Large-scale vortex formation in protoplanetary disks

Understanding the stability of radially structured fluid disks has important astrophysical applications. Examples include protoplanetary disks containing dead zones or gaps due to disk-planet interaction. It is well established that localized axisymmetric structures can undergo a non-axisymmetric dynamical instability known as the Rossby wave instability (RWI) in the context of thin accretion disks. The RWI leads to vortex formation, and has important consequences for the evolution of protoplanetary disks and planet formation theory. Modern computational resources allow the RWI to be readily simulated into the non-linear regime, with additional features that were absent in the original description of the RWI by Lovelace et al (1999), such as three-dimensionality (3D). It is therefore necessary to generalize the linear stability problem. I will discuss some recent efforts to extend the original 2D linear stability calculations carried out by Li et al (2000) to 3D disks with different equations of state. I will describe the application of classic orthogonal polynomials to treat the partial differential equation eigenvalue problem, including its advantages and disadvantages. Time-permitting, I will also discuss the effect of self-gravity on the RWI, for which elegant proofs can be obtained in the linear problem, and present three-dimensional,  self-gravitating, non-linear hydrodynamical simulations of the RWI occurring at planetary gap edges.

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