The effect of dissipation on the vertical propagation of planetary waves in the vicinity of critical levels

Planetary waves are excited at an initial time by the switch-on of vertical motion at the base of a stratified, isothermal atmosphere on a -plane. Dissipation in the form of linear drag and Newtonian cooling is allowed for. Simple zonal wind profifes are used with linear shear and critical or zero wind levels. Dissipation rapidly dampens out residual time-dependent motion such that a steady state is reached in no more than a few weeks at all heights. Dissipation also permits the absorption of significant amounts of planetary-wave energy such that the basic flow cannot be considered invariant with time. The need for more accurate estimates of dissipation time scales in the upper atmosphere is pointed out. An important step toward this end will be a final solution to the problem of the photochemistry of ozone.Supported by the National Science Foundation under grant GA-31408 and through the National Center for Atmospheric Research.     

Hemispheric simulation of the Asian summer monsoon

A three-level, -plane, filtered model is used to simulate the Northern Hemisphere summer monsoon. A time-averaged initial state, devoid of sub-planetary scale waves, is integrated through 30 days on a 5° latitude-longitude grid. Day 25 through day 30 integrations are then repeated on a 2.5° grid. The planetary-scale waves are forced by time-independent, spatially varying diabatic heating. Energy is extracted via internal and surface frictional processes. Orography is excluded to simplify synoptic-scale energy sources.During integration the model energy first increases, but stabilizes near day 10. Subsequent flow patterns closely resemble the hemisphere summer monsoon. Climatological features remain quasi-stationary. At 200 mb high pressure dominates the land area, large-scale troughs are found over the Atlantic and Pacific Oceans, the easterly jet forms south of Asia, and subtropical jets develop in the westerlies. At 800 mb subtropical highs dominate the oceans and the monsoon trough develops over the Asian land mass. The planetary scales at all levels develop a realistic cellular structure from the passage of transient synoptic-scale features, e.g., a baroclinic cyclone track develops near 55°N and westward propagating waves form in the easterlies.Barotropic redistribution of kinetic energy is examined over a low-latitude zonal strip using a Fourier wave-space. In contrast to higher latitudes where the zonal flow and both longer and shorter waves are fed by barotropic energy redistribution from the baroclinically unstable wavelengths, the low-latitude waves have a planetary-scale kinetic energy source. Wave numbers 1 and 2 maintain both the zonal flow and all shorter scales via barotropic transfers. Transient and standing wave processes are examined individually and in combination.Wave energy accumulates at wave numbers 7 and 8 at 200 mb and at wave number 11 in the lower troposphere. The 800-mb waves are thermally indirect and in the mean they give energy to the zonal flow. These characteristics agree with atmospheric observation. The energy source for these waves is the three wave barotropic transfer. The implications of examining barotropic processes in a Fourier wave-space, vice the more common approach of separating the flow into a mean plus a deviation are discussed.     

The approach to charge equilibrium in a stored aerosol during aging

Summary The approach during natural aging to charge equilibrium of an aerosol produced and stored in a polyester «Mylar» balloon gasometer with metallized internal surface and 4200 litres content is studied. The number of charged condensation nuclei at any instant is related to the number of charged nuclei present at the same moment in electrical equilibrium produced by alpha-irradiation of the aerosol.It is shown that a stored aerosol consisting of small nuclei of moderate concentration is not later than 15 minutes after their birth in electrical equilibrium. With increasing size and concentration of the nuclei it takes longer and longer until the stored aerosol attains charge equilibrium. Stored large nuclei appear not to reach exact charge equilibrium even after several days.The reasons for replacing the rubber balloon gasometer, used previously, by the Mylar balloon for this investigation are given.In connection with the ionizing radiation required for producing charge equilibrium, the generation of condensation nuclei by alpha-radiation in stagnant and moving nucleus-free air has been investigated. It has been found that no condensation nuclei are being produced in filtered (nucleus-free) air for air-flows of between 0.1 and 20 litres/min in a tube of 4.2 cm diameter by the alpha-rays of Polonium 210 of about 125 c.

