Angular Momentum Budget Research Articles

Constraining the mass transfer in massive binaries through progenitor evolution models of Wolf-Rayet+O binaries

Since close WR+O binaries are the result of a strong interaction of both stars in massive close binary systems, they can be used to constrain the highly uncertain mass and angular momentum budget during the major mass transfer phase. We explore the progenitor evolution of the three best suited WR+O binaries HD 90657, HD 186943 and HD 211853, which are characterized by a WR/O mass ratio of ~0.5 and periods of 6...10 days. We are doing so at three different levels of approximation: predicting the massive binary evolution through simple mass loss and angular momentum loss estimates, through full binary evolution models with parametrized mass transfer efficiency, and through binary evolution models including rotation of both components and a physical model which allows to compute mass and angular momentum loss from the binary system as function of time during the mass transfer process. All three methods give consistently the same answers. Our results show that, if these systems formed through stable mass transfer, their initial periods were smaller than their current ones, which implies that mass transfer has started during the core hydrogen burning phase of the initially more massive star. Furthermore, the mass transfer in all three cases must have been highly non-conservative, with on average only ~10% of the transferred mass being retained by the mass receiving star. This result gives support to our system mass and angular momentum loss model, which predicts that, in the considered systems, about 90% of the overflowing matter is expelled by the rapid rotation of the mass receiver close to the Ω-limit, which is reached through the accretion of the remaining 10%.

The Annual Cycle of the Axial Angular Momentum of the Atmosphere

Abstract Earlier analyses of the annual cycle of the axial angular momentum (AAM) are extended to include mass flows and vertical transports as observed, and to establish angular momentum budgets for various control volumes, using the European Centre for Medium-Range Forecasts (ECMWF) Re-Analyses (ERA) for the years 1979–92, transformed to height coordinates. In particular, the role of the torques is examined. The annual cycle of the zonally averaged angular momentum is large in the latitude belt 20° ⩽ |ϕ| ⩽ 45°, with little attenuation in the vertical up to a height of ∼12 km. The oscillation of the mass term (AAM due to the earth’s rotation) dominates in the lower troposphere, but that of the wind term (relative AAM) is more important elsewhere. The cycle of the friction torque as related to the trade winds prevails in the Tropics. Mountain torque and friction torque are equally important in the extratropical latitudes of the Northern Hemisphere. The annual and the semiannual cycle of the global angular momentum are in good balance with the global mountain and friction torques. The addition of the global gravity wave torque destroys this agreement. The transports must be adjusted if budgets of domains of less than global extent are to be considered. Both a streamfunction, representing the nondivergent part of the fluxes, and a flux potential, describing the divergences/convergences, are determined. The streamfunction pattern mainly reflects the seasonal shift of the Hadley cell. The flux potential links the annual oscillations of the angular momentum with the torques. It is concluded that the interaction of the torques with the angular momentum is restricted to the lower troposphere, in particular, in the Tropics. The range of influence is deeper in the Northern Hemisphere than in the Southern Hemisphere, presumably because of the mountains. The angular momentum cycle in the upper troposphere and stratosphere is not affected by the torques and reflects interhemispheric flux patterns. Budgets for the polar as well as for the midlatitude domains show that fluxes in the stratosphere are important.

