DPS 35th Meeting, 1-6 September 2003
Session 25. Planet and Satellite Origins I: Disks, Nebulae and Giant Planets
Oral, Chairs: A. P. Boss and J. J. Lissaurer, Thursday, September 4, 2003, 1:30-3:20pm, DeAnza I-II

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[25.05] Hydrodynamical Shear Instability in Accretion Disks?

I. Mosqueira (NASA Ames/SETI Institute), S. Kassinos (Univ. of Cyprus/Stanford Univ.), K. Shariff, J. N. Cuzzi (NASA Ames)

For Keplerian disks to accrete a source of enhanced angular momentum transport must be present in the disk. A key issue is whether, in the absence of ``stirring'', hydrodynamic shear turbulence can be self-sustaining in Keplerian disks or has to be transient. Simulations by Hawley et al. (1999) with resolutions up to 2563 using two codes with different dispersion properties showed no evidence of a non-linear shear instability. These authors interpreted this result to mean that the stabilizing Coriolis force easily overcame the non-linear terms in the Navier-Stokes equation and led to the complete viscous decay of the turbulence. Recently, on the basis of phenomenological arguments, it has been claimed (Longaretti 2002) that this result stems from a lack of resolution of the numerical codes, which results in too low a Reynolds number for the non-linear instability to be observed. Even if true, however, the mechanism for sustaining turbulence remains to be elucidated. Kato and Yoshizawa (1997) took steps in this direction by treating non-linear pressure-strain fluctuating terms in a one-point Reynolds-stress closure model, and argued that these terms serve to re-distribute the energy of the fluctuations in shear-driven anisotropic flows, and can counter the effects of the energy sink due to the Coriolis term at sufficiently small scales, thus possibly resulting in self-sustaining shear turbulence. Yet, these authors did not model the dissipation of turbulence.

More recently, Kassinos and Reynolds (2003, 2001) and Reynolds, Kassinos and Langer (2002) have greatly improved on prior one-point closure models of rotating shear flows by adding turbulent structure information to the modeling of the production and redistribution of turbulent kinetic energy, as well as explicitly including the effects of rotation in the dissipation of turbulence. In particular, the dissipation rate \epsilon is obtained from a large-scale enstrophy equation, which differs from standard local treatments of the dissipation equation by incorporating the inhibition of the energy cascade from large to small scales due to the scrambling effects of inertial waves in rotating frames of reference (Cambon et al. 1997). Here we report on the results of direct numerical simulations with resolution of 5123 (and possibly 10243) conducted by Kassinos et al. We will also discuss structure-based modeling of unbounded turbulent shear flows rotated about a spanwise axis, the success in fitting low to medium Reynolds number numerical simulations, current indications as to the regime of stability in Keplerian flows, and the prospects for such modeling to provide reliable high Reynolds number results.

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Bulletin of the American Astronomical Society, 35 #4
© 2003. The American Astronomical Soceity.