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At least 379 records · Page 21

Geodynamic Effects of Ocean Tides: Progress and Problems

Satellite altimetry, particularly Topex/Poseidon, has markedly improved our knowledge of global tides, thereby allowing significant progress on some longstanding problems in geodynamics. This paper reviews some of that progress. Emphasis is given to global-scale problems, particularly those falling within the mandate of the new IERS Special Bureau for Tides: angular momentum, gravitational field, geocenter motion. For this discussion I use primarily the new ocean tide solutions GOT99.2, CSR4.0, and TPXO.4 (for which G. Egbert has computed inverse-theoretic error estimates), and I concentrate on new results in angular momentum and gravity and their solid-earth implications. One example is a new estimate of the effective tidal Q at the M_2 frequency, based on combining these ocean models with tidal estimates from satellite laser ranging. Three especially intractable problems are also addressed: (1) determining long-period tides in the Arctic [large unknown effect on the inertia tensor, particularly for Mf]; (2) determining the global psi_l tide [large unknown effect on interpretations of gravimetry for the near-diurnal free wobble]; and (3) determining radiational tides [large unknown temporal variations at important frequencies]. Problems (2) and (3) are related.

Richard, Ray↗

Nonlinear evolution of tidally distorted accretion disks: Two-dimensional simulations

According to a previously published linear analysis, the tidal distortion of accretion disks in binary star systems produces a local hydrodynamic instability to m = 1 internal waves, which may have arbitrarily small wavelengths in the absence of viscosity. The instability is three-dimensional and approximately incrompressible. To explore the nonlinear outcome of this instability, we develop a shearing-sheet approximation on scales comparable to the disk thickness. The large-scale azimuthal variation of the disk is represented by varying the local metric with time (local orbital phase). The hydrodynamic equations can then be posed two-dimensionally on local meridional planes. We solve these equations with a second-order gasdynamical code based on the Total-Variation-Diminishing scheme. Our simulations confirm the predicted linear growth rate. The modes saturate chaotically at velocities scaling as the product of the linear growth rate and the wavelength. If the wavelength is small compared with the disk thickness, the modes remain nearly incompressible even when nonlinear. The two-dimensional power spectrum of velocities after saturation is roughly isotropic and extends over a broad range of scales in an approximately power-law fashion. We measure the heating rate associated with the nonlinear dissipation of the modes. The dissipation implies a secular torque on the disk and a return of angular momentum to the secondary star via the tidal potential. The estimated torque is somewhat larger than the tidal torque produced by maximal disk viscosity (alpha approximately 1). At least in these two-dimensional simulations, however, there is no significant angular momentum flux within the disk.

Ryu, Dongsu↗

Lessons Learned

This paper is organized around three themes that have interested me over my career: covariance analysis, constrained estimation, and angular momentum. Both analytical and numerical approaches to covariance analysis are discussed. The section on constraints begins with general considerations arising from the nature of the rotation group before moving to Wahba's Problem and quaternion Kalman filters. The discussion of angular momentum includes its use in attitude determination and control as well as in the detection and diagnosis of spacecraft anomalies. Relevant illustrative examples are included.

Markley, F. Landis↗

Parsec-Scale Accretion and Winds Irradiated by a Quasar

We present numerical simulations of properties of a parsec-scale torus exposed to illumination by the central black hole in an active galactic nucleus (AGN). Our physical model allows to investigate the balance between the formation of winds and accretion simultaneously. Radiation-driven winds are allowed by taking into account radiation pressure due to UV and IR radiation along with X-ray heating and dust sublimation. Accretion is allowed through angular momentum transport and the solution of the equations of radiative, viscous radiation hydrodynamics. Our methods adopt flux-limited diffusion radiation hydrodynamics for the dusty, infrared pressure driven part of the flow, along with X-ray heating and cooling. Angular momentum transport in the accreting part of the flow is modeled using effective viscosity. Our results demonstrate that radiation pressure on dust can play an important role in shaping AGN obscuration. For example, when the luminosity illuminating the torus exceeds L greater than 0.01 L(sub Edd), where L(sub Edd) is the Eddington luminosity, we find no episodes of sustained disk accretion because radiation pressure does not allow a disk to form. Despite the absence of the disk accretion, the flow of gas to smaller radii still proceeds at a rate 10(exp -4)-10(exp -1)M dot yr(exp -1) through the capturing of the gas from the hot evaporative flow, thus providing a mechanism to deliver gas from a radiation-pressure dominated torus to the inner accretion disk. As L L(sub edd) increases, larger radiation input leads to larger torus aspect ratios and increased obscuration of the central black hole. We also find the important role of the X-ray heated gas in shaping the obscuring torus.

