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Nonlinear stability of Newtonian fibres

The stability of steady isothermal flow of one-dimensional Newtonian fibres is considered. Bifurcation theory yields a stable supercritical Hopf bifurcation, with frequency decreasing for increasing winder speeds near the critical winder speed. A new Chebyshev expansion procedure is used with time-marching to obtain accurate numerical solutions valid far from the critical point. Our numerical solution agrees well with our analytical solution near the critical winder speed, but differs significantly from those of previous numerical models. There is qualitative agreement with a previous isothermal experiment for oscillation amplitude but not for oscillation frequency. These comparisons are discussed.