Response of a global atmospheric forecast model to various drag parametrizations

Various drag mechanisms are currently parametrized in numerical models of the atmosphere. For global models that include the middle atmosphere in particular, these mechanisms profoundly affect weather forecast as well as climate simulation.We have developed an extended-top version of the Navy Operational Global Atmospheric Prediction System (NOGAPS) to include the middle atmosphere by modifying some physical parametrizations and the vertical coordinate. We performed a series of ensemble simulations corresponding to January 2000 for investigating the response of the model to various drag mechanisms, such as mountain drag, orographic gravity wave drag, surface friction drag, and artificial model top drag. Based on the monthly mean fields obtained from the simulations, we first investigate the effect of gravity wave drag due to its direct impact through planetary wave activity as well as indirect impact through induced meridional circulation.We discuss the difficulties in partitioning between the mountain drag due to resolved orography and the gravity wave drag due to unresolved orography, first using conventional diagnostic measures. From analyses of the atmospheric angular momentum budget, we show that various model drag mechanisms when modified interact with one another by redistributing their drag while conserving the total amount. In particular, an overestimation of mountain drag is accompanied by an underestimation of gravity wave drag in the Northern Hemisphere mid-latitudes to conserve the total amount of drag in the model while likely breaking an optimal balance among the mechanisms. Under such a condition, the inclusion of a gravity wave drag parametrization — even if the drag amount itself is reasonable – does not necessarily improve the performance of the model. Diagnosis of this type of imbalance is not clear by conventional monthly mean fields of variables. In this paper, we argue that the budget of atmospheric angular momentum is a useful measure to diagnose impact of such changes in model physics with regard to the partition and balance among drag mechanisms. We also discuss the experimental results that led to the replacement of silhouette orography by mean orography in our model.

Resolution dependence of orographic torques

AbstractAn evaluation of the performance of the subgrid orography parametrization scheme in the ECMWF Integrated Forecast System is made by examining the variation with resolution of the orographic torques (resolved and parametrized) in short‐range global forecasts. As the spectral resolution is increased from T95 to T511, the magnitudes of the resolved torques increase while those of the parametrized torques decrease. In general the changes in the total orographic torques are reasonably small, but an important exception is between 20°N and 50°N in winter. Here the total orographic torque decreases significantly with increasing resolution. Through examination of errors in the modelled angular momentum budgets, it is suggested that the problems lie primarily at the low resolution end, where the parametrized orographic torques seem to be excessive. Furthermore, recent work with the NCEP reanalysis data suggests that this result may not be unique to the ECMWF system. Copyright © 2004 Royal Meteorological Society

The vorticity and angular momentum budgets of Asian summer monsoon

The study delineates the vorticity and angular momentum balances of Asian summer monsoon during the evolution and established phases. It also elucidates the differences between these balances in the National Centre for Environmental Prediction/National Centre for Atmospheric Research (NCEP/NCAR) reanalysis and the National Centre for Medium Range Weather Forecasts (NCMRWF) analysis fields. The NCEP/NCAR reanalysis for a 40 year period (1958-97) and the NCMRWF analysis for a three year (1994-96) period are made use of for the purpose. The time mean summer monsoon circulation is bifurcated into stable mean and transient eddy components and the mean component is elucidated.The generation of vorticity due to stretching of isobars balances most of the vorticity transported out of the monsoon domain during the evolution period. However, during the established period, the transportation by the relative and planetary vorticity components exceeds the generation due to stretching. The effective balancing mechanism is provided by vorticity generation due to sub-grid scale processes. The flux convergence of omega and relative momenta over the monsoon domain is effectively balanced by pressure torque during the evolution and established phases. Nevertheless, the balance is stronger during the established period due to the increase in the strength of circulation.Both the NCMRWF and NCEP fields indicate the mean features related to vorticity and angular momentum budgets realistically. Apart from the oceanic bias (strong circulation over oceans rather than continents), the summer monsoon circulation indicated by the NCEP is feeble compared to NCMRWF. The significant terms in the large-scale budgets of vorticity and angular momentum enunciate this aspect

Mountain Torques and Northern Hemisphere Low-Frequency Variability.Part II: Regional Aspects

The NCEP‐NCAR reanalysis dataset for 1958‐97 is used to analyze intraseasonal variations in mountain torques and the large-scale atmospheric circulation patterns associated with them. Spectral analysis of the atmospheric angular momentum (AAM) budget shows that the dominant variations of mountain torque have periodicities near 30 days and shorter, while the dominant AAM variations occur in the 40‐60-day band. This difference is due to the 40‐60-day AAM variations being primarily related to equatorial processes, while mountain torque variations are associated mostly with extratropical processes. The Northern Hemisphere (NH) mountain torque has enhanced power and significant spectral peaks in the 20‐30-day band. The signal in this band accounts for 33% of the NH mountain torque variance, once the seasonal cycle has been removed. Lag composites of the NH 700-hPa geopotential heights based on the 20‐30-day mountain torque signal show the latter to be associated with coherent large-scale patterns that resemble lowfrequency oscillations identified in this band by previous authors. The composite patterns that are in phase quadrature with the 20‐30-day NH mountain torque have a pronounced zonally symmetric component. These patterns are associated with substantial AAM variations, arguably driven by the NH mountain torque in this band. Principal component (PC) analysis of the NH 700-hPa heights shows that, in the 20‐30-day band, the mountain torque is also in phase quadrature with the two leading PCs; the first corresponds to changes in the midlatitude jet intensity near the subtropics, while the second corresponds to the Arctic Oscillation. The relationships with AAM of the latter essentially occurs through the mass term. Mountain torques are, furthermore, nearly in phase with dominant patterns of low-frequency variability that exhibit substantial pressure gradients across the Rockies and the Tibetan Plateau.