accretion disks - galaxies: active - galaxies: Sey↗

Rotating wind solution and the acceleration of the cosmic radio jets

A wind-type solution is obtained in an axisymmetric spacetime in the case when matter has angular momentum. An application of the solution in understanding the acceleration of matter in radio jets as it flows along the funnel of a thick accretion disk is suggested. It is observed that the location of the critical point depends strongly upon the angular momentum of the wind. Apart from the usual acceleration of matter due to the expansion of the flow tube, the energy due to the rotational motion is found to contribute to the poloidal motion, hence enhancing the flow speed.

Chakrabarti, S. K.↗

Application of Core Dynamics Modeling to Core-Mantle Interactions

Observations have demonstrated that length of day (LOD) variation on decadal time scales results from exchange of axial angular momentum between the solid mantle and the core. There are in general four core-mantle interaction mechanisms that couple the core and the mantle. Of which, three have been suggested likely the dominant coupling mechanism for the decadal core-mantle angular momentum exchange, namely, gravitational core-mantle coupling arising from density anomalies in the mantle and in the core (including the inner core), the electromagnetic coupling arising from Lorentz force in the electrically conducting lower mantle (e.g. D-layer), and the topographic coupling arising from non-hydrostatic pressure acting on the core-mantle boundary (CMB) topography. In the past decades, most effort has been on estimating the coupling torques from surface geomagnetic observations (kinematic approach), which has provided insights on the core dynamical processes. In the meantime, it also creates questions and concerns on approximations in the studies that may invalidate the corresponding conclusions. The most serious problem is perhaps the approximations that are inconsistent with dynamical processes in the core, such as inconsistencies between the core surface flow beneath the CMB and the CMB topography, and that between the D-layer electric conductivity and the approximations on toroidal field at the CMB. These inconsistencies can only be addressed with numerical core dynamics modeling. In the past few years, we applied our MoSST (Modular, Scalable, Self-consistent and Three-dimensional) core dynamics model to study core-mantle interactions together with geodynamo simulation, aiming at assessing the effect of the dynamical inconsistencies in the kinematic studies on core-mantle coupling torques. We focus on topographic and electromagnetic core-mantle couplings and find that, for the topographic coupling, the consistency between the core flow and the CMB topography is critical for correct evaluation of the coupling torque.

Kuang, Weijia↗

The effect of cumulus friction on the simulation of the January Hadley Circulation by the GLAS model of the general circulation

A method of parameterizing the vertical mixing of horizontal momentum by cumulus convection was added to the GLAS model of the general circulation of the tropics. Addition of the cumulus friction term strengthened the winter Hadley circulation and smoothed the mean meridional wind field, with a slight increase in the eddy kinetic energy. The results showed that the intensity of the meridional circulation is regulated by the atmosphere's angular momentum budget, changes in the zonally-averaged Coriolis force correlate with the new cumulus friction term, and the intensification of Hadley circulation is a response of the mean meridional flow field to the downward cumulus field of relative angular momentum in the winter hemisphere.