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Zusammenfassung Es wurde die während natürlicher Alterung stattfindende Annäherung an das elektrische Gleichgewicht eines Aerosols, welches in einem «Mylar» Ballon-Gasometer aus Polyester mit metallisierter Innenfläche und von 4200 Litern Inhalt erzeugt und gespeichert wurde, studiert. Die in jedem Augenblick vorhandene Anzahl der geladenen Kondensationskerne wurde zu der Zahl der geladenen Kerne im elektrischen Gleichgewicht für den gleichen Moment in Beziehung gesetzt, welches durch Bestrahlung des Aerosols mit Alpha-Teilchen erzeugt wurde.Es wird gezeigt, dass ein gespeichertes Aerosol, welches aus kleinen Kernen von mässiger Konzentration besteht, nicht später als 15 Minuten nach der Geburt der Teilchen im elektrischen Gleichgewicht ist. Mit zunehmender Grösse und Konzentration der Kerne dauert es länger und länger bis das gespeicherte Aerosol sein Gleichgewicht erreicht. Gespeicherte grosse Kerne scheinen selbst nach mehreren Tagen nicht das volle Gleichgewicht zu erreichen.Die Gründe für die Einführung des Mylar Ballons statt des früher benützten Gummiballons werden gegeben.In Zusammenhang mit der radioaktiven Bestrahlung, welche für die Erzeugung des Ladungsgleichgewichtes gebraucht wird, wurde die Produktion von Kondensationskernen durch Alpha-Teilchen in stagnierender und bewegter kernfreier Luft untersucht. Es wurde festgestellt, dass keine Kondensationskerne erzeugt werden, wenn kernfreie Luft, welche sich mit 0.1 bis 20 Litern per Minute durch ein Rohrsystem mit 4.2 cm Durchmesser bewegt, von Polonium 210 mit 125 c bestrahlt wird.

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The research reported in this article has been supported in part by the Geophysics Research Directorate of the Air Force Cambridge Research Laboratories, through the European Office of the Air Research Division, United States Air Force under Contract AF 61 (052)-26 and by the Instrumentation Engineering Physics & Analysis Laboratory of the General Electric Co., Schenectady, New York under Retainer Agreement.     

Form-drag instability in a barotropic and a baroclinic atmosphere

We discuss the form-drag instability for a quasi-geostrophic channel flow. We first study the characteristics of this instability in a barotropic flow, considering in detail the influence of the meridional scale and discussing which structure of the perturbation zonal flow must be chosen in order to describe properly this instability.We then consider a continuous quasi-geostrophic channel model in which the topography enters only through the bottom boundary condition, and we discuss how in this case the effects of the form-drag are felt by the mean zonal flow through the ageostrophic mean meridional circulation. Because the meridional structure of the perturbation zonal flow cannot simply be extended from the barotropic to the continuous case, we show how to modify it properly.We then study the baroclinic model in the particular case of constant (in the vertical) basic-state zonal flow and show how this case closely resembles the barotropic, demonstrating the barotropic nature of the form-drag instability.Symbols _t is the partial derivative with respect tot. - _x is the partial derivative with respect tox. - _y is the partial derivative with respect toy. - represents the geostrophic stream function. - u is the eastward component of the geostrophic wind. - v is the northward component of the geostrophic wind. - u _a is the eastward component of the ageostrophic wind. - v _a is the northward component of the ageostrophic wind. - w is the vertical component of the wind. - f is the Coriolis parameter=2 sin f _o+y. - f _o is the Coriolis parameter evaluated at mid-latitude. - N is the Brunt-Vaisala frequency. - [A] is the zonal (x) average ofA at constantp andy. - <A> is the horizontal (x andy) average ofA at constantp     

