Showing papers in "Journal of the Atmospheric Sciences in 1963"
TL;DR: In this paper, it was shown that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states, and systems with bounded solutions are shown to possess bounded numerical solutions.
Abstract: Finite systems of deterministic ordinary nonlinear differential equations may be designed to represent forced dissipative hydrodynamic flow. Solutions of these equations can be identified with trajectories in phase space For those systems with bounded solutions, it is found that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states. Systems with bounded solutions are shown to possess bounded numerical solutions.
16,554 citations
TL;DR: In this article, the authors discuss the likely differences between the diffusion of gaseous and particulate matter in the atmosphere, as would be observed by fixed point instruments (absolute diffusion).
Abstract: This paper discusses the likely differences between the diffusion of gaseous and particulate matter in the atmosphere, as would be observed by fixed point instruments (“absolute” diffusion). The potential complicating factor of an “inertia effect” (which would cause a heavy particle not to participate in the higher-frequency oscillations of its fluid-particle neighborhood) is shown to be negligible in the atmosphere. Two interrelated effects termed here the “effect of crossing trajectories” and the “continuity effect,” could be, on the other hand, of great practical importance. Both are caused by the relatively rapid travel of heavy particles across the atmospheric eddies and both could result in an appreciable reduction of dispersion rates. Some estimates of the likely magnitude of these effects are given in the paper.
567 citations
432 citations
335 citations
TL;DR: In this paper, the equations governing a symmetrically heated rotating viscous fluid are reduced to a system of fourteen ordinary differential equations, by a succession of approximations, which contain two external parameters-an imposed thermal Rossby number and a Taylor number.
Abstract: The equations governing a symmetrically heated rotating viscous fluid are reduced to a system of fourteen ordinary differential equations, by a succession of approximations. The equations contain two external parameters-an imposed thermal Rossby number and a Taylor number. Solutions where the blow is purely zonal, and solutions with superposed “steady” waves which progress without changing their shape, are obtained analytically. Additional solutions exhibiting vacillation, where the waves change shape in a regular periodic manner in addition to their progression, and solutions exhibiting irregular nonperiodic flow, are obtained by numerical integration. For a given imposed thermal Rossby number, the flow becomes more complicated as the Taylor number increases. Exceptions occur at very high Taylor numbers, where the equations become unrealistic because of truncation. For values of the external parameters where steady-wave solutions are found, solutions with purely zonal flow also exist, but are un...
294 citations
TL;DR: In this paper, the vorticity equation of a wind-driven ocean model is put in non-dimensional form and solutions are obtained by a numerical integration of the corresponding initial value problem.
Abstract: Solutions are obtained for a time dependent, nonlinear model of a wind-driven ocean by a numerical integration of the corresponding initial value problem. Without time dependence the model and boundary conditions are equivalent to those of Munk, Groves and Carrier (1950). The vorticity equation of the model may be put in nondimensional form so that solutions are governed solely by the pattern of the wind stress, a Rossby number for the interior flow, and an effective Reynolds number for the western boundary current. For a Rossby number in the geophysical range, two regimes are found, depending on the Reynolds number. Below a critical value between 50 and 100 a steady-state solution is approached asymptotically. Above this transition a train of moving disturbances forms in the boundary current due to shear flow instability. There is no tendency for the boundary current to break away from the wall in the region of maximum wind curl for the range of Reynolds numbers (0 through 100) investigated. In ...
200 citations
TL;DR: With Eulerian and Lagrangian spectra approximated by their "inertial subrange" forms between appropriate wave number and frequency limits, it was found that the Lagrangians integral time scale is roughly equal to the Eulerians integral length scale divided by the root-mean-square velocity as mentioned in this paper.
Abstract: With Eulerian and Lagrangian spectra approximated by their “inertial subrange” forms between appropriate wave number and frequency limits, it is found that the Lagrangian integral time scale is roughly equal to the Eulerian integral length scale divided by the root-mean-square velocity The corresponding estimate for the “microscale” ratio shows fair agreement with the large Reynolds number form of Heisen-berg's result A similar approach to Eulerian time scales gives values approximately equal to the Lagrangian scales
172 citations
TL;DR: Thermal convection - fluctuations in velocity, temperature and linear stability of horizontal surfaces as discussed by the authors, is a well-known term for convection on horizontal surfaces, and is related to convection in the literature.
