Experimental and theoretical investigation of Kolmogorov flow on a cylindrical surface

Abstract

A laboratory model of Kolmogorov flow in a channel on a cylindrical surface, which eliminates the channel end effect observed in plane channels, has been investigated theoretically and experimentally. The number of half-periods of the external force could be varied from two to 22. It is shown that the type of secondary flow depends on the number of half-periods of the basic flow: traveling wave for an odd number of half-periods, quasisteady vortex structure for an even number of half-periods, and a self-oscillating regime when the channel width is equal to four half-periods. The theoretical analysis is based on the use of the Galerkin approximation of the equations of hydrodynamics. The system of equations obtained is solved numerically in conjunction with an analysis of the naturally arising eigenvalue problems.