Optical heterodyne test of perturbation expansions for the Taylor instability

Abstract

The velocity field for the Taylor instability in a rotating fluid has been studied in order to test detailed theoretical predictions based on perturbation expansions about the critical point. Optical heterodyne methods were used to measure the spatial variation (along the axis of symmetry z) and time evolution of the local radial velocity component V_r(ε,z,t), where ε= (f−f_c)/f_c is a measure of the difference between the rotation rate f and the critical value f_c. Measurements of the steady state spatial Fourier coefficients A_p(ε) of V_r are presented as a function of ε in order to determine both the asymptotic power laws and the correction terms which are necessary for large ε. Measurements of the time dependence of A₁ after a sudden change in rotation rate are consistent with a heuristically useful analogy between hydrodynamic instabilities and certain second‐order phase transitions.