Engineering topics

Papaloizou, J. C. B.

Publications and source records attributed to Papaloizou, J. C. B..

10 records

NASA NTRS1995

0n the dynamics of warped accretion disks

We present some analyses of warping modes in inviscid near Keplerian disks taking the three-dimensional structure fully into account. The results of this investigation verify the validity of a vertical averaging approximation for thin disks when the radial wavelength is significantly longer than the disk thickness. They also indicate that long wavelength disturbances may persist for long times. Shorter wavelength disturbances in non-self gravitating disks are found to propagate with little dispersion at a speed related to the sound speed. When self-gravity becomes important, fast and slow waves are found which also propagate with little dispersion. When a small viscosity is included, the evolution of the disturbances becomes more diffusive in character.

Papaloizou, J. C. B.↗

NASA NTRS1993

Two-dimensional viscous accretion disk models. II - On viscous overstability

Accretion disks have been shown to be susceptible to pulsational overstability when the viscosity coefficient increases upon compression. In this study, the stability of an axisymmetric accretion disk with vertical structure is considered. 2D axisymmetric calculations were performed by solving the set of fully nonlinear hydrodynamic equations, including radiation transport. The time evolution of a representative section (ring) of a thin radiative accretion disk is studied. The existence of the overstability in 2D is confirmed. It is found that the presence of periodic oscillations near the outer boundary of a real disk might account for some of the low-amplitude flickering observed in dwarf novae.

Kley, W.↗

NASA NTRS1993

On the tidal interaction between protostellar disks and companions

Formation of protoplanets and binary stars in a protostellar disk modifies the structure of the disk. Through tidal interactions, energy and angular momentum are transferred between the disk and protostellar or protoplanetary companion. We summarize recent progress in theoretical investigations of the disk-companion tidal interaction. We show that low-mass protoplanets excite density waves at their Lindblad resonances and that these waves are likely to be dissipated locally. When a protoplanet acquires sufficient mass, its tidal torque induces the formation of a gap in the vicinity of its orbit. Gap formation leads to the termination of protoplanetary growth by accretion. For proto-Jupiter to attain its present mass, we require that (1) the primordial solar nebula is heated by viscous dissipation; (2) the viscous evolution time scale of the nebula is comparable to the age of typical T Tauri stars with circumstellar disks; and (3) the mass distribution in the nebula is comparable to that estimated from a minimum-mass nebula model.

Lin, D. N. C.↗

NASA NTRS1990

Propagation of tidal disturbance in gaseous accretion disks

Linear wave propagation is studied in geometrically thin accretion disks where the equilibrium variables, such as density and temperature, are stratified in the direction normal to the plane of the disk; i.e., the vertical direction. It is shown, due to refraction effects, that waves excited by tidal disturbances induced by a satellite or a companion of the central object are not expected to reach the interior regions of the disk with a significant amplitude.

Lin, D. N. C.↗

NASA NTRS1990

Wave propagation in gaseous accretion disks

Linear wave propagation is studied in geometrically thin accretion disks where the equilibrium variables, such as density and temperature, are stratified in the direction normal to the plane of the disk, i.e., the vertical direction. Temperature stratification causes refraction such that initially radially propagating waves are deflected in the vertical direction. For moderate temperature contrast between the disk's midplane and its surface, wave transmission into the tenuous upper atmosphere is allowed. In typical astrophysical accretion disks, these two effects inhibit wave propagation through large distances in the radial direction.

Lin, D. N. C.↗

NASA NTRS1989

Accretion disc flows around FU Orionis stars

The accretion disk model of FU Orionis systems in outburst is investigated by examining the time-dependent behavior of a disk around a low-mass protostar that accretes at 0.00001-0.0001 solar masses/yr. It is found that the disk may be stabilized against the thermal ionization instability by the effect of advective heat transport and that it may therefore exist in the quasi-steady-state observed in post-outburst FU Orionis systems. The disk models are used to discuss the cosmochemical consequences of possible FU Ori events during the evolution of the primordial solar nebula.

Clarke, C. J.↗

NASA NTRS1988

On the pulsational overstability in narrowly confined viscous rings

Viscous accretion disks and rings are subject to pulsational overstability if the effective viscous stress is a rapidly increasing function of the disks' (or rings') surface density. Such a phenomenon is induced by the transfer of energy from shear to normal mode oscillations through viscous stress. The paper examines the global response of viscous accretion disks or rings to pulsational overstabilities. The analytic and preliminary numerical results indicate that all modes with wavelength longer than the scale height of the disk or ring are overstable. From the results, some examples of the complex time-dependent structure which may be induced by this overstability are illustrated. Finally, results are applied to narrow planetary rings to address the issues of maintenance of uniform precession and origin of eccentricity.

Papaloizou, J. C. B.↗

NASA NTRS1988

Axisymmetric perturbations of thin gaseous disks. I - Unstable convective modes and their consequences for the solar nebula

The axisymmetric perturbations of a thin, differentially rotating gas disk in which the vertical temperature stratification is superadiabatic are analyzed. The growth rate of adiabatic convective normal modes is calculated, departures from simple polytropic disk models are briefly discussed, and the detailed vertical structure of the eigenfunctions is analyzed. The stabilizing effect of radiative diffusion on convective modes is considered. It is found that rotation and compressibility tend to reduce the rate of growth of the disturbances, and that the growth rate increases without limit and is proportional to the square root of the radial wavenumber in polytropic equilibria. The maximum radial size of convective eddies scales like the square root of the degree of superadiabaticity times the size of the convective zone. There is significant convective penetration into radiatively stable layers only for the fundamental and low-order harmonic modes, whose vertical wavelength is comparable to the size of the convective layer.

Ruden, Steven P.↗

NASA NTRS1988

On the collapse and violent relaxation of protoglobular clusters

During the formation of stellar systems such as globular clusters, low-mass subcondensations which eventually form stars must retain a geometric size throughout the collapse process that is small compared to the characteristic distance separating them. If the local velocity dispersion of the subcondensations is small, the overall dimension of the system can decrease substantially before reaching a dynamical equilibrium state. The maximum collapse factor is deduced by examining the growth of the velocity dispersion and the spread in arrival times at the origin caused by local and global fluctuations. It is shown, analytically as well as in a series of N-body simulations, that the maximum reduction in the characteristic dimension of a system of N fragments with an initial homogeneous distribution subject to N exp 1/2 fluctuations is proportional to N exp 1/3. Direct physical collisions between low-mass subcondensations are therefore unlikely to occur in protoglobular clusters. The results are discussed in the context of fragmentation and violent relaxation.

Aarseth, S. J.↗

NASA NTRS1987

On the confinement of planetary arcs

The necessary conditions for planetary arc confinement are investigated, concentrating on the limiting case where the arc is marginally confined. It is shown that periodic perturbations due to a discrete Lindblad resonance can induce a secular change of Jacobian energy as well as orbital eccentricity. If the particles are subject to the perturbation of only one inner (outer) Lindblad resonance, the Lindblad resonance's location must be exterior (interior) to that of the corotation resonance if the perturbations are to lead to confinement. The trajectories of particles that are subject to inelastic collisions and pertubations due to corotation and Lindblad resonances are computed, showing that the confinement mechanism can indeed operate provided the perturbation due to the Lindblad resonance is sufficiently strong to balance viscous effects. The possibility that internal nonradial oscillations of Neptune may provide the necessary perturbations for arc confinement is considered.

Lin, D. N. C.↗