Mountain Torques and Northern Hemisphere Low-Frequency Variability. Part I: Hemispheric Aspects

The NCEP–NCAR reanalysis dataset for 1958–97 is used to analyze intraseasonal variations in mountain torques and the large-scale atmospheric circulation patterns associated with them. Spectral analysis of the atmospheric angular momentum (AAM) budget shows that the dominant variations of mountain torque have periodicities near 30 days and shorter, while the dominant AAM variations occur in the 40–60-day band. This difference is due to the 40–60-day AAM variations being primarily related to equatorial processes, while mountain torque variations are associated mostly with extratropical processes. The Northern Hemisphere (NH) mountain torque has enhanced power and significant spectral peaks in the 20–30-day band. The signal in this band accounts for 33% of the NH mountain torque variance, once the seasonal cycle has been removed. Lag composites of the NH 700-hPa geopotential heights based on the 20–30-day mountain torque signal show the latter to be associated with coherent large-scale patterns that resemble low-frequency oscillations identified in this band by previous authors. The composite patterns that are in phase quadrature with the 20–30-day NH mountain torque have a pronounced zonally symmetric component. These patterns are associated with substantial AAM variations, arguably driven by the NH mountain torque in this band. Principal component (PC) analysis of the NH 700-hPa heights shows that, in the 20–30-day band, the mountain torque is also in phase quadrature with the two leading PCs; the first corresponds to changes in the midlatitude jet intensity near the subtropics, while the second corresponds to the Arctic Oscillation. The relationships with AAM of the latter essentially occurs through the mass term. Mountain torques are, furthermore, nearly in phase with dominant patterns of low-frequency variability that exhibit substantial pressure gradients across the Rockies and the Tibetan Plateau.

Atmospheric Contributions to Earth Nutation: Geodetic Constraints and Limitations of the Torque Approach

Abstract Atmospheric motions in the retrograde diurnal (S1) band are of interest to a wide community of researchers in earth dynamics and geodesy, due to their potential contribution to the low-frequency motions of the rotation axis known as nutations. Previous studies of these effects have noted an order-of-magnitude discrepancy between estimates of atmosphere-induced nutation based on the torque and angular momentum approaches. In this note, angular momentum budgets computed from NCEP reanalysis data are examined in order to isolate the reasons for this discrepancy, and associated constraints on the atmospheric response to solar diurnal forcing are considered.

Response of a global atmospheric forecast model to various drag parametrizations

Various drag mechanisms are currently parametrized in numerical models of the atmosphere. For global models that include the middle atmosphere in particular, these mechanisms profoundly affect weather forecast as well as climate simulation.We have developed an extended-top version of the Navy Operational Global Atmospheric Prediction System (NOGAPS) to include the middle atmosphere by modifying some physical parametrizations and the vertical coordinate. We performed a series of ensemble simulations corresponding to January 2000 for investigating the response of the model to various drag mechanisms, such as mountain drag, orographic gravity wave drag, surface friction drag, and artificial model top drag. Based on the monthly mean fields obtained from the simulations, we first investigate the effect of gravity wave drag due to its direct impact through planetary wave activity as well as indirect impact through induced meridional circulation.We discuss the difficulties in partitioning between the mountain drag due to resolved orography and the gravity wave drag due to unresolved orography, first using conventional diagnostic measures. From analyses of the atmospheric angular momentum budget, we show that various model drag mechanisms when modified interact with one another by redistributing their drag while conserving the total amount. In particular, an overestimation of mountain drag is accompanied by an underestimation of gravity wave drag in the Northern Hemisphere mid-latitudes to conserve the total amount of drag in the model while likely breaking an optimal balance among the mechanisms. Under such a condition, the inclusion of a gravity wave drag parametrization — even if the drag amount itself is reasonable — does not necessarily improve the performance of the model. Diagnosis of this type of imbalance is not clear by conventional monthly mean fields of variables. In this paper, we argue that the budget of atmospheric angular momentum is a useful measure to diagnose impact of such changes in model physics with regard to the partition and balance among drag mechanisms. We also discuss the experimental results that led to the replacement of silhouette orography by mean orography in our model.

