Global Angular Momentum Research Articles

Potential-harmonic and Generalized Laguerre Function Expansion for Atomic Wave Function

The hyperspherical-harmonic (HH) method is a wonderful tool for directly solving the Schrǒdinger equation of atoms with two or more electrons.However, the HH degeneracy grows dramatically with the global angular momentum, which prevents one

The Atmospheric Angular Momentum Cycle Associated with a Madden–Julian Oscillation

Abstract The period 1 December 1984 to 3 February 1985 was associated with strong intraseasonal fluctuations in both the global atmospheric angular momentum (AAM) and tropical convection. Consistent changes were observed in the length of day. The AAM budget for the 65-day period is examined here using circulation data from the National Meteorological Center. Surprisingly well-balanced global and zonal budgets are obtained for the vertically integrated AAM. This enables a closer examination of regional changes, to assess how they might be responsible for the changes in the global AAM. Both friction and mountain torques are important in the global AAM budget. The increase of AAM is associated first with a positive friction torque, then with a positive mountain torque. The subsequent decrease of AAM results from a negative friction torque. The accompanying regional changes are mostly confined to the Northern Hemisphere, with high global AAM associated with a stronger and southward-displaced subtropical jet. ...

Principal Modes of Atmospheric Circulation Anomalies Associated with Global Angular Momentum Fluctuations

This paper provides a description of the variability of global atmospheric angular momentum (GAM) and its relationship with principal modes of three-dimensional atmospheric circulation anomalies. The data used are 5-day mean global wind fields from the European Centre for Medium-Range Weather Forecasts initialized dataset for 1980–1989. Significant seasonal variation of GAM is observed with maxima in April and November and a minimum during late July. The amplitude of the annual cycle is largest in the upper troposphere and decreases toward the surface. Although the lower tropospheric contribution to the total angular momentum is relatively small, its annual cycle is out of phase with those of the upper atmosphere and GAM. Also identified is a distinct semiannual component, with double peaks appearing in April and November. This signal is most noticeable in the upper troposphere above the 300-mb level. The principal modes of zonal-mean angular momentum and meridional circulation anomalies and their coupled modes are obtained by using empirical orthogonal function analysis and singular value decomposition. It is shown that the leading modes of the angular momentum and meridional circulation are coupled with each other and are responsible for much of the variability in GAM. The coupled modes represent fluctuations of upper-level subtropical zonal flow, which are linked to the modulation of Hadley circulation intensity in both hemispheres. It is found that GAM is highly correlated with the first eigenvector of upper-level streamfunction anomalies, which consists of a superrotational flow in the tropics and subtropics, except over the central Pacific where a “blocked” flow with two subtropical anticyclonic circulation cells straddling the equator is found. Much of the blocked flow is due to the establishment of dipole anomalies in the velocity potential with centers over the central Pacific and the Maritime Continent on the interannual time scale. On the intraseasonal time scale, GAM fluctuation is dominated by superrotational flow in the tropics, with the blocked flow present to a much lesser extent. The associated velocity potential anomaly has a weak dipole structure with centers over the Indian Ocean and the eastern Pacific. The implications of the above results on the total angular momentum balance of the earth-atmosphere system are also discussed.

Taub numbers extended to Einstein–Maxwell space–time

Mass and angular momentum of asymptotically flat systems are computed by Taub number τ1. This work extends the Taub number method from a vacuum region outside the central source to a region with stationary electric and magnetic fields while preserving global mass and angular momentum. The Reissner–Nordström and Kerr–Newman solutions are treated. Function spaces for curves of solutions of the coupled Einstein–Maxwell equations are discussed, together with the linearized field equations which are directional derivatives of the field equations along the solution curves in the direction of the perturbation.

Determining torques over the ocean and their role in the planetary momentum budget

Knowledge of wind torques at the atmosphere‐ocean interface is important in understanding the global angular momentum balance. A surface wind data set that combines special sensor microwave/imager (SSM/I) and European Centre for Medium Range Weather Forecasts (ECMWF) wind products and covers the period July 1987 to June 1989 is used to estimate zonal torques over the global ocean. Comparison of these fields and fields computed from ECMWF wind analyses alone shows substantial differences in the statistics of both locally and globally integrated torques; the impact of SSM/I data on the torque analysis is largest over the Indian Ocean and eastern Pacific regions. The characteristics of the torques from the combined SSM/I‐ECMWF data set are evaluated. In general, local torques show the largest means and variances over mid‐latitudes (especially in the southern ocean), with fluctuations at periods shorter than 1 month dominating the records. In contrast, variability in the globally integrated ocean torque is largest at seasonal time scales (3 months to 1 year); midsouthern and tropical northern latitudes contribute substantially to this variability. Comparison between the global ocean torque and atmospheric angular momentum M indicates that indirect exchanges of momentum between the atmosphere and solid Earth via oceanic stresses cannot be neglected at seasonal time scales. Intraseasonal fluctuations (1–3 months) in both tropical and global ocean torques are coherent with M, but too weak to account alone for the variability in M. At submonthly periods the ocean torque is apparently not important in the atmospheric momentum balance.

