The purpose of this paper is to explore how accretion discs manifest the phenomenon of transient growth on a global scale .
We investigate analytically the time response of a thin accretion disc to particular axisymmetric perturbations .
To facilitate an analytical treatment we replace the energy equation with a general polytropic assumption .
The asymptotic expansion of Kluźniak & Kita ( 2000 ) , which extended the method of Regev ( 1983 ) to a full steady polytropic disc ( with n = 3 / 2 ) , is further developed and implemented for both the steady ( for any polytropic index ) and time-dependent problems .
The spatial form and temporal behaviour of selected dynamical disturbances are studied in detail .
We identify the perturbation space which leads to transient growth and provide analytical solutions which manifest this expected transient growth behaviour .
Three terms ( physical causes ) responsible for the appearance of transient growth are identified .
Two depend explicitly on the viscosity while the third one is relevant also for inviscid discs .
The main conclusion we draw is that the phenomenon of transient growth exists in discs on a global scale .