The Deep-Atmosphere Euler Equations in a Generalized Vertical Coordinate

Abstract Previous analysis of the hydrostatic primitive equations using a generalized vertical coordinate is extended to the deep-atmosphere nonhydrostatic Euler equations, and some special vertical coordinates of interest are noted. Energy and axial angular momentum budgets are also derived. This would facilitate the development of conserving finite-difference schemes for deep-atmosphere models. It is found that the implied principles of energy and axial angular momentum conservation depend on the form of the upper boundary. In particular, for a modeled atmosphere of finite extent, global energy conservation is only obtained for a rigid lid, fixed in space and time. To additionally conserve global axial angular momentum, the height of the lid cannot vary with longitude.

Angular Momentum Transports by Moving Spiral Waves

Theoretical results based on the shallow water equations show that outgoing spiral waves generated by a nonaxisymmetric vortex can effectively remove angular momentum from the vortex, and the removal rate is sensitive to the strength of the vortex. When the model is applied to tropical cyclones, the results suggest that radiation of spiral waves may play a noticeable role in the total angular momentum budget of the core and affect the intensification of a tropical cyclone. An Eliassen‐Palm relation is derived for the shallow water equations. It shows that the total angular momentum carried by shallow water waves does not change during their propagation through an axisymmetric mean flow.

Systematic Strategies for Stochastic Mode Reduction in Climate

A systematic strategy for stochastic mode reduction is applied here to three prototype ‘‘toy’’ models with nonlinear behavior mimicking several features of low-frequency variability in the extratropical atmosphere. Two of the models involve explicit stable periodic orbits and multiple equilibria in the projected nonlinear climate dynamics. The systematic strategy has two steps: stochastic consistency and stochastic mode elimination. Both aspects of the mode reduction strategy are tested in an a priori fashion in the paper. In all three models the stochastic mode elimination procedure applies in a quantitative fashion for moderately large values of « 0.5 or even « 1, where the parameter « roughly measures the ratio of correlation times of unresolved variables to resolved climate variables, even though the procedure is only justified mathematically for « K 1. The results developed here provide some new perspectives on both the role of stable nonlinear structures in projected nonlinear climate dynamics and the regression fitting strategies for stochastic climate modeling. In one example, a deterministic system with 102 degrees of freedom has an explicit stable periodic orbit for the projected climate dynamics in two variables; however, the complete deterministic system has instead a probability density function with two large isolated peaks on the ‘‘ghost’’ of this periodic orbit, and correlation functions that only weakly ‘‘shadow’’ this periodic orbit. Furthermore, all of these features are predicted in a quantitative fashion by the reduced stochastic model in two variables derived from the systematic theory; this reduced model has multiplicative noise and augmented nonlinearity. In a second deterministic model with 101 degrees of freedom, it is established that stable multiple equilibria in the projected climate dynamics can be either relevant or completely irrelevant in the actual dynamics for the climate variable depending on the strength of nonlinearity and the coupling to the unresolved variables. Furthermore, all this behavior is predicted in a quantitative fashion by a reduced nonlinear stochastic model for a single climate variable with additive noise, which is derived from the systematic mode reduction procedure. Finally, the systematic mode reduction strategy is applied in an idealized context to the stochastic modeling of the effect of mountain torque on the angular momentum budget. Surprisingly, the strategy yields a nonlinear stochastic equation for the large-scale fluctuations, and numerical simulations confirm significantly improved predicted correlation functions from this model compared with a standard linear model with damping and white noise forcing.

