  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.
