On the Stability of a Kármán Vortex Street in a Channel of Finite Breadth, II

Abstract

As a continuation of the previous investigation, the stability of a vortex street in a channel of finite breadth has been discussed once more, by expressing the complex velocity potential for the vortex street in terms of proper doubly periodic functions and applying to it a small disturbance which is evidently wore general than that previously assumed. Under the condition that the vortices must retain their positions on the two straight lines parallel to the channel walls we have obtained, as in the former paper, two possible types of configuration of the vortices, namely, the symmetric and unsymmetric types. We have next discussed the stability of the system, by applying to it a possible small disturbance which is most general under the present circumstances, and have arrived at the following results. Firstly, the vortex street of symmetric type is absolutely unstable. Secondly, the vortex street of unsymmetric type may have one (at least) or two (at. most) essentially stable configurations, if the ratio of the breadth of the street now under discussion to that of the