  Aims: To quantify the transient growth of nonaxisymmetric perturbations in
unstratified magnetized and stratified non-magnetized rotating linear shear
flows in the shearing sheet approximation of accretion disc flows. Method: The
Rayleigh quotient in modal approaches for the linearized equations (with
time-dependent wavenumber) and the amplitudes from direct shearing sheet
simulations using a finite difference code are compared. Results: Both
approaches agree in their predicted growth behavior. The magneto-rotational
instability for axisymmetric and non-axisymmetric perturbations is shown to
have the same dependence of the (instantaneous) growth rate on the wavenumber
along the magnetic field, but in the nonaxisymmetric case the growth is only
transient. However, a meaningful dependence of the Rayleigh quotient on the
radial wavenumber is obtained. While in the magnetized case the total
amplification factor can be several orders of magnitude, it is only of order
ten or less in the nonmagnetic case. Stratification is shown to have a
stabilizing effect. In the present case of shearing-periodic boundaries the
(local) strato-rotational instability seems to be absent.