The Generation of Ultralow-Frequency Variations in a Simple Global Model

Fluctuations in the global angular momentum of a two-layer zonally homogeneous global model of the atmosphere are dominated by very low frequencies, periods longer than 100 days. This variability is confined to the tropics, where it is associated with variations of approximately ±5 m s−1 in the zonal winds. Lagged correlations suggest that the variations in angular momentum are a response to variability in the zonally averaged eddy flux of vorticity in the tropics. A zonally symmetric model is constructed to determine the response to an impulsive rearrangement of vorticity across the tropics. The response of the angular momentum in the zonally symmetric model, in convolution with the tropical eddy flux of vorticity derived from the full model, provides a successful model of the variations in angular momentum in the full model. The relevance of the results to James and James' finding ultralow-frequency variability in a five-layer model and to the possibility of ultralow-frequency variability in the atmosphere is discussed.

Orographically forced oscillations in a dynamical model of the Martian atmosphere

A single-layer shallow-water model with realistic topography and idealized zonal forcing is used to analyze barotropic, orographically forced, intraseasonal oscillations in the Martian atmosphere. A robust oscillation with a mean period near 85 Martian days (sols) is observed in a time series of the model global atmospheric angular momentum (AAM). Its robustness with respect to changes of the model parameters is verified. This oscillation is still present when an annual component is added to the forcing to account for seasonal variations in the Sun's declination and for the redistribution of atmospheric mass in connection with condensation and sublimation of carbon dioxide in the polar caps. Composites of the surface height anomaly field keyed to filtered AAM time series are examined to identify the spatial features associated with the 85-sol oscillation and its relation to the spatial distribution of the most prominent aspects of the Martian mountain field. The oscillation has a standing zonal component, with centers of action located upstream and downstream of salient orographic features, and a global meridional component. A resemblance is detected between its northern hemisphere (NH) features and those of the terrestrial 40-day oscillation. This resemblance is attributed to the similarity between the two planets' NH orographic covers. It is noted that interferences between the 85-sol oscillation and shorter-timescale phenomena which cause a redistribution of the Martian atmosphere's heat and momentum content, such as global dust storms, will have to be examined with a more complete model and/or with long records from the imminent Mars Observer mission.

Potential-harmonic expansion for atomic wave functions.

One way to reduce the large degeneracy of the hyperspherical-harmonic basis for solving few- and many-body bound-state problems is to introduce an optimal basis truncation called the potential-harmonic (PH) basis. In this paper we introduce various potential-harmonic truncation schemes and assess their accuracies in predicting the energies of the helium and H{sup {minus}} ground states and the excited 2 {sup 1}{ital S} level of the helium atom. We first find that the part of the PH basis that accounts for one-body correlations gives a better ground-state energy for He than Hartree-Fock (2.8790 a.u. versus 2.8617 for Hartree-Fock and 2.9037 exact). When an orthogonal complement is introduced to the basis to account for {ital e}-{ital e} correlations, we find that the error in the binding energy is 0.000 25 a.u., and 0.000 15 a.u. for ground-state and excited helium, and 0.000 35 a.u. for {ital H}{sup {minus}}. Furthermore, the PH truncation is about 99.9% accurate in accounting for contributions coming from large values of the global angular momentum. This PH scheme is also much more accurate than previous versions based on the Faddeev equations. The present results indicate that the PH truncation can render the hyperspherical-harmonic method useful for systems withmore » {ital N}{gt}3.« less

Spin evolution in wind-fed X-ray binaries

Global angular momentum balance suggests that the neutron stars in Be/X-ray binaries are not spinning in equilibrium. This requires an X-ray lifetime ≤ 10 5 yr, and suggests that there are many dead Be/X-ray binaries in the Galaxy. Some of these may be turned up as millisecond radio pulsars with Be star companions

A Gauss type law for gravity with a cosmological constant

It is shown that Komar's conserved quantities can be generalized to space-times with a cosmological constant in which matter, electric charge, and massless scalar field are sources. In the special case of the Kerr-Newman-de Sitter solution, treated as a solution external to matter sources, these quantities are equal to the global mass and angular momentum of its source. They are determined regardless of any local distribution of the mass and angular momentum of sources in addition to the electric charge given by the classical Gauss' law.