Abstract: Thermal convection - fluctuations in velocity, temperature and linear stability of horizontal surfaces
162 citations
TL;DR: In this article, data gathered during consecutive traverses through summer clouds in southern Missouri have been interpreted to indicate that the glaciating characteristics of commonly occurring small cumulonimbus clouds in this region are dependent upon the size distribution of the liquid phase prior to the inception of glaciation, and clouds having large liquid-water drops rapidly form high concentrations of ice particles regardless of the concentrations of foreign ice-forming nuclei.
Abstract: Data gathered during consecutive traverses through summer clouds in southern Missouri have been interpreted to indicate that: (1) the glaciating characteristics of commonly occurring small cumulonimbus clouds in this region are dependent upon the size distribution of the liquid phase prior to the inception of glaciation; (2) clouds having large liquid-water drops rapidly form high concentrations of ice particles regardless of the concentrations of foreign ice-forming nuclei; (3) the ice phase within the clouds does not begin anew; it builds upon the size distribution that has been achieved by the liquid phase and consequently a continuous modification of the particle size distribution within the cloud occurs; and (4) coalescence continues to be a dominant growth mechanism and growth by sublimation essentially is by-passed. The data appear to he compatible with a chain reaction process propagated by the formation of satellite ice particles during the solidification of water drops.
151 citations
TL;DR: In this paper, an analysis of nine weathership records indicates that maritime precipitation is significantly more frequent at night than during the day and that the diurnal variation is related to the absorption of solar radiation.
Abstract: Analysis of nine weathership records indicates that maritime precipitation is significantly more frequent at night. The effect varies with season and latitude. The diurnal variation is related to the absorption of solar radiation. Non-adiabatic heating may cause a reduction of liquid water production within rising clouds; this factor becomes important when vertical velocities are not too high. At the top of layer clouds, the diurnal rhythm of irradiation can also cause a time-lagged diurnal change of inversion levels and cloud thickness. The last inference is supported by observational data.
145 citations
TL;DR: In this paper, a two-layer model with inflow and outflow is considered and several simple integrations are performed to determine to what extent a steady, symmetrical hurricane model can be used to approximate observed storm structure.
Abstract: Several simple integrations are performed to determine to what extent a steady, symmetrical hurricane model can be used to approximate observed storm structure. A two-layer model with inflow and outflow is considered. In the outflow, the absolute angular momentum about the vertical axis at the hurricane center is conserved. In the inflow, conservation of potential vorticity is assumed. For specified outer boundary conditions this assumption determines the distribution of momentum transport from air to ocean and there-with the radial profile of the tangential wind component. The local heat source at the ocean surface is assumed to supply the energy for the generation of hurricane winds. Given this heat source and the vertical wind shear between inflow and outflow layers from the dynamic model, a relation must exist between heat source and momentum sink at the air-water interface, if a particular wind field is to exist in steady state. This relation is computed. Various empirical tests are performe...
TL;DR: In this article, the authors analyzed the Geary storm using data mainly from a vertically-scanning FPS-6 radar and found that it was remarkably similar in many respects to the severe Wokingham hailstorm in England, analyzed by Browning and Ludlam.
Abstract: The thunderstorm that produced tornadoes near Geary, Okla., on 4 May 1961 is analyzed using data mainly from a vertically-scanning FPS-6 radar. The storm configuration was remarkably similar in many respects to the severe Wokingham hailstorm in England, analyzed by Browning and Ludlam. Each attained a fairly steady state during which certain characteristic features were displayed. Most important of these was the vault, a region of low reflectivity beneath the highest parts of the storm which is believed to be symptomatic of an intense and persistent updraft. This and other features of its structure are analyzed in conjunction with nearby soundings to give a model of the airflow associated with the Geary storm. Like the Wokingham storm, it comprised a persistent updraft which entered and left on the downshear side. This kind of airflow is believed to be representative of an important class of persistently intense cumulonimbus which travel within a strongly sheared environment.
TL;DR: In this article, the spectral forms of tile energy equations for zonal and eddy kinetic energies were used to measure energy changes and energy conversions at 50 mb during the period 25 January-9 February 1957.
