Accretion disk viscosity and internal waves in disks

Details Accretion disk viscosity and internal waves in disks Accretion disk viscosity and internal waves in disks

Jan 1992

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992phdt........71h&link_type=abstract

Ph.D. Thesis Texas Univ., Austin.

Computer Science

Sound

1

Accretion Disks, Angular Momentum, Internal Waves, Magnetic Fields, Mathematical Models, Momentum Transfer, Dynamo Theory, Scale Height, Sound Waves

Scientific paper

Recently, Vishniac, Jin and Diamond suggested that internal waves in accretion disks play a critical role in generating magnetic fields, and consequently are indirectly responsible for angular momentum transfer in thin, conducting, and non-self-gravitational disk systems. A project in which we will construct a quantitative model of the internal wave spectrum in accretion disks is started. It includes two aspects of work. The physical properties of the waves in a thin, non-self-gravitational, and non-magnetized accretion disk with realistic vertical structure is cataloged and examined. Besides the low frequency internal waves discovered by Vishniac and Diamond, it was found that sound waves with low frequency and low axisymmetry (with small absolute value of m) are capable of a driving dynamo because they are (1) well confined in a layer with thickness 2(absolute value of m)H where H is the disk scale height; (2) highly dispersive so they may survive the strong dissipation caused by the coherent nonlinear interaction their high frequency partners experience; and (3) elliptically polarized because they are confined in the z-direction. As a first step towards constructing a quantitative theory of this dynamo effect, a framework of calculating resonant nonlinear interaction among waves in disk is established. We are developing a numerical code which will compute the steady spectrum of the wave field in this framework. For simplicity, we only include the low frequency internal waves suggested by Vishniac and Diamond in the present stage. In the vicinity of the static state, the time step whose length is determined by the evolution of the modes with the largest amplitudes is too large for the modes with smaller amplitudes and overshooting occurs. Through nonlinear coupling, this overshooting is amplified and appears as a numerical instability affecting the evolution of the large amplitude modes. Shorter time steps may delay the appearance of the instability but not cure it. Additionally, shorter and shorter time steps make the computation more and more inefficient. Two ways to improve the codes are suggested.

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