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

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. 14, 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.

Pattern selection in the absolutely unstable regime as a nonlinear eigenvalue problem: Taylor vortices in axial flow

“…Thus, they show the same growth behavior with µ that the axial Fourier modes [48,57,58,49,50] of stationary Taylor vortices without through-flow show as a function of ǫ. The reason is that all fields in the PV state have the form of propagating waves at the apertures were used as nonrotating boundaries at in-and outlet [28,29].…”

“…It should be noted that the control parameter range of µ over which (2.12) gives an accurate description of the full velocity field of PV flow, say, on a percent level is indeed very small: The asymmetry between radial in-and outflow intensities rapidly grows with µ and causes higher axial Fourier contributions ∼ e inkz [48][49][50] to the velocity field that are discarded in the µ → 0 asymptotics of the GLE approximation (2.12). However, the modulus of the first Fourier mode of the vortex structures agrees for Re = 0 as well as for Re = 0 quite well with the one predicted by the GLE -cf.…”

Velocity and current measurements in electroconvecting smectic films

“…In analogy with the analysis of velocity fields measured for Rayleigh-Benard convection [44] and Taylor vortex flow [45,46], we expect the amplitudes B, to behave close to the bifurcation as 8,where d is an appropriate dimensionless stress parameter.…”

Molecular dynamics simulation: a tool for exploration and discovery using simple models

“…Numerical results using the conventional continuum approach are described in [22,23]. Experimental studies have employed a variety of measurement techniques in examining different aspects of the flow; examples include [24][25][26][27][28][29]. Several additions to the standard MD approach are needed to formulate an atomistic simulation of the Taylor-Couette system.…”