Abstract: The spectral forms of tile energy equations for zonal and eddy kinetic energies and zonal and eddy available-potential energies are used to measure energy changes and energy conversions at 50 mb during the period 25 January–9 February 1957 The warming, which was of the bipolar type, could he divided into two phases, a first phase in which the meridional temperature gradient had its usual poleward direction at high latitudes and a second phase in which the gradient was reversed During the first, or amplifying phase, the eddy energy increased and the energy of the zonal flow decreased, the decrease in zonal kinetic energy outweighing that of zonal available potential energy The energy flow corresponded to that of a baroclinic instability Zonal available-potential energy was transformed to eddy available-potential energy, eddy available-potential energy to eddy kinetic energy, and eddy kinetic energy to zonal kinetic energy Indirect meridional circulations with descending motion in the middle l
TL;DR: In this article, the equations of motion for a square ocean basin of dimension L on the β-plane are solved approximately for the case where a wind-strew curl of the form sin (x/L) sin (y/L)[0≤x,y≤πL] is applied to the surface.
Abstract: The equations of motion for a square ocean basin of dimension L on the β-plane are solved approximately for the case where a wind-strew curl of the form sin (x/L) sin (y/L)[0≤x,y≤πL] is applied to the surface. The stream function is expanded in a double Fourier sine series and this representation is truncated after only four terms. The resulting set of equations contains the effects of non-linearity, time dependence, linear variation of the Coriolis parameter, friction, and wind-stress. Multiple solutions to the steady-state equations exist when the wind-stress is sufficiently strong. One of the solutions can be related to Sverdrup's (1947) solution for an ocean basin with one longitudinal boundary. A second solution is dominated by the non-linear interactions of the system. Integration of the non-linear transient equations are carried out for the case where the wind-stress starts at some initial time. In some cases the system goes through a series of oscillations of decreasing amplitude before i...
TL;DR: In this article, the development of an axially-symmetric convective circulation generated by release of an isolated light mass of moist air in an unstable stratification was investigated by integrating the dynamic equations numerically.
Abstract: The development of an axially-symmetric convective circulation generated by release of an isolated light mass of moist air in an unstable stratification has been investigated by integrating the dynamic equations numerically. The equations include eddy viscous forces and heating by condensation of water vapor. All the condensed water is assumed to remain in the system (reversible process). Unlike the spherical shape envisaged in bubble theories, the cloud generated here developes into a tall and slender current. The top is characterized by a sharp gradient of the condensed liquid water content and the rate of ascent of the top agrees approximately with the local vertical velocity. Physical variables such as vertical velocity and excess temperature take their maximum values near the cloud top. The trunk, extending from the cloud base to a little below the top, exhibits a columnar or cylindrical shape, rather than the cone typical of a thermal in neutral surroundings. When the environment is saturat...
TL;DR: In this article, hot-wire measurements of fluctuations of downwind velocities at a height of 1 to 2 m above the sea surface were used to support Kolmogoroff's theory of local isotropy.
Abstract: Further support to Kolmogoroff's theory of local isotropy is provided by hot-wire measurements of fluctuations of downwind velocities at a height of 1 to 2 m above the sea surface. The results agree with those obtained from observations made in a tidal stream by Grant, Stewart and Moilliet (1962) and with measurements of skewness of velocity differences in air over land, made by Gurvich (1960).
TL;DR: In this article, the stability of a two-layer incompressible fluid system on a rotating earth was investigated and the linearized potential vorticity equation was used for the stability investigation.
Abstract: The stability of a two-layer incompressible fluid system on a rotating earth is investigated. The upper layer has infinite depth and is inert; the lower layer has finite depth and a basic west to east zonal velocity of form sech2y. The linearized potential vorticity equation is used for the stability investigation. It is found that both the beta effect due to the curvature of the earth and the divergence tend to stabilize the jet if the winds are from west to cast everywhere. However, if there are easterly winds away from the center of the jet, the divergence may not be stabilizing. This stability theory is applied to a jet at 45 deg latitude in the atmosphere. The maximum wind is 60 m sec1 and the half-width of the jet is 1000 km. For the case of no divergence the most unstable wavelength is 5500 km and this disturbance has an e-fold amplification in 1.8 days. If we include divergence, the most unstable wavelength is again 5500 km but the e-fold amplification time is 14 days. The theory can also...
TL;DR: In this article, the feasibility of a dynamical model for forecasting the development and dissipation of fog and stratus is studied and several simple models based on numerical solutions of the diffusion equation are developed and tested.
Abstract: The feasibility of a dynamical model for forecasting the development and dissipation of fog and stratus is studied. Several simple models based on numerical solutions of the diffusion equation are developed and tested. The resulting predictions are examined with regard to the likelihood of achieving any degree of success with this type of model. The observational data required for the predictions, and the time and space scales on which the observations must be made are noted.