A numerical study of rotating annulus flows using a modified Galerkin method

Summary Physical phenomena fundamental to rotating, baroclinically driven flows are studied with reference to results of numerical simulation of rotating annulus flows, using a modified Galerkin Model. Both local and global effects of sources, sinks, and transports of heat and momentum are discussed. A convenient energy exchange diagram reveals detailed information that is used to analyze nonlinear equilibration and amplitude vacillation of quasi-geostrophic baroclinic eddies. Transient inertial oscillations, sidewall boundary layers, and internal boundary layers are also discussed.A detailed study of symmetric flows is made, eleven of which are tested numerically for stability with respect to three-dimensional disturbances of a given zonal wave number. Two of the four unstable cases are integrated to a numerical steady state with finite-amplitude, quasi-geostrophic baroclinic waves. With the rigid-lid geometry assumed, the average zonal velocity is zero, resulting in zero phase velocity of the waves. The structure of the thermal wave is nearly coherent in the vertical. These numerical results are consistent with laboratory observations.The eddy flow is quasi-geostrophic except in horizontal boundary layers, where the flow is driven toward low pressure. A small cross-isotherm advection is sufficient to maintain the temperature wave against diffusion and vertical advection. The eddy flow adjusts spontaneously toward the form of the fastest growing or slowest decaying disturbance representable by the truncated space resolution. The eddy flow feeds energy into the mean zonal flow in barotropic-type interactions reflected mainly by the familiar tilted trough. During equilibration, the eddy flow alters the mean zonal flow in such a way that eddy energy sources are reduced relative to energy sinks. However, this adjustment is small compared to the change of total flow, which reflects a relatively large change of eddy amplitude. This suggests that small errors in the mean zonal flow representation can lead to relatively large errors in total flow representation.In most flows studied the kinetic energy dissipation is concentrated in thin boundary layers. In spite of this thinness, the basically laminar character of these dissipative boundary layers allows accurate and economical numerical simulation through the use of characteristic functions, which is a natural refinernent of the basic Galerkin method used. (In this prototype study, only moderately characteristic functions are used, thus sacrificing numerical economy while simplifying the programming.) Similarly, the generation of potential energy, which is transformed into the kinetic energy of the flow, is accurately simulated. In most cases studied, this generation is also concentrated in thin boundary layers where thermal energy is extracted from cold fluid and added to warm fluid.Contribution number 76 of the Geophysical Fluid Dynamics Institute, Florida State University, USA.     

Mechanics of eddy processes in the tropical troposphere

Summary It is suggested on the basis of the study of observational data gathered byJ. P. Peixoto that the eddy processes in the tropical regions of the middle troposphere operate in an inverse manner as compared with a normal heat engine. Thus, in common with the situation in the lower stratosphere, the region is characterized by a countergradient horizontal eddy heat transport and a rising of colder air and sinking of warmer air on the scale of the large eddy processes.The research reported in this paper was sponsored by the Air Force Cambridge Research Laboratory, under Contract Nos. AF19(604)-6108 and AF19(628)-2408.     

Truncated model of a barotropic atmosphere with a periodic forcing

The effect of variations in time of the zonal flow is investigated by the study of a simplified truncated model of a barotropic atmosphere in the presence of an oscillating zonal forcing. Long-time numerical simulations of a triadic model in spherical geometry are carried out for various values of both the frequency and the amplitude of the oscillating part of the zonal forcing. It is found that the reaction of the system to simple sinusoidal forcing is characterized, as happens for strongly nonlinear systems, by complicated trajectories in the phase-space and that the spectrum of the zonal component is much more complicated than that of the forcing function, with interesting relative maxima in the range of very low climatological frequencies. Moreover it is shown that, for proper values of both the frequency and the amplitude of the sinusoidally oscillating part of the forcing function, our simplified model of the large-scale planetary circulation oscillates between an essentially zonal regime (a flow pattern dominated by the zonal flow component) and a wave regime (a flow pattern characterized by significant values of the meridional component of the velocity field associated with the wave components). The transitions between the two regimes are strongly asymmetric: in fact, the time needed for a wave-like flow to evolve into an essentially zonal one is, in the limit of our model, typically 4 to 5 times greater than that needed for the inverse transition. The results are intuitively interpreted in the limit of very long periods of the oscillations of the forcing function. Other interesting features of the results are considered.     

