  This paper is on the effect of nonlinearity in the equations for propagation
of disturbances on transition in the class of Spiral Poiseuille Flows. The
problem is approached from the fundamental point of view of following the
growth of initially infinitesimally small disturbances into their nonlinear
stage when the effect of Reynolds stresses makes itself felt. To this end a
rational scheme of an iterative solution method for the set of Generalised
Nonlinear Orr-Sommerfeld, Squire and Continuity equations is proposed. The
present proposal for Spiral Poiseuille Flows closely follows that put forth in
1971 by Stuart and Stewartson in their seminal papers on the influence of
nonlinear effects during transition in bench-mark flows, which are the flow in
the gap between concentric circular cylinders (Taylor instability), and in the
plane walled channel flow.
  The basic feature of the proposed method is the introduction of an Amplitude
Parameter and of a slow/long scale variable to account for the effect of
growing disturbances within the framework of a rational iteration scheme. It is
shown that the effect of amplified disturbances is captured, as in the
bench-mark flows, by a Ginzburg-Landau type differential equation for an
Amplitude Function in terms of suitably defined slow/long scale variables.
However, the coefficients in this equation are numbers that depend upon the
flow parameters of the Spiral Poiseuille Flow, which are the Reynolds Number,
the Swirl Number, and the geometric parameter of transverse curvature of the
flow geometry.