A modified quasigeostrophic equation for barotropic mean flow over topography

The standard mean flow equation of quasigeostrophic theory omits the mass term in the angular momentum budget. A modification of this equation is proposed for barotropic flow over topography where the mass term is incorporated. The modified equation is applied to a topographic instability problem. It is found that the growth rates are substantially reduced if the mass term is taken into account.

Tests on the validity of atmospheric torques on Earth computed from atmospheric model outputs

The effect of the atmosphere on the Earth rotation is usually computed using the angular momentum budget equation. In particular, the interaction torque between the solid Earth/ocean and the atmosphere can be computed from the output of global circulation models. This torque is composed of three parts: a mountain torque due to the pressure action on the topography, a gravitational torque due to the interaction between the mass inside the solid Earth and inside the atmosphere, and a friction torque. The purpose of the paper is to test the torque computed from the output of different atmospheric global circulation models (GEOS‐1, National Centers for Environmental Protection reanalysis, and ERA‐15) in order to see to what extent they are reliable in the frame of Earth rotation studies. The test has been performed by comparing each part of the torque computed from the different models, as well as by verifying of the angular momentum budget equation for the atmosphere.

Gravity wave drag and global angular momentum: geostrophic adjustment processes

Current gravity wave drag schemes alter the flow field of a numerical model by changing the velocity.It is argued that this is essentially the situation considered in the theory of geostrophic adjustment.The reduction of velocity at one moment does not necessarily lead to a reduction of the global meanvelocity after adjustment in that case. It is best to discuss these processes in terms of angular momentumconservation, so that the initial loss of velocity can be seen as a reduction of the wind term which maybe converted into a reduction of the mass term. Observations are used to see if this process can bedetected in the angular momentum budget of the atmosphere. The data indeed reveal a rapid positiveresponse of the mass term to the gravity wave drag.

Influence of the seasonal winds and the CO2 mass exchange between atmosphere and polar caps on Mars' rotation

The Martian atmosphere and the CO2 polar ice caps exchange mass. This exchange, together with the atmospheric response to solar heating, induces variations of the rotation of Mars. Using the angular momentum budget equation of the system solid‐Mars–atmosphere–polar ice caps, the variations of Mars' rotation can be deduced from the variations of the angular momentum of the superficial layer; this later is associated with the winds, that is, the motion term, and with the mass redistribution, that is, the matter term. For the “mean” Martian atmosphere, without global dust storms, total amplitudes of 10 cm on the surface are obtained for both the annual and semiannual polar motion excited by the atmosphere and ice caps. The atmospheric pressure variations are the dominant contribution to these amplitudes. Length‐of‐day (lod) variations have amplitudes of 0.253 ms for the annual signal and of 0.246 ms for the semiannual signal. The lod variations are mainly associated with changes in the atmospheric contribution to the mass term, partly compensated by the polar ice cap contribution. We computed lod variations and polar motion for three scenarios having different atmospheric dust contents. The differences between the three sets of results for lod variations are about one order of magnitude larger than the expected accuracy of the NEtlander Ionosphere and Geodesy Experiment (NEIGE) for lod. It will thus be possible to constrain the global atmospheric circulation models from the NEIGE measurements.

Planetary Wave Diagnostics on the QBO Effects on the Deceleration of the Polar-night Jet in the Southern Hemisphere.

A composite analysis with respect to the phases of the equatorial quasi-biennial oscillation (QBO) is made for the zonal-mean zonal flow and the Eliassen-Palm (EP) flux during late winter to spring in the Southern Hemisphere. It is shown that deceleration in the lower stratosphere in September to October is more rapid in the easterly phase of the QBO than in the westerly phase, which makes the stratospheric zonal wind in November weaker. Such deceleration is consistent with the larger convergence of the EP flux observed in the easterly phase, which is associated with the stronger upward flux from the troposphere. It is also found that the equatorward flux in the upper troposphere is stronger in the westerly phase. These results for the EP flux diagnostics are discussed in terms of angular momentum budget of the atmosphere within a supposed zonally symmetric “body-of-rotation”. The composite difference of the upward flux is dominated by zonal wavenumber 1-3 component, whereas wavenumber 4-6 is predominant for the equatorward flux. Accordingly, it is suggested to be inappropriate to explain the difference of these fluxes between the QBO phases by considering the alternative directions of propagation of particular wave components due to change in refractive index. It seems that activities of wave disturbances in both scales are modified respectively by the QBO.