Radiation Fog Prediction Using a Simple Numerical Model

—A simple one-dimensional numerical-analytical model was developed by Meyer and Rao (1995) to predict the onset of radiation fog. The model computes radiative cooling and turbulent diffusion of heat and vapor through the lower boundary layer and produces heat and vapor fluxes at the soil–atmosphere interface. The model is designed for Air Force forecasters who have access to a personal computer, an early evening surface observation of the dry bulb and dewpoint temperature, wind speed, the lapse rate in the upper boundary layer, and the previous 24-h precipitation amount. These initial data are used to predict the diurnal variation of the dry bulb and dewpoint temperatures at 10 m above the surface. In accordance with conventional synoptic observing practices, fog is defined as a restriction of the surface visibility generally to less than 1000 m. Fog is assumed to occur in the model predictions when the dewpoint depression falls to less than 1°C. Observations, from several Air Force bases for selected days when fog was observed to occur, were used to test the model. The present model with default parameters appears to predict the onset of fog slightly ahead of its occurrence. Better verification results are expected when site-relevant parameters are used in model predictions.     

The joint influence of the Coriolis force and the stratification on stationary motions in the zonal model of equatorial atmosphere

Summary In the framework of a zonal model of the equatorial atmosphere, the joint influence of the Coriolis force and stratification on stationary motion is studied. In addition we assume a Boussinesq approximation and consider the equatorial region as a macrodisturbance localized round the Equator, against a background of an isothermal atmosphere with a zonal distribution. Exact analytical solutions of the system of equations (1)–(5) are obtained and analyzed. An interesting result is that the equatorial atmosphere could exist in different stationary states in each of them separately, as well as in a number of them simultaneously.     

Numerical studies of transient planetary circulations in a wind-driven ocean

Summary The time-dependent primitive equations for a shallow homogeneous ocean with a free surface are solved for a bounded basin on the sphere, driven by a steady zonal wind stress and subject to lateral viscous dissipation. These are the vertically integrated equations for a free-surface model, and are integrated to 60 days from an initial state of rest by an explicit centered-difference method with zero-slip lateral boundary conditions. In a series of comparative numerical solutions it is shown that at least a 2-deg resolution is needed to resolve the western boundary currents adequately and to avoid undue distortion of the transient (Rossby waves. The -plane formulation is shown to be an adequate approximation for the mean circulation in the lower and middle latitudes, but noticeably intensifies the transports poleward of about 50 deg and both slows and distorts the transients in the central basin. The influence of the (southern) zonal boundary on the transport solutions is confined to the southernmost gyre, except in the region of the western boundary currents where its influence spreads to the northern edge of the basin by 30 days. The total boundary current transport is shown to be approximately proportional to the zonal width of the basin and independent of the basin's (uniform) depth, while the elevation of the free water surface is inversely proportional to the basin depth, in accordance with linear theory. The introduction of bottom friction has a marked damping effect on the transient Rossby waves, and also reduces the maximum boundary-current transport. The solutions throughout are approximately geostrophic and are only slightly nonlinear.The root-mean-square (rms) transport variability during the period 30 to 60 days is concentrated in the southwest portion of the basin through the reflection of the transient Rossby waves from the western shore and has a maximum corresponding to an rms current variability of about 3 cm sec^–1. The transport variabilities are about 10 percent of the mean zonal transport and more than 100 percent of the mean meridional transport over a considerable region of the western basin (outside the western boundary current regime). Some 99 percent of the total kinetic energy is associated with the zonal mean and standing zonal waves, which are also responsible for the bulk of the meridional transport of zonal angular momentum. Although the transient Rossby waves systematically produce a momentum flux convergence at the latitude of the maximum eastward current, much in the manner of their atmospheric counterparts, this is only a relatively small contribution to the zonal oceanic momentum balance; the bulk of the mean zonal stress is here balanced by a nearly stationary net pressure torque exerted against the meridional boundaries by the wind-raised water. In an ocean without such boundaries the role of the transient circulations may be somewhat more important.     

