  A parametric numerical study of three-dimensional instability of steady flows
in a helical pipe of arbitrary curvature and torsion is carried out. The
computations are performed by a numerical approach verified against independent
experimental and numerical results in a previous study. The results are
reported as dependences of the critical Reynolds number, critical wavenumber
and the critical frequency on the dimensionless pipe curvature and torsion. A
multiplicity of different disturbance modes becoming most unstable at different
values of the governing parameters, is observed. Patterns of the most unstable
modes are reported and classified. Different routes to instability including
viscous and inviscid mechanisms, locally developing boundary and mixing layers,
interaction between the Dean vortices and the through flow are described.
