Laboratory and numerical experiments were conducted to quantitatively determine the modal structure of transient, nonaxisymmetric modes observed during the instability of an impulsively initiated circular‐Couette flow. The instability develops initially as an axisymmetric, Go¨rtler‐vortex state and persists ultimately as a steady, axisymmetric Taylor‐vortex state of different wavelength. The transition between these two states results from the instability of the Go¨rtler mode combined with the underlying developing swirl flow and is dominated by nonaxisymmetric modes. The laboratory experiments employed flow visualization coupled with digital video and image‐processing techniques; numerical experiments were performed using the spectral‐element code,nekton. ©1995 American Institute of Physics.