The dynamics of small global perturbations in the form of linear combination of a finite number of non-axisymmetric eigenmodes is studied in two-dimensional approximation .
The background flow is assumed to be an axisymmetric perfect fluid with the adiabatic index \gamma = 5 / 3 rotating with power law angular velocity distribution \Omega \propto r ^ { - q } , 1.5 < q < 2.0 , confined by free boundaries in the radial direction .
The substantial transient growth of acoustic energy of optimized perturbations is discovered .
An optimal energy growth G is calculated numerically for a variety of parameters .
Its value depends essentially on the perturbation azimuthal wavenumber m and increases for higher values of m .
The closer the rotation profile to the Keplerian law , the larger growth factors can be obtained but over a longer time .
The highest acoustic energy increase found numerically is of order \sim 10 ^ { 2 } over \sim 6 typical Keplerian periods .
Slow neutral eigenmodes with corotation radius beyond the outer boundary mostly contribute to the transient growth .
The revealed linear temporal behaviour of perturbations may play an important role in angular momentum transfer in toroidal flows near compact relativistic objects .