Two-stage rifting of Pangea by two different mechanisms

Two types of rifting may have characterized the two-stage breakup of Pangea—passive rifting during Early Jurassic rapid supercontinental motion and active rifting during Cretaceous supercontinental stillstand. This suggestion is based primarily on the observation that global continental angular momentum in the hotspot reference frame was very high from 180 to 150 Ma and very low from 140 to 90 Ma. From 180 to 150 Ma, motion of the continents was probably too high to allow active rifting. Instead, rifting may have been due to stresses associated with the motion. The pole of rotation for the continents was very close to that for opening of the central Atlantic. Africa lagged behind the other continents in its progress over the mantle, perhaps because of the anchoring effect of a mantle slab under the Alleghenian suture. From 140 to 90 Ma, the low continental momentum is consistent with Anderson's model for continental breakup, in which stillstand of a supercontinent leads to mantle up-welling and continental dispersal through active rifting and sea-floor spreading. Major breakup of the hemispherical supercontinent occurred during the low-momentum period, and the geoid anomaly coincides with the supercontinent's position at that time. The two types of rifting have different geological and paleomagnetic signatures that may allow recognition of them for earlier supercontinents.

Principal modes of intraseasonal variations in atmospheric angular momentum and tropical convection

The seasonal and intraseasonal variation of angular momentum and its relationship with tropical convection is studied using 5‐day mean wind and outgoing longwave radiation (OLR). It was found that the zonally averaged u component and OLR both show pronounced periodicities around 30–60 days in the tropics. The globally averaged zonal wind at 250 mbar exhibits a very pronounced peak at 50 days, with strong seasonal and intraseasonal variations that are linked to the expansion and contraction of the lower level easterlies and the equatorward and poleward migration of the subtropical jet streams at upper levels. In the 30‐ to 60‐day time scale, three basic meridional modes of angular momentum are found. First, the tropical modes have Gaussianlike meridional structures, which decay rapidly away from the equator. These modes are related to both symmetric and antisymmetric tropical heating about the equator. Second, the tropical‐subtropical modes feature a strong amplitude in angular momentum in the tropics and subtropics. They are likely to be related to the seasonal and intraseasonal fluctuations of tropical heating, subtropical jet streams, and transfer of angular momentum through localized meridional circulations. Finally, the extratropical modes have a large amplitude poleward of 30° latitude. They appear to have some relationship with tropical convection, but it is not very strong. Most importantly, they do not seem to contribute significantly to the global angular momentum fluctuations in the 30‐ to 60‐day time scale. Our results indicate that angular momentum generated within the tropics and subtropics contributes to a large part of the observed global angular momentum changes in the intraseasonal and interannual time scales. In these time scales, angular momentum inside the tropics is exported outside the tropics (poleward of 20°N) via jet stream variations associated with regional atmospheric teleconnections.

Parametrization and influence of subgridscale orography in general circulation and numerical weather prediction models

The problem of representing the drag due to subgridscale orography is examined. Results from model simulations are used to illustrate clear deficiencies in the global angular momentum budgets and possible ways of correcting for these deficiencies are considered. It is argued that a formulation for the stress due to subgridscale gravity waves is required, as was first recognized by Boer et al. (1984a, b), and the impact of a scheme based on Palmer et al. (1986) is presented. The scheme is improved by using directionally-dependent subgridscale orographic variances. Results from 90-day integrations using the ECMWF and UKMO models with similar resolutions are very much in accord both with and without a wave drag parametrization scheme; showing much improved wintertime circulations. The relationship between the wave drag and the model orography is examined with the use of idealized stress profiles whereby the wave drag is limited to either near the surface or in the stratosphere. A combination of parametrized wave drag with an envelope orography performs best at this stage of development. Results are presented from a substantial series of ten-day forecast experiments with the ECMWF operational model using mean and (1 σ) envelope orographies, these show significant improvements in forecast skill.

Contribution of tropical winds to subseasonal fluctuations in atmospheric angular momentum and length of day

Changes in the globally integrated angular momentum of the atmosphere from 1983 to 1987 were computed from Fleet Numerical Oceanography Center wind analyses and compared to astronomically measured changes in length of day obtained from the U.S. Naval Observatory. In agreement with previous studies, the two time series are highly coherent and in phase at periods ranging from 40 days up to the longest periods that are resolved by the data. By examining the contribution to the global atmospheric angular momentum from the tropical and extratropical regions separately, it is found that fluctuations in the Earth's angular momentum and length of day at subseasonal periods of 50–100 days are dominated by wind changes in the tropics.

