Stability and nonlinear adjustment of vortices in Keplerian flows

TL;DR

This study uses high-resolution simulations to analyze the stability, nonlinear evolution, and equilibrium states of vortices in Keplerian flows, highlighting the role of shocks and vortex properties independent of initial conditions.

Contribution

It introduces the concept of nonlinear adjustment for vortex evolution and demonstrates that vortex properties depend only on local disk parameters, independent of initial conditions.

Findings

Vortices reach long-lived equilibrium states determined by local disk parameters.

Spiral shocks attached to vortices influence their evolution and stability.

Anticyclonic vortices are promising candidates for promoting planetary formation.

Abstract

We investigate the stability, nonlinear development and equilibrium structure of vortices in a background shearing Keplerian flow. We make use of high-resolution global two-dimensional compressible hydrodynamic simulations. We introduce the concept of nonlinear adjustment to describe the transition of unbalanced vortical fields to a long-lived configuration. We discuss the conditions under which vortical perturbations evolve into long-lived persistent structures and we describe the properties of these equilibrium vortices. The properties of equilibrium vortices appear to be independent from the initial conditions and depend only on the local disk parameters. In particular we find that the ratio of the vortex size to the local disk scale height increases with the decrease of the sound speed, reaching values well above the unity. The process of spiral density wave generation by the vortex, discussed in our previous work, appear to maintain its efficiency also at nonlinear amplitudes and we observe the formation of spiral shocks attached to the vortex. The shocks may have important consequences on the long term vortex evolution and possibly on the global disk dynamics. Our study strengthens the arguments in favor of anticyclonic vortices as the candidates for the promotion of planetary formation. Hydrodynamic shocks that are an intrinsic property of persistent vortices in compressible Keplerian flows are an important contributor to the overall balance. These shocks support vortices against viscous dissipation by generating local potential vorticity and should be responsible for the eventual fate of the persistent anticyclonic vortices. Numerical codes have be able to resolve shock waves to describe the vortex dynamics correctly.