  Subject of this paper falls under the broad heading of the propagation of
disturbances causing transition in a fully developed spiral annular flow. The
problem is approached through reformulation of the linearised equations of
motion governing small-amplitude disturbances in a parameter space that differs
from that conventionally employed for this purpose. The alternative parameter
space comprises a suitably defined Reynolds number that is formed with a
resultant characteristic velocity which is a vector sum of the axial and
azimuthal characteristic velocities, a swirl parameter that is the ratio of the
azimuthal to the axial characteristic velocity, and the ratio of the annular
gap to the mean diameter of the cylinders. In the limits of the swirl parameter
assuming very small or very large values, the newly derived generalised
Orr-Sommerfeld and Squire equations for disturbance propagation in the revised
parameter space reduce to the corresponding equations that are known and well
established for the limiting cases of disturbance propagation as the swirl
parameter goes to zero or infinity respectively. Furthermore, they also lead
naturally to the criterion that determines from the equations themselves the
analytical expression for the location of the critical layer in spiral annular
flow, the scaling behaviour of the thickness of the critical layer with the
Reynolds number and the swirl parameter, and the equation governing the
dynamics of the flow in the critical layer. They thus explicitly reveal the
effect of swirl on the critical layer.