Atmospheric Effects on Earth Rotation and Polar Motion

The variability in the earth's rotation rate not due to known solid body tides is dominated on time scales of about four years and less by variations in global atmospheric angular momentum (M), as derived from the zonal wind distribution. Among features seen in the length of day (Δl.o.d.) record produced by atmospheric forcing are the strong seasonal cycle, quasi-periodic fluctuations around 40–50 days, and an interannual signal forced by a strong Pacific warming event, known as the El Niño. Momentum variations associated with these time scales arise in different latitudinal regions. Furthermore, winds in the stratosphere make a particularly important contribution to seasonal variability.Other related topics discussed here are (i) comparisons of the M series from wind fields produced at different weather centers, (ii) the torques that dynamically link the atmosphere and earth, and (iii) longer-term non-atmospheric effects that can be seen upon removal of the atmospheric signal. An interesting application for climatological purposes is the use of historical earth rotation series as a proxy for atmospheric wind variability prior to the era of upper-air data. Lastly, results pertaining to the role of atmospheric pressure systems in exciting rapid polar motion are presented.

The Zonal Men Westerlies over the Southern Hemisphere

A brief review and evaluation of various analyses of the Southern Hemisphere westerlies is given along with the presentation of some relent results. Several features characterize the westerlies of the Southern Hemisphere as quite different from those in the Northern Hemisphere and, in the past, thew have typically been difficult to reproduce well in general circulation modes. They are the double jet structure in winter, the stronger midlatitude tropospheric winds in summer than in winter, and the ensuing much smaller amplitude of the annual cycle which is associated with a maximum of global atmospheric angular momentum in January. New values for the hemispheric angular momentum integrals are than previously reported. Two estimates of the distribution and strength of the southern westerlies that have been widely used are considered to be seriously biased. Factors contributing to discrepancies among different results am large natural variability, missing data and biases in observing systems, and methods of analysis. Over the sparsely observed Southern Hemisphere, the latter is the main reason why biases exist in analyses based only on mean station data, and the absence of imposed dynamical constraints has led to internally inconsistent fields. Even recent estimates of the southern westerlies from global operational analyses should be used judiciously with proper consideration given to reliability and biases.

Accuracy of Atmospheric Angular Momentum Estimates from Operational Analyses

Modern, high resolution atmospheric and geodetic data are finding increasing use in geophysical studies of the angular momentum balance of the earth-atmosphere system. Such studies require knowledge of the level of uncertainty associated with each data set. Here we attempt to assess the accuracy of global atmospheric angular momentum determinations by comparing time series of this quantity derived from both the NMC and ECMWF zonal wind analyses for 1981–85. We find that over this period the rms difference between the two atmospheric series is comparable to the difference between an atmospheric momentum series and the series that is consistent with observed (nontidal) changes in earth rotation. Most of the difference between the NMC and ECMWF global momentum values comes from the region 33°S–16°N. Differences between NMC and ECMWF regional momentum values become vanishingly small in the high latitudes of the Northern Hemisphere, but they remain large throughout the entire Southern Hemisphere. An annual signal of up to 0.5 m s−1 exists in the difference between the NMC and ECMWF tropospheric zonal wind fields. Although seemingly small, this signal is vertically coherent and leads to a marked annual component in the NMC-ECMWF difference momentum values in the tropics and also for the Northern Hemisphere as a whole.

Accuracy of the optimal subset approximation.

The accuracy of the optimal subset approximation, which reduces the number of coupled equations in the hyperspherical harmonic method, is checked theoretically and numerically. The critical parameter that determines the error of the method is shown to be proportional to the product of potential matrix elements connecting the K=0 state to states with K>0, and the matrix elements between K>0 states. In particular this means that the accuracy is largely independent of the degree of excitation of the system. The numerical precision of the optimal subset method in calculating energies and expectation values of Coulomb-bound three-body systems is checked by comparison of optimal subset results with exact results for fixed maximum global angular momentum ${K}_{\mathrm{max}}$. Errors range from less than one percent for the helium atom ground state energy to 100 percent or more for certain positronium ion expectation values. This precision is consistent with the theoretically determined error parameters.

The global atmospheric angular momentum balance inferred from analyses made during the fgge

AbstractUsing analyses made during the First GARP Global Experiment (FGGE), a study has been made of the angular momentum budget of the atmosphere. the time evolution of atmospheric angular momentum has been compared with the calculated torques acting upon it. This comparison has shown for the first time that the mountain torque is the main contributor to the short‐term variation in the global atmospheric angular momentum. the variation of the torques as functions of latitude has also been compared with the total torque implied by the meridional transport of angular momentum by the atmosphere. the torques calculated agree qualitatively with the angular momentum transport, but there are some significant differences in magnitude; some possible reasons for these differences are discussed in the light of results from a general circulation model and from a second set of analyses made during the FGGE.

The global atmospheric angular momentum balance inferred from analyses made during the FGGE

The global atmospheric angular momentum balance inferred from analyses made during the FGGE