An improved model of the condensation nucleus counter with stereo-photomicrographic recording

Summary A new model of the condensation nucleus counter with stereo-photomicrographic recording is described which is distinguished by perfect symmetry in its construction, reduced turbulence, two separate microscopes with photographic attachments and a novel dark-field illumination which eliminates completely fogging of the graticule even after prolonged use of the instrument. A view-finder microscope permits observations of the graticule so that the instrument can also be used for counting nuclei by eye. When the graticule is removed the droplets can be photographed in space stereoscopically.The use of the counter and its accessories is described and the dimensions and range of the instrument given.

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Zusammenfassung Es wird ein neues Model des Kondensationskernzählers mit stereo-photomikrographischer Registrierung beschrieben, welches sich durch vollkommene Symmetrie der Konstruktion, reduzierte Turbulenz, zwei gesonderte Mikroskope mit photographischen Zusatzeinrichtungen und einer neuartigen Dunkelfeldbeleuchtung auszeichnet, welche das Beschlagen der Zählplatte, selbst nach langem Gebrauche des Instrumentes, völlig eliminiert. Ein Suchermikroskop gestattet die Beobachtung des Zählglases, so dass das Instrument auch als Kernzähler für Augenbeobachtungen gebraucht werden kann. Wenn die Zählplatte entfernt wird, können die Tröpfchen im Raume stereoskopisch photographiert werden.Der Gebrauch des Kernzählers und seines Zugehörs wird beschrieben, sowie die Dimensionen des Instrumentes und der mit ihm mögliche Umfang der Kernzählungen angegeben.

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The research reported in this article has been sponsored and supported in part by the Geophysics Research Directorate of the Air Force Cambridge Research Center, Air Research and Development Command, United States Air Force, under Contract AF 61(052)-26, through the European Office, ARDC in Brussels.     

Internal gravity wave selection in the upper troposphere and lower stratosphere observed by the MU radar: Preliminary results

Marked wavelike variations of the lower stratospheric wind observed on 7–10 May, 1985 by an MST radar in Japan (by the MU radar) are analyzed assuming that they are induced by monochromatic internal inertio-gravity waves. These variations are mainly composed of two modes (periods: 22 and 24 hours), both of which have zonal phase velocities (C _X ) slower than the mean westerly wind (). A statistical analysis of the zonal phase velocity shows thatC _X above andC _X below the tropopause jet stream, which is considered to be a vivid proof of wave selection due to the tropospheric mean flow and upward wave emission from the tropopause jet. A comparison between the MU radar results and routine meteorological observations leads to the conclusion that the marked waves appear when the jet stream takes a maximum wind speed.     

Analysis of various large-scale disturbances and the associated zonal mean motions in the atmosphere

Summary In this article, we present a scale analysis of planetary waves, extended long waves, and long waves. (We mean the extended long waves to be the disturbances whose east-west length is of order 10⁶ m and north-south extension 10⁷ m). We find for the extended long waves the two terms, the interaction between kinetic and available potential energy of the disturbances, and the interaction between the zonal mean available potential energy, and the eddy available potential energy, are of two orders of magnitude larger than the kinetic energy interaction between the disturbances and the associated zonal mean flow. This theoretical result concerning the relative importance of the various interaction terms may be of use in explaining the observational findings thus far available.It is also shown theoretically that the kinetic energy interaction between the planetary waves, the horizontal size of which is 10⁷ m, and the long waves, whose horizontal size is 10⁶ m, is of the same order as the interaction of kinetic energy between the zonal mean motion and the disturbances. This agrees fairly well with the observational estimates thus far obtained.     

