Transient dynamics of perturbations in astrophysical disks

TL;DR

This paper explores the transient growth of perturbations in astrophysical accretion disks, examining their potential role in energy transfer and disk viscosity without relying on magnetorotational instability.

Contribution

It provides a detailed analysis of transient perturbation growth mechanisms in Keplerian flows, including variational methods for identifying optimal perturbations.

Findings

Transient perturbations can grow significantly due to nonnormality of the flow operator.

Optimal perturbations can be identified using variational methods involving direct and adjoint equations.

Transient growth may contribute to effective viscosity in accretion disks.

Abstract

This paper reviews some aspects of one of the major unsolved problems in understanding astrophysical (in particular, accretion) disks: whether the disk interiors may be effectively viscous in spite of the absence of marnetorotational instability? In this case a rotational homogeneous inviscid flow with a Keplerian angular velocity profile is spectrally stable, making the transient growth of perturbations a candidate mechanism for energy transfer from the regular motion to perturbations. Transient perturbations differ qualitatively from perturbation modes and can grow substantially in shear flows due to the nonnormality of their dynamical evolution operator. Since the eigenvectors of this operator, alias perturbation modes, are mutually nonorthogonal, they can mutually interfere, resulting in the transient growth of their linear combinations. Physically, a growing transient perturbation is a leading spiral whose branches are shrunk as a result of the differential rotation of the flow. This paper discusses in detail the transient growth of vortex shear harmonics in the spatially local limit as well as methods for identifying the optimal (fastest growth) perturbations. Special attention is given to obtaining such solutions variationally, by integrating the direct and adjoint equations forward and backward in time, respectively. The material is presented in a newcomer-friendly style.