Vortices in Thin, Compressible, Unmagnetized Disks

Abstract

We consider the formation and evolution of vortices in a hydrodynamic shearing-sheet model. The evolution is done numerically using a version of the ZEUS code. Consistent with earlier results, an injected vorticity field evolves into a set of long-lived vortices, each of which has a radial extent comparable to the local scale height. But we also find that the resulting velocity field has a positive shear stress, <Sigma delta v_r delta v_phi>. This effect appears only at high resolution. The transport, which decays with time as t^-1/2, arises primarily because the vortices drive compressive motions. This result suggests a possible mechanism for angular momentum transport in low-ionization disks, with two important caveats: a mechanism must be found to inject vorticity into the disk, and the vortices must not decay rapidly due to three-dimensional instabilities.Comment: 8 pages, 10 figures (high resolution figures available in ApJ electronic edition

Three‐dimensional Compressible Hydrodynamic Simulations of Vortices in Disks

“…We suggest that the reason previous studies (Umurhan & Regev 2004;JG05b) did not find destruction of shearing vortical waves is that they used only small initial perturbation amplitudes and intermediate amplification factors (small j k x;0 /k y j), which did not satisfy the KH instability condition equation (15).…”

“…is the peak amplification factor (e.g., Chagelishvili et al 2003;Umurhan & Regev 2004;JG05a). Note that A is also the peak amplification factor of the kinetic energy in the wave.…”

“…A variety of authors have studied the evolution of random vorticity in both 2D and 3D and in both incompressible and compressible gases. Long-lived, anticyclonic (with rotation opposite to the background shear) vortices have been found in 2D Keplerian disks (e.g., Godon & Livio 1999, 2000Umurhan & Regev 2004;JG05b). The work of JG05b is particularly relevant to this study in that they considered the evolution of a spectrum of vorticity consistent with Kolmogorov turbulence in fully compressible 2D simulations.…”

Quasi-steady vortices in protoplanetary disks

“…A detailed study of the role of vortices in the evolution of solid particles (see Chavanis 2000;Chang & Oishi 2010) or in the transport of angular momentum in disks (Paardekooper et al 2010;Johnson & Gammie 2005) requires a better understanding of their structure and evolution. This paper addresses the problem by studying the possible shape and strength of the vortices.…”

“…Such properties were never pointed out for isolated vortices and we have called them "dwarf vortices". The existence of these vortices could also affect the evolution of small scale turbulence as described by (Johnson & Gammie 2005;Mamatsashvili & Chagelishvili 2007;Mamatsashvili & Rice 2009) with the possible formation of small scale persistent structures. Our model would be well suited to mimic such a situation.…”