Helfand, H. M.↗

Formation and evolution of a circumterrestrial disk Constraints on the origin of the moon in geocentric orbit

A data base of about 25,000 numerically integrated trajectories of earth-encountering planetesimals is used to study the angular momentum problem of forming the moon out of material captured into a circumterrestrial disk from heliocentric orbits. Mass-orbital element distributions of incoming planetesimals are combined with this data base to calculate, as a function of distance from earth, the net geocentric specific angular momentum of disk-encountering material on heliocentric orbits. Results suggest that a permanent disk population is not possible.

Herbert, Floyd↗

Sporadic mass ejection in red supergiants

A general mechanism first proposed by Burke (1969) is applied to red supergiants for determining the spin-down rate and angular-momentum loss of rotating stars. This model relies principally on sporadic mass ejection, which is assumed to be the result of turbulent elements accelerating material in cool supergiant atmospheres. Mass is preferentially expelled in the forward direction of rotation, resulting in a rapid loss of angular momentum on time scales of 10,000 to 1 million years in the supergiant evolutionary phase. Such rotational breaking will occur if the turbulent elements have characteristic sizes a few percent of the stellar radius and rms velocities one-third the escape speed of the star. This model predicts the formation of a cool silicate disk or torus around the star because of the preferred expulsion of material near equatorial regions of the supergiant.

Kafatos, M.↗

Hydrodynamics of coalescing binary neutron stars: Ellipsoidal treatment

We employ an approximate treatment of dissipative hydrodynamics in three dimensions to study the coalescence of binary neutron stars driven by the emission of gravitational waves. The stars are modeled as compressible ellipsoids obeying a polytropic equation of state; all internal fluid velocities are assumed to be linear functions of the coordinates. The hydrodynamics equations then reduce to a set of coupled ordinary differential equations for the evolution of the principal axes of the ellipsoids, the internal velocity parameters, and the binary orbital parameters. Gravitational radiation reaction and viscous dissipation are both incorporated. We set up exact initial binary equilibrium configurations and follow the transition from the quasi-static, secular decay of the orbit at large separation to the rapid dynamical evolution of the configurations just prior to contact. A hydrodynamical instability resulting from tidal interactions significantly accelerates the coalescence at small separation, leading to appreciable radial infall velocity and tidal lag angles near contact. This behavior is reflected in the gravitational waveforms and may be observable by gravitational wave detectors under construction. In cases where the neutron stars have spins which are not aligned with the orbital angular momentum, the spin-induced quadrupole moment can lead to precession of the orbital plane and therefore modulation of the gravitational wave amplitude even at large orbital radius. However, the amplitude of the modulation is small for typical neutron star binaries with spins much smaller than the orbital angular momentum.

Lai, Dong↗

Hubble Space Telescope

The Hubble Space Telescope will employ magnetic torque controllers, which make use of the Earth's magnetic field augmented by four reaction wheels. DC torques are easily allowed for, but variations, orbit by orbit, can result in excessive wheel speeds which can excite vibratory modes in the telescope structure. If the angular momentum from aerodynamic sources exceeds its allocation of 100 Nms, the excess has to come out of the maneuvering budget since the total capacity of the momentum storage system is fixed at 500 Nms. This would mean that maneuvers could not be made as quickly, and this would reduce the amount of science return. In summary, there is a definite need for a model that accurately portrays short term (within orbit) variations in density for use in angular momentum management analyses. It would be desirable to have a simplified model that could be used for planning purposes; perhaps applicable only over a limited altitude range (400 to 700 km) and limited latitude band.

Nurre, G.↗

Rapidly rotating neutron stars in general relativity: Realistic equations of state

We construct equilibrium sequences of rotating neutron stars in general relativity. We compare results for 14 nuclear matter equations of state. We determine a number of important physical parameters for such stars, including the maximum mass and maximum spin rate. The stability of the configurations to quasi-radial perturbations is assessed. We employ a numerical scheme particularly well suited to handle rapid rotation and large departures from spherical symmetry. We provide an extensive tabulation of models for future reference. Two classes of evolutionary sequences of fixed baryon rest mass and entropy are explored: normal sequences, which behave very much like Newtonian sequences, and supramassive sequences, which exist for neutron stars solely because of general relativistic effects. Adiabatic dissipation of energy and angular momentum causes a star to evolve in quasi-stationary fashion along an evolutionary sequence. Supramassive sequences have masses exceeding the maximum mass of a nonrotating neutron star. A supramassive star evolves toward eventual catastrophic collapse to a black hole. Prior to collapse, the star actually spins up as it loses angular momentum, an effect that may provide an observable precursor to gravitational collapse to a black hole.

