Experimental test of the perturbation expansion for the Taylor instability at various wavenumbers

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Abstract
Measurements of the Fourier components of the axial variation of the velocity component w in a Taylor–Couette apparatus containing ten pairs of vortices at various average wavenumbers q, as a function of ε≡R/Rc−1, are reported. For all values of q studied, excellent agreement with the perturbation expansion of Davey [J. Fluid Mech. 1 4, 336 (1962)] for the amplitudes of the Fourier components was obtained, provided the power law dependence on ε was taken as a function of ε̃≡ε−εm(q). Here εm(q) is the marginal stability curve, below which the laminar flow state is stable against perturbations of wavenumber q. The wavenumber dependence of the leading coefficients in the expansions for the fundamental and first harmonic was also measured, and it was found that while the coefficient for the fundamental was independent of q, the coefficient for the first harmonic monotonically decreased with increasing q, over the range studied.