TL;DR: In this article, the authors studied the coalescence of two liquid drops, pressed against each other while a voltage is applied across the drops, and showed that the rate of coalescence is proportional to the voltage between the drops at low voltages and to the square of the voltage at high voltages.
Abstract: The coalescence of two liquid drops, pressed against each other while a voltage is applied across the drops, has been studied with high-speed photography. The delay between contact and coalescence is of the order of milliseconds for distilled water, alcohols, and aqueous solutions of hydrochloric acid. The inverted value of this time, the rate of coalescence, is proportional to the voltage between the drops at low voltages and to the square of the voltage at high voltages. In both cases, the plot of rate against voltage extrapolates to zero rate at zero voltage. In the linear case the rate is proportional to (ϵ–1)½, in the parabolic case to ϵ, where ϵ is the dielectric constant. The following interpretation of the data is offered: Coalescence is effected by the formation of bonds across the interface between the drops. This may occur in two ways, by breaking of bonds and formation of new bonds, or by gradual rearrangement of bonds. In the former case, the rate is proportional to the energy in the...
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TL;DR: In this article, a study of the morphology of large sporadic enhancements of F-region electron density in the darkened portions of the polar cap reveals a close connection between "sporadic F" and ionospheric current systems.
Abstract: A study of the morphology of large sporadic enhancements of F-region electron density in the darkened portions of the polar cap reveals a close connection between “sporadic F” and ionospheric current systems. This connection arises from electric fields which are set up by these currents and then transferred to the F-region along an essentially vertical magnetic field. Under the influence of the electric and magnetic fields, a horizontal drift of ionization may become sufficiently strong to cause the development of sporadic F. Drift velocities obtained from synoptic analyses range between 2000 and 5000 kilometers per hour and agree with theoretical estimates. Criteria are presented for the development of sporadic F events, and the general diurnal and seasonal variations in the frequency of occurrence are inferred.
TL;DR: In this article, a meridional heat budget for the atmosphere below the 25-mb level and between 2ON and 7ON latitude is presented, where the significant components and balance requirements of the budget are presented as a function of height, latitude and season.
Abstract: With the aid of recent climatological data and laboratory radiation data, a meridional heat budget has been formed for the atmosphere below the 25-mb level and between 2ON and 7ON latitude. The significant components and balance requirements of the budget are presented as a function of height, latitude and season. Components of the budget include infrared radiative cooling, solar heating, net latent beating, the heat flux across the lower boundary, and the rate of heat storage. Balance requirements are those demanded solely of the atmospheric motions. Each item of the budget is discussed and some comparisons with related studies are included. Although the heat sources produced an extensive lower layer of excessive heating, except in the arctic winter region, the total atmospheric columns revealed thermal deficits almost everywhere within the model. The convergences of the large-scale eddy heat transports determined by other investigators are sufficient to balance the deficits north of 50N latitud...
TL;DR: In this article, the authors studied the poleward flux and convergence of relative angular momentum in both seasons of the IGY data at eight pressure levels (850, 700, 500, 400, 300, 200, 100 and 50 mb) for 121 Southern Hemisphere plus 22 Northern Hemisphere equatorial stations during the calendar year 1958.
Abstract: Tabulations of daily winds from IGY data were made at eight pressure levels (850, 700, 500, 400, 300, 200, 100 and 50 mb) for 121 Southern Hemisphere plus 22 Northern Hemisphere equatorial stations during the calendar year 1958, in order to study by seasons the poleward flux and convergence of relative angular momentum. The overwhelming importance in both seasons of the transports of relative angular momentum by the transient eddies is demonstrated. These transports are enough to balance the drain of atmospheric angular momentum in the belt of surface westerlies. The mean meridional motions and the standing eddies are ineffective in the fulfilment of the angular momentum balance requirements of this hemisphere. On the other hand the standing eddies are the main agents in the interhemispheric exchanges of relative angular momentum. There are insignificant seasonal variations in the vertically integrated horizontal momentum transport across latitude belts equatorward of 50S, although there is evide...
TL;DR: In this article, the authors described convection between a uniform surface and the bases of small fair-weather cumuli, and found areas of steady uniform temperature, interspersed with areas in which the temperature fluctuates about some higher value.