Cook, Gregory B.↗

Asteroid collisional history - Effects on sizes and spins

The effects of asteroid collisional history on sizes and spins of present-day objects are discussed. Collisional evolution studies indicate that collisions have altered the spin-rates of small bodies, but that the largest asteroids may have retained their primordial rotation rates. Most asteroids larger than 100 km diam have probably been shattered, but have gravitationally recaptured their fragments to form a rubble-pile structure. Large angular momentum asteroids appear to have Maclaurian spheroidal or Jacobi-ellipsoid-like shapes; some of them may have fissioned into binaries. An integrated size and spin collisional evolution model is presented, with two critical parameters: one which determines the spin rates for small fragments resulting from a shattering collision, and the other determines the fraction of impact angular momentum that is retained by the target.

Davis, Donald R.↗

Laboratory Study of Magnetorotational Instability and Hydrodynamic Stability at Large Reynolds Numbers

Two plausible mechanisms have been proposed to explain rapid angular momentum transport during accretion processes in astrophysical disks: nonlinear hydrodynamic instabilities and magnetorotational instability (MRI). A laboratory experiment in a short Taylor-Couette flow geometry has been constructed in Princeton to study both mechanisms, with novel features for better controls of the boundary-driven secondary flows (Ekman circulation). Initial results on hydrodynamic stability have shown negligible angular momentum transport in Keplerian-like flows with Reynolds numbers approaching one million, casting strong doubt on the viability of nonlinear hydrodynamic instability as a source for accretion disk turbulence.

Ji, H.↗

Water sprays in space retrieval operations

Recent experiments involving liquid jets exhausting into a vacuum have led to significant conclusions regarding techniques for detumbling and despinning disabled spacecraft during retrieval operations. A fine water spray directed toward a tumbling or spinning object may quickly form ice over its surface. The added mass of water will absorb angular momentum and slow the vehicle. As this ice sublimes it carries momentum away with it. Thus, a complete detumble or despin is possible by simply spraying water at a disabled vehicle. Experiments were conducted in a ground based vacuum chamber to determine physical properties of water-ice in a space-like environment. Additional ices, alcohol and ammonia, were also studied. An analytical analysis based on the conservation of angular momentum, resulted in despin performance parameters, i.e., total water mass requirements and despin times. The despin and retrieval of a disabled spacecraft was considered to illustrate a potential application of the water spray technique.

Freesland, D. C.↗

Dynamics of the Venus atmosphere

The superrotation of the Venus atmosphere is a major unanswered problem in planetary science. At cloud-top levels (65-70 km altitude) the atmosphere rotates with a five-day period, corresponding to an equatorial wind speed of 90 m/s. Angular velocity is roughly constant on spherical shells, and decreases linearly with altitude to zero at the surface. The direction of rotation is the same as that of the solid planet, which is retrograde--opposite to the direction of orbital motion, but the 5-day period is short compared to the 243-day spin period of the solid planet or to the mean solar day, which is 117 Earth-days at the surface. The problem with the superrotation is that shearing stresses tend to transfer angular momentum downward, and would slow the atmosphere until it is spinning with the solid planet. Some organized circulation pattern is counteracting the tendency, but the pattern has not been identified. A simple Hadley-type circulation cannot do it because such a circulation is zonally symmetric and Hide's Theorem states that in an axisymmetric circulation an extremum in angular momentum per unit mass M can exist only at the surface. Venus violates the last condition, having a maximum of retrograde M on the equator at 70-80 km altitude. This leaves waves and eddies to maintain the superrotation but the length scales and forcing mechanisms for these motions need to be specified. Possible forcing mechanisms associated with waves, eddies and tides are discussed.

