Wave-number restriction and mode interaction in Taylor vortex flow: Appearance of a short-wavelength instability

Abstract

In the stability analysis of wide-gap axisymmetric Taylor vortex flow, a new instability is found to supersede the Eckhaus instability for sufficiently high Reynolds numbers. Like the Eckhaus instability it is axisymmetric, but it represents a short-wavelength rather than a long-wavelength modulation of the pattern: It tends to eliminate every other vortex pair. In experiments it is therefore expected to change the wave number of the periodic solution more efficiently than the Eckhaus instability. Its origin is traced back to the resonant interaction of modes with wave numbers q and 2q. The essential features of the bifurcation diagrams connected with this mode interaction can be obtained by considering a degenerate codimension-2 bifurcation.