Phase relations for high frequency core–mantle coupling and the Earth’s axial angular momentum budget

Although it has long been thought that dynamical core–mantle coupling is necessary for understanding decadal variations in the length of day (LOD), the physics of the coupling mechanism are very poorly constrained. There several hypotheses — electromagnetic, topographic, gravitational, viscous — but it is notoriously difficult to distinguish between them on observational grounds. There is both an expectation [Geophys. J. Int. 138 (1999) 679] and some evidence [J. Geophys. Res. 100 (1995) 8233; Geophys. Res. Lett. 24 (1997a) 1799] that there is significant core–mantle coupling on much faster timescales, down to subannual periods. At such frequencies, the core would no longer be the dominant driving force for LOD, but would instead interact with both the mantle and external reservoirs of angular momentum such as the atmosphere and ocean. On these much faster timescales, it is possible that some information that is obscured on decadal timescales becomes available: in particular, any characteristic timescales at very short periods may become observable. Here, I examine the angular momentum budget of the Earth on subannual to annual timescales for any additional implied constraints on the physics of angular momentum exchange between the core and the mantle. I find that the discrepancy between atmospheric angular momentum and mantle angular momentum on timescales where the ocean is thought to be unimportant has a distinctive signature which is difficult to reproduce using simple models of core–mantle coupling, although an ad hoc “frictional” model does moderately well. Rather than indicating simplicity, this may instead be symptomatic of great complexity in the physics of the core–mantle boundary region.

Lunisolar torque on the atmosphere and Earth's rotation

The atmospheric effect on Earth's rotation is classically computed from atmospheric angular momentum (AAM) series by considering that the whole AAM variations are transmitted to the solid Earth. In fact, such a procedure is an approximation because it ignores that the atmosphere exchanges also angular momentum with the moon and the sun. The computation of the lunisolar gravitational torque on the atmosphere is the core of the present study. It is derived analytically and then estimated from pressure data over the period 1975–2000. The mean surface pressure is the main contributor, at the level of 10 17 N m for the equatorial component, 10 16 N m for the axial one, whereas the thermally driven pressure variations provide about 10% of the variance. This torque plays a significant role in the budget of the atmospheric angular momentum, but does not account for the inconsistency between the present series of the atmospheric angular momentum and the interaction torque between the solid Earth and the atmosphere. From the tidal waves of this torque we derive accurately the contribution of the atmosphere to the lunisolar precession–nutation of the Earth ( 0.31 marcsec/year for the precession in longitude, 46 microarcseconds for the nutation in 18.6 years).

Diurnal angular momentum budget of the atmosphere and its consequences for Earth's nutation

The three‐dimensional diurnal atmospheric angular momentum (AAM) budget is investigated, and its geographical features and meteorological dynamics are explored. It is shown that the diurnal atmospheric torques are associated with mass effect (ellipsoidal torque for the equatorial component and mountain torque for the axial component). It is shown that there is an important difference between the torque and angular momentum approaches on diurnal timescales, with the AAM time derivative generally exceeding the calculated torques. For the retrograde diurnal band, however, which is of interest for Earth nutation, the torque approach predicts much larger AAM changes than those observed. The AAM budget equation is also investigated theoretically, in order to give condition on the torques and AAM in order to verify the equation. Alternatively to the condition proposed by Bell, [1994], a condition on the local torque is shown sufficient to verify the AAM budget equation in the retrograde band, that is, the local torque have to balance the ellipsoidal effect. This condition is shown to be verified qualitatively. However, when separating the AAM budget equation into prograde and retrograde part, this last part become very sensitive to the error on the computation of the local torque. This explains why the torque approach always give one order of magnitude larger than the AAM approach at the retrograde diurnal frequencies.