Engineering topics

Yuan, Chi

Publications and source records attributed to Yuan, Chi.

5 records

NASA NTRS1994

Resonantly driven nonlinear density waves in protostellar disks

Recent observations of binary, pre-main-sequence, solar-type stars provide evidence that such systems may coexist with circumstellar disks. The binary disk systems, besides being of general interest for the study of star formation, potentially provide useful tests of companion-disk interaction theories prominent in current hypotheses of planet formation. In this paper, we apply an asymptotic analysis of the nonlinear, resonant interaction of a stellar companion with a disk to understand the dependence of such interactions on the properties of the system: the binary mass ratio, the physical properties of the disk, and the effective dissipation (treated herein as viscosity). The method is based on a WKBJ approximation and exploits the conditions that the disk is thin and much less massive than the primary, but does not require that the companion-induced disturbance be small. Both isothermal and adiabatic responses are treated. Only circular orbit resonances are considered in this paper. It is demonstrated that the temperature of the disk as well as the relative mass of the companion affects the degree of nonlinearity, and that nonlinearity promotes high wave compression ratios, long wavelengths, and increased propagation distances. Nevertheless, the total torque exerted between the companion and the disk is well represented by linear theory. The amplitudes of density disturbances are reduced by viscosity and nonisothermality. Because resonant interactions are generally strong and capable of driving rapid evolution, one might expect observations of systems undergoing strong, resonant-driven evolution to be rare. In this connection, it is pointed out that the m = 1 resonance is distinguished by being anomalously weaker than the others and is therefore of observational interest. It is speculated that, in conditions of intrinsically small dissipation, the propagation of resonant-driven density waves is limited by the tendency of their wavelength to diminish with distance, and that the propagation distance (and therefore the region of the disk to which angular momentum is redistributed) is set by the distance at which the wavelength becomes comparable to the disk thickness.

Yuan, Chi↗

NASA NTRS1993

Spiral density waves resonantly excited by a rapidly rotating bar

Recent observations at millimeter wavelengths have revealed bar-spiral structures in the central regions of several nearby spiral galaxies. Moreover, new infrared data and even COBE data seem to support the idea that there is a bar in the central regions of the Milky Way. All of these new findings have rekindled the interest in bar-driven spirals again. First, the mechanism that is responsible for exciting the spiral density waves near the resonances is reviewed, and then a theory to account for the highly nonlinear behavior of the gas associated with the waves is presented. The new results have again demonstrated that the 3 kpc arm phenomenon can be reproduced by a rapidly rotating bar in the galactic center. Similarly, in terms of the resonance excitation mechanism, the recent high-resolution radio observations of the bar-spiral structure in the central regions of nearby galaxies can be explained.

Yuan, Chi↗

NASA NTRS1991

Resonance excitation of spiral density waves in a gaseous disk. II - A nonlinear theory and application to the 3 kiloparsec arm

The present nonlinear theory of spiral density waves in a thin, viscous, self-gravitating gaseous disk views the waves as generated near the Lindblad resonance by periodic disturbances through an excitation mechanism. The suggestion of Yuan (1984), that either a minor oval distortion or an uneven distribution of mass in the center can excite a spiral density wave whose radial velocity and mass concentration are in excellent agreement with observations of the 3 kpc arm of the Galaxy, is confirmed. Reliable results are obtained for nonlinear density waves either in a gaseous disk or in the gas components of a galactic disk.

Yuan, Chi↗

NASA NTRS1990

Equilibrium models of self-gravitating inviscid disks resulting from the collapse of rotating clouds

A method is presented for the construction of velocity and surface density profiles of infinitely thin, self-gravitating disks formed from the collapse of spherical clouds, under the condition that the angular momentum of each material parcel is conserved. Results are presented for initially uniformly rotating clouds with density distributions varying as R exp -n and n = 0, 1, 2. The resulting disk surface density distributions are well represented by power laws in the cylindrical radius over most of their extent. The form of the zeroth-order approximation provides a useful representation of the final surface density function near the center for all three cases, and for n = 2 this result holds throughout the disk. This result is not generally true for the velocity functions, however.

Stemwedel, Sally W.↗

NASA NTRS1989

Resonance excitation of spiral density waves in a gaseous disk. I - A linear theory

The wave propagation in a gaseous disk which is self-gravitating and viscous is studied. Waves are generated by an external disturbance and are maintained in motion among forces due to rotation, self-gravity, and pressure. A linear theory is developed for the general case in which all factors are taken into account. The general solution can be applied to the photostellar disk of the solar nebula and the circumstellar disk of a binary in which the effects of self-gravity and pressure are equally important. The theory confirms in great detail that a long wave is excited at one of the Lindblad resonances gravitationally by the external periodic potential, propagates toward the corotation, is reflected before reaching there at the Q-barrier, and finally propagates in the reverse direction toward and past the Lindblad resonance as a short wave.

Yuan, Chi↗