Abstract: Some features are described of convection between a uniform surface and the bases of small fair-weather cumuli. Areas of steady uniform temperature are found, interspersed with areas in which the temperature fluctuates about some higher value. These thermal structures are not apparent in regions close to the surface, and their temperature excess falls to undetectable levels well below cloud base where other temperature patterns have been observed. The nature of these thermals and the origin of the fair weather cumuli are discussed.
TL;DR: In this paper, the difference between surface, atmospheric, & outer space spectral regions is compared to the infrared horizon of planet earth, and spacecraft sensors are used to choose spacecraft sensors.
Abstract: Infrared horizon of planet earth - difference between surface, atmospheric, & outer space spectral regions - choosing spacecraft sensors
TL;DR: In this article, the supercooling of aqueous solution with millipore filters of 0.01 micron pore size was investigated and the results showed that all solutes investigated enhanced the super cooling of pure water, while the non-equilibrium freezing point depression increased with increasing concentration of the solute.
Abstract: While the temperature at which ice is in equilibrium with a solution (equilibrium freezing point of the solution) is invariably lower than the corresponding value for pure water, in actual experiments in which the temperature of a sample of solution is reduced until freezing starts (non-equilibrium freezing point of the solution) the supercooling is frequently less than that for pure water, in spite of theoretical expectations to the contrary. New experiments on the supercooling of aqueous solutions were carried out with a special experimental technique. Reproducible, non-contradictory results were obtained only if the solutions were filtered through millipore filters of 0.01 micron pore-size. All solutes investigated enhanced the supercooling of pure water. The non-equilibrium freezing point depression (Δt)f increased with increasing concentration of the solute. Comparison of (Δt)f with the sum of the equilibrium freezing point depression (Δt)e and the supercooling of water (Δt)w showed that the...
TL;DR: In this article, the changes brought about in the distribution through coalescence among raindrops, by accretion of cloud droplets, and by evaporation are considered, and the numerical procedures which are used remove all restraints on the form of the initial raindrop-size distribution and on the properties of the cloud and the atmosphere through which the drops are falling.
Abstract: Computations of the changes of the raindrop-size distributions with distance fallen are made with a computer. With the assumption of a steady mass flux of raindrops just below the melting level, changes brought about in the distribution through coalescence among raindrops, by accretion of cloud droplets, and by evaporation are considered. The numerical procedures which are used remove all restraints on the form of the initial raindrop-size distribution and on the properties of the cloud and the atmosphere through which the drops are falling. Raindrop-size distributions may frequently be expressed satisfactorily by a function of the form:where D is the drop diameter, NDdD the number of drops of diameter between D and D + dD in unit volume of space, N0 the value of ND for D = 0, and Λ is the magnitude of the slope of the distribution. It is found that an initial distribution having a relatively large slope is considerably modified by the processes of coalescence, accretion and evaporation. Whereas ...
TL;DR: In this article, the authors set up and solved general equations for the heat balance and material transfer between a spherical hailstone and its environment, and showed how the different variables such as air temperature, air pressure, liquid water content of the air (in the form of drops), hailstone diameter, speed of fall of the hailstone, its surface temperature and growth rate are interdependent.
Abstract: By setting up and solving general equations for the heat balance and the material transfer between a spherical hailstone and its environment it is possible to show how the different variables such as air temperature, air pressure, liquid water content of the air (in the form of drops), hailstone diameter, speed of fall of the hailstone, its surface temperature and growth rate are interdependent. At the same time growth zones can he delimited within which accretion is accompanied by evaporation or sublimation of H20, or where an increase of mass by sublimation exceeds the amount of accretion. From the growth conditions it is possible to classify the resulting ice deposits on a physical basis.
TL;DR: In this paper, the number of active ice nuclei depends upon the temperature and it is deduced that the nuclei effective above about −26C are predominantly in the size range 0.02μ to 0.2μ in diameter.
Abstract: Ice nucleus concentrations measured at latitude 78S with a mixing cold chamber from 1 December 1961 to 10 February 1962 were found to be as high as or higher than those measured in sub-tropical latitudes in the southern hemisphere at the same season with similar equipment. From the way in which the number of active ice nuclei depends upon the temperature it is deduced that the nuclei effective above about −26C are predominantly in the size range 0.02μ to 0.2μ in diameter. The concentrations varied over a similar range to those in low latitudes but fluctuations were generally more orderly and less abrupt than elsewhere, and the nuclei appeared to be more thoroughly mixed with the air than is usually the case. It is suggested that ice nuclei are supplied by subsidence from a world-wide stratospheric reservoir.