Ingersoll, A. P.↗

Results of a zonally truncated three-dimensional model of the Venus middle atmosphere

Although the equatorial rotational speed of the solid surface of Venus is only 4 m s(exp-1), the atmospheric rotational speed reaches a maximum of approximately 100 m s(exp-1) near the equatorial cloud top level (65 to 70 km). This phenomenon, known as superrotation, is the central dynamical problem of the Venus atmosphere. We report here the results of numerical simulations aimed at clarifying the mechanism for maintaining the equatorial cloud top rotation. Maintenance of an equatorial rotational speed maximum above the surface requires waves or eddies that systematically transport angular momentum against its zonal mean gradient. The zonally symmetric Hadley circulation is driven thermally and acts to reduce the rotational speed at the equatorial cloud top level; thus wave or eddy transport must counter this tendency as well as friction. Planetary waves arising from horizontal shear instability of the zonal flow (barotropic instability) could maintain the equatorial rotation by transporting angular momentum horizontally from midlatitudes toward the equator. Alternatively, vertically propagating waves could provide the required momentum source. The relative motion between the rotating atmosphere and the pattern of solar heating, which as a maximum where solar radiation is absorbed near the cloud tops, drives diurnal and semidiurnal thermal tides that propagate vertically away from the cloud top level. The effect of this wave propagation is to transport momentum toward the cloud top level at low latitudes and accelerate the mean zonal flow there. We employ a semispectral primitive equation model with a zonal mean flow and zonal wavenumbers 1 and 2. These waves correspond to the diurnal and semidiurnal tides, but they can also be excited by barotropic or baroclinic instability. Waves of higher wavenumbers and interactions between the waves are neglected. Symmetry about the equator is assumed, so the model applies to one hemisphere and covers the altitude range 30 to 110 km. Horizontal resolution is 1.5 deg latitude, and vertical resolution is 1.5 km. Solar and thermal infrared heating, based on Venus observations and calculations drive the model flow. Dissipation is accomplished mainly by Rayleigh friction, chosen to produce strong dissipation above 85 km in order to absorb upward propagating waves and limit extreme flow velocities there, yet to give very weak Rayleigh friction below 70 km; results in the cloud layer do not appear to be sensitive to the Rayleigh friction. The model also has weak vertical diffusion, and very weak horizontal diffusion, which has a smoothing effect on the flow only at the two grid points nearest the pole.

Newman, M.↗

The scientific case for magnetic field satellites

To make full use of modern magnetic data and the paleomagnetic record, we must greatly improve our understanding of how the geodynamo system works. It is clearly nonlinear, probably chaotic, and its dimensionless parameters cannot yet be reproduced on a laboratory scale. It is accessible only to theory and to measurements made at and above the earth's surface. These measurements include essentially all geophysical types. Gravity and seismology give evidence for undulations in the core-mantle boundary (CMB) and for temperature variations in the lower mantle which can affect core convection and hence the dynamo. VLBI measurements of the variations in the Chandler wobble and length of day are affected by, among other things, the electromagnetic and mechanical transfer of angular momentum across the CMB. Finally, measurements of the vector magnetic field, its intensity, or its direction, give the most direct access to the core dynamo and the electrical conductivity of the lower mantle. The 120 gauss coefficients of degrees up to 10 probably come from the core, with only modest interference by mantle conductivity and crustal magnetization. By contrast, only three angular accelerations enter the problem of angular momentum transfer across the CMB. Satellite measurements of the vector magnetic field are uniquely able to provide the spatial coverage required for extrapolation to the CMB, and to isolate and measure certain magnetic signals which to the student of the geodynamo represent noise, but which are of great interest elsewhere in geophysics. Here, these claims are justified and the mission parameters likely to be scientifically most useful for observing the geodynamo system are described.

Backus, George E.↗