The amplitude equation for Taylor vortices with spatially varying amplitude in long but finite cylinders is derived for arbitrary gap width. The boundary condition to be satisfied by the amplitude at the end of the cylinders is obtained by a simple scaling argument. The same argument also yields a scaling property of the boundary-layer flow at the cylinder ends. The results for boundary conditions and correlation length are compared with recent measurements of Pfister and Rehberg, and excellent agreement is obtained.

• Received 26 April 1982

DOI:https://doi.org/10.1103/PhysRevA.26.1572