Philip Marcus, Univ. of California-Berkeley

Vortices in Protoplanetary Disks

Coherent, long-lived vortices in protoplanetary disks (PPDs) may be important in the late-stages of star formation due to their ability to transport angular momentum and energy radially. They may also play a role in planet formation due to their ability to accumulate dust in both two and three dimensions. We show that off-mid-plane, anticyclonic vortices in Keplerian disks are robust, but mid-plane vortices, unless very weak and elongated, are not likely to be stable. We also show that in numerical simulations of protoplanetary disks that Poincaré waves, those neutrally stable waves due to rotation (inertial waves) and/or density stratification (internal gravity waves), are  almost always present (and are, in fact, difficult to avoid). Small perturbations, including oscillating vortices, produce Poincaré waves. As the waves propagate from the mid-plane of the disk, their kinetic energy flux rv³/2 remains approximately constant, so as the density r decreases away from the mid-plane (approximately as a Gaussian) the velocity becomes large and the waves break. The breaking is shown to produce robust vortices, which obey scaling laws that we have derived and review. The shear in PPDs produces critical layers where neutral eigenmodes of the disk have logarithmic singularities. Weak dissipation blunts the singularities, but the layers grow to large amplitude, deriving their kinetic energy from the Keplerian differential rotation. Thus, the growth of these layers is an example of finite-amplitude instability in a linearly, neutrally-stable disk that derives its energy from the Keplerian motion. With sufficiently large amplitude, critical layers can spawn off-midplane vortices. Our calculations are done with spectral methods, and we discuss the pitfalls of the shearing-sheet approximation, computational domains that are too small, and calculations with insufficient spatial resolution.

Host:  Ira Wasserman