Six circumpolar currents—on the forcing of the Antarctic Circumpolar Current by wind and mixing

The transport of the Antarctic Circumpolar Current (ACC) is influenced by a variety of processes and parameters. A proper implementation of basin geometry, ocean topography and baroclinicity is known to be a fundamental requisite for a realistic simulation of the circulation and transport. Other, more subtle parameters are those of eddy-induced transports and diapycnal mixing of thermohaline tracers or buoyancy, either treated by eddy resolution or by a proper parameterization. Quite a number of realistic numerical simulations of the circulation in the Southern Ocean have recently been published. Many concepts on relations of the ACC transport to model parameters and forcing function are in discussion, however, without much generality and little success. We present a series of numerical simulations of circumpolar flow with a simplified numerical model, ranging from flat-bottom wind-driven flow to baroclinic flow with realistic topography and wind and buoyancy forcing. Analysis of the balances of momentum, vorticity, and baroclinic potential energy enables us to develop a new transport theory, which combines the most important mechanisms driving the circulation of the ACC and determining its zonal transport. The theory is based on the importance of the bottom vertical velocity in generating vorticity and shaping the baroclinic potential energy of the ACC. It explains the breaking of the -constraint by baroclinicity and brings together in one equation the wind and buoyancy forcing of the current. The theory emphasizes the role of Ekman pumping and eddy diffusion of buoyancy to determine the transport. It also demonstrates that eddy viscosity effects are irrelevant in the barotropic vorticity balance and that friction arises via eddy diffusion of density. In this regime, the classical Stommel model of vorticity balance is revived where the bottom friction coefficient is replaced by (with the Gent–McWilliams coefficient and the baroclinic Rossby radius ) and a modified wind curl forcing appears.     

A new tree-ring date for the “floating island” lava flow,Mount St. Helens,Washington

Anomalously narrow and missing rings in trees 12 m from Mount St. Helens' floating island lava flow, and synchronous growth increases in trees farther from the flow margin, are evidence that this andesitic flow was extruded between late summer 1799 and spring 1800 a.d., within a few months after the eruption of Mount St. Helens' dacitic layer T tephra. For ease of reference, we assign here an 1800 a.d. date to this flow. The new date shows that the start of Mount St. Helens' Goat Rocks eruptive period (1800–1857 a.d.) resembled the recent (1980–1986) activity in both petrochemical trends and timing. In both cases, an initial explosive eruption of dacite was quickly succeeded by the eruption of more mafic lavas; dacite lavas then reappeared during an extended concluding phase of activity. This behavior is consistent with a recently proposed fluid-dynamic model of magma withdrawal from a compositionally zoned magma chamber.     

The effect of horizontal resolution on gravity waves simulated by the GFDL “SKYHI” general circulation model

To examine the effects of horizontal resolution on internal gravity waves simulated by the 40-level GFDL SKYHI general circulation model, a comparison is made between the 3° and 1° resolution models during late December. The stratospheric and mesospheric zonal flows in the winter and summer extratropical regions of the 1° model are much weaker and more realistic than the corresponding zonal flows of the 3° model. The weaker flows are consistent with the stronger Eliassen-Palm flux divergence (EPFD).The increase in the magnitude of the EPFD in the winter and summer extratropical mesospheres is due mostly to the increase in the gravity wave vertical momentum flux convergence (VMFC). In the summer extratropical mesosphere, the increase in the resolvable horizontal wavenumbers accounts for most of the increase in the gravity wave VMFC. In the winter extratropical mesosphere, the increase of VMFC associated with large-scale eastward moving components also accounts for part of the increase in the gravity wave VMFC.The gravity waves in the summer and winter mesosphere of the 1° model are associated with a broader frequency-spectral distribution, resulting in a more sporadic time-distribution of their VMFC. This broadening is due not only to the increase in resolvable horizontal wavenumbers but also occurs in the large-scale components owing to wave-wave interactions. It was found that the phase velocity and frequency of resolvable small-scale gravity waves are severely underestimated by finite difference approximations.     

Atmosphere and Earth's rotation

The theoretical aspects of the transfer of angular momentum between atmosphere and Earth are treated with particular emphasis on analytical solutions. This is made possible by the consequent usage of spherical harmonics of low degree and by the development of large-scale atmospheric dynamics in terms of orthogonal wave modes as solutions of Laplace's tidal equations.An outline of the theory of atmospheric ultralong planetary waves is given leading to analytical expressions for the meridional and height structure of such waves. The properties of the atmospheric boundary layer, where the exchange of atmospheric angular momentum with the solid Earth takes place, are briefly reviewed. The characteristic coupling time is the Ekman spin-down time of about one week.The axial component of the atmospheric angular momentum (AAM), consisting of a pressure loading component and a zonal wind component, can be described by only two spherical functions of latitude : the zonal harmonicP ₂ ⁰ (), responsible for pressure loading, and the spherical functionP ₁ ¹ () simulating supperrotation of the zonal wind. All other wind and pressure components merely redistributeAAM internally such that their contributions toAAM disappear if averaged over the globe. It is shown that both spherical harmonics belong to the meridional structure functions of the gravest symmetric Rossby-Haurwitz wave (0, –1)^*. This wave describes retrograde rotation of the atmosphere within the tropics (the tropical easterlies), while the gravest symmetric external wave mode (0, –2) is responsible for the westerlies at midlatitudes. Applying appropriate lower boundary conditions and assuming that secular angular momentum exchange between solid Earth and atmosphere disappears, the sum of both waves leads to an analytical solution of the zonal mean flow which roughly simulates the observed zonal wind structure as a function of latitude and height. This formalism is used as a basis for a quantitative discussion of the seasonal variations of theAAM within the troposphere and middle atmosphere.Atmospheric excitation of polar motion is due to pressure loading configurations, which contain the antisymmetric functionP ₂ ¹ () exp(i) of zonal wavenumberm=1, while the winds must have a superrotation component in a coordinate system with the polar axis within the equator. The Rossby-Haurwitz wave (1, –3)^* can simulate well the atmospheric excitation of the observed polar motion of all periods from the Chandler wobble down to normal modes with periods of about 10 days. Its superrotation component disappears so that only pressure loading contributes to polar motion.The solar gravitational semidiurnal tidal force acting on the thermally driven atmospheric solar semidiurnal tidal wave can accelerate the rotation rat of the Earth by about 0.2 ms per century. It is speculated that the viscous-like friction of the geomagnetic field at the boundary between magnetosphere and solar wind may be responsible for the westward drift of the dipole component of the internal geomagnetic field. Electromagnetic or mechanical coupling between outer core and mantle may then contribute to a decrease of the Earth's rotation rate.     

Effects of the earth's rotation and the balance of zonal kinetic energy

Summary According to the symmetric formulation of the zonal kinetic energy equation, positive generations arise through countergradient transports of angular momentum. Five years of northern hemispheric upper air data are used to investigate two of the terms in the equation, which represent the effects of the transport, by the mean general circulation cells, of the angular momentum associated with the earth's rotation. These two -generation terms do not usually appear in the more traditional form of the conservation equation, and results of their evaluation have not appeared previously. It is found that positive generation largely dominates in the -term involving horizontal (meridional) transports of angular momentum, and negative generation in the -term involving vertical transport. In fall and particularly winter, both terms are responsible for very large amounts of generation of opposing sign for the whole atmosphere.The five years of data are also used to evaluate the balance of zonal kinetic energy implied by the symmetric equation in northern hemispheric polar caps of various pressure thicknesses. The vertical processes involved are not directly measured but rather are obtained from observed horizontal motions through use of continuity of mass and angular momentum requirements. Possible reasons for the lack of a perfect balance are offered, but in any case the residuals are generally not large enough to be of too much concern. Vertical eddies are found to play an important role in the balance of zonal kinetic energy. A study of the balance in the upper half of the atmosphere reveals that in spring the vertical eddies (summed for all scales) must tranport angular momentum and zonal kinetic energy upward toward the jet in order to counter the net effect of the mean cells in reducing the zonal kinetic energy in this volume. In the fall however, there is a dramatic change in the direction in which these vertical eddies act, as they now remove zonal kineticenergy from the upper half of the atmosphere in this season.The research reported in this paper was sponsored by the U.S. National Science Foundation under Grant No. GA-1310X.     

Some laboratory model experiments on the mechanism of two-dimensional momentum transfer in the atmosphere

Summary Investigating the jetstream formation in the upper troposphere, it becomes evident that two-dimensional transfer processes are, to a high degree, responsible for the accumulation of kinetic energy and momentum in those upper tropospheric regions. To shed light on these processes a series of barotropic model experiments has been carried out using a special dynamic procedure for vortex generation. In a large, rotating, cylindrical vessel (filled with water, rotation rate ₀) three smaller cylinders have been fitted eccentrically. Their rotation relative to the vessel (rotation rate _i ,i=1, 2, 3) produces a sharply limited narrow region around each of them, where a nearly two-dimensional relative motion can be observed. Beyond this region — we call it friction zone — there is no motion. Now if we impose some perturbation on this steady mean flow (e.g. by setting _i = 0) the zonal current breaks down into a definite number of vortices which show a random distribution. The dynamic behaviour of these nearly two-dimensional vortices can then be studied.The main results are: I) After the sudden breakdown of the friction zones the most intensive eddies, which are cyclonic, drift more or less directly towards the centre to be organized there into a larger vortex. This development is strongly influenced by the -effect and the ratio = _i /₀, which controls the supply of rotational energy. II) If there exists a steady zonal basic current, the vortices will be more and more deformed when approaching and penetrating the zonal flow until they are wholly incorporated.     

Lagrangian motion of air parcels in the stratosphere in the presence of planetary waves

Development of thoughts on tracer transport mechanisms in the stratosphere which lead to new approaches to two-dimensional modeling of the tracer problem is reviewed.Three-dimensional motions of individual air parcels affected by a planetary wave are investigated theoretically, treating a steady, upward propagating wave in a uniform flow. It is shown that trajectories of air parcels are of elliptical form when projected onto the meridional plane and that they have no mean meridional or vertical motion, even though the usual zonal Eulerian-mean vertical motion exists. The origin of the difference between the mean air parcel motion and the Eulerian-mean motion is discussed.On the basis of the knowledge of air parcel motion, two approaches to two-dimensional modeling are considered. The generalized Lagrangian mean motion (quasi-zonal weighted mean taken over a meandering material tube), recently introduced by Andrews and McIntyre, is identical with the mean motion of an air parcel in a steady state. Such a mean meridional circulation may be used for advecting a tracer in the meridional plane in a two-dimensional model. The transport effect is represented solely by the advection and an eddy transport does not appear in this scheme, to a first approximation.The finding that trajectories of air parcels are elliptical necessitates a reexamination of the Reed-German eddy diffusivity currently used in two-dimensional chemical-dynamical models. By applying a mixing length type hypothesis, we derive an eddy diffusivity formula for use in Eulerian-mean calculations, which, in the case of a conservative tracer is dominated by an anti-symmetric tensor. The eddy transport due to this anti-symmetric tensor diffusivity is of advective type (not diffusive) and has the effect of taking the Stoke drift effect into account, when used in the usual Eulerian-mean formulation.