldo - k Konstante - L langwelliger Strahlungssaldo - N Niederschlagsmenge - n Anzahl Beobachtungen - Gebietsfläche - p Korrelationsparameter - Q Saldo sensibel und latent übertragener Wärme - q Wärmeübergangszahl - Stefan-Boltzmann-Konstante - T Temperatur - V Windgeschwindigkeit - W Schmelzwassermenge;W 1 undW 2 abgeschätzte und beobachtete Abflussintensität - Bewölkungsgrad - Z vertikale Höhe - Æ Äquivalenttemperatur - bezüglich Bewölkung 3/10 - bezüglich Bewölkung >3/10 - * bezüglich Schneeoberfläche - ' (Index) bezeichnet Referenzwert  相似文献   

14.
¶rt;m nmaumuu uma a nuu amma. aa, m ua u ua um ¶rt; nm am ¶rt;au u nuu uma. aumaa mu ¶rt; u a au nu u mau. aa ua u ua . n¶rt; nnau anum¶rt; aamumu aa nuu . aa, m nm a¶rt; u um a aau a amm 56°/h, ma aa a au mau. aamuam au u m u.

Presented at the meeting of Working Group 3.3. of the KAPG (Prague, November 1975).  相似文献   

15.
Summary One of the important atmospheric levels, the mean energetic level (MEL), which in a sense reflects the energetics of the whole atmosphere, is defined. Its fundamental properties are shown. In order to describe the MEL correctly a new vertical coordinate is introduced and discussed. The new coordinate, , is defined as the ratio of height and temperature. The MEL is shown to be a level with constant value of . Some incorrect conclusions concerning the MEL, derived in the past, have been corrected.List of symbols used c p specific heat of air at constant pressure - c v specific heat of air at constant volume - e base of natural logarithms - E total potential energy - f Coriolis parameter - g acceleration of gravity - i specific internal energy - I internal energy - J enthalpy - k unit vector pointing upwards - p pressure - Q diabatic heating rate - R gas constant of the air - t time - T temperature - v horizontal velocity - v (3) three-dimensional velocity - w vertical velocity in thez-system - z height - temperature growth rate (T/z) - Pechala's vertical coordinate (z/T) - generalized vertical velocity in the -system (d/dt) - specific potential energy - potential energy - density of the air - Ruppert function - T(1–)–1 - ( ) S quantity at the sea level - ( )* quantity at the MEL  相似文献   

16.
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   

17.
Calculations of the compression and temperature gradient of the core are facilitated by the use of the thermodynamic Grüneisen ratio, =3Ks/C P . A pressure-dependent factor in is found to have the same numerical value for the core as for laboratory iron, justifying the use of a constant value for (1.6) in core calculations. The density of the outer core is satisfied by the assumption that it contains about 15% of light elements, particularly sulphur, whereas the inner core is probably ironnickel with very little lighter component. The presence of sulphur in the outer core reduces its liquidus at least 600° below pure iron, so that the adiabatic gradient does not intersect the liquidus, as Higgins and Kennedy have shown would occur in a pure iron core. The inner core is probably close to its melting point, 4700 K, and the adiabatic temperature gradient of the outer is calculated with this as a fixed point, giving 3380 K at the core-mantle boundary. The estimated electrical resistivity of the outer core, 3×10–6 m, corresponds to a thermal conductivity of 28 W·m–1·deg–1, which, with the adiabatic core gradient gives a minimum of 3.9×1012 W of heat conduction to the mantle. The only plausible source of this much heat is the radioactive decay of potassium in the core. As pointed out by Goles, Lewis, and Hall and Murthy, the presence of potassium becomes geochemically probable once sulphur is admitted as a core constituent. Thus it appears that the recognition of sulphur in the core resolves the two major difficulties which we have faced in attempting to understand the core.List of Symbols a equilibrium atomic spacing at zero pressure, also a constant - A surface area of core - b a constant - c a constant - C V ,C P specific heat at constant volume, constant pressure - D dimension of core (or core eddy) - E(r) atomic interaction energy - E energy due to atomic displacement from equilibrium - lattice energy of material - f 1,f 2 structure-dependent constants - F(P) pressure dependent factor in Grüneisen's ratio - g gravitational acceleration; also a constant (Equation (13)) - H latent heat of solidification - I integral (Equation (23)) - k Boltzmann's constant - K incompressibility (bulk modulus) - K T ,K S isothermal, adiabatic incompressibilities - N number of atoms in a volume of material - P pressure - dQ/dt core to mantle heat flux - r atomic spacing - r e equilibrium value ofr under pressure - R m magnetic Reynolds number - T temperature - T c critical temperature - T R reduced temperature (Equation (39)) - U specific internal energy of a material - v velocity of internal core motion - V volume - 3 volume expansion coefficient - compressibility - thermodynamic Grüneisen ratio (Equation(2)) - magnetic diffusivity - thermal conductivity - e electronic contribution to - 0 permeability of free space - density - e electrical resistivity - R reduced conductivity,eM/e  相似文献   

18.
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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19.
Summary The paper presents, in a condensed form, the fundamentals of global atmospheric energetics that have a bearing on the linear theory of compensation of non-equilibrium states in the Earth's atmosphere. The author introduces a new coordinate system with the vertical coordinate *=Z*/T*, which suits global atmospheric energetice.The relation between the energetics of the atmospheric system as a whole and the mean energetics level (MEL) is shown. Contrary to what has been assumed so far, it is proved that this level is neither an isopycnic level nor a physical surface, where */t=0 applies everywhere.List of Symbols Used x, y, z space coordinates in thez-system - x, y, space coordinates in the -system - t time - p, T, pressure, thermodynamic temperature and air density - p*, T*, pressure, temperature, density and geopotential on the mean energy level - g acceleration of the Earth's gravity - c p ,c v ,R specific temperature under constant pressure, volume and specific gas constant - = c p /c v Poisson's constant - E k ,E v ,E p kinetic, internal and potential energies of the atmospheric system - r'(x,y) correction function to inhomogeneous atmosphere - v, v n magnitude of motion velocity, magnitude of the normal component of velocity - O, S, S 0 volume of the whole atmospheric system, surface limiting volumeO and the Earth's surface - Z S height of surfaceS - arbitrary scalar quantity - H , horizontal differential operators in thez- andp-systems Dedicated to Corresponding Member Vojtch Vítek, Director of the Institute of Physics of the Atmosphere of the Czechoslovak Academy of Sciences, at the occasion of his sixtieth birthday.  相似文献   

20.
Simple models are discussed to evaluate reservoir lifetime and heat recovery factor in geothermal aquifers used for urban heating. By comparing various single well and doublet production schemes, it is shown that reinjection of heat depleted water greatly enhances heat recovery and reservoir lifetime, and can be optimized for maximum heat production. It is concluded that geothermal aquifer production should be unitized, as is already done in oil and gas reservoirs.Nomenclature a distance between doublets in multi-doublet patterns, meters - A area of aquifer at base temperature, m2 drainage area of individual doublets in multidoublet patterns, m2 - D distance between doublet wells, meters - h aquifer thickness, meters - H water head, meters - Q production rate, m3/sec. - r e aquifer radius, meters - r w well radius, meters - R g heat recovery factor, fraction - S water level drawdown, meters - t producing time, sec. - T aquifer transmissivity, m2/sec. - v stream-channel water velocity, m/sec. - actual temperature change, °C - theoretical temperature change, °C - water temperature, °C - heat conductivity, W/m/°C - r rock heat conductivity, W/m/°C - aCa aquifer heat capacity, J/m3/°C - aCr rock heat capacity, J/m3/°C - WCW water heat capacity, J/m3/°C - aquifer porosity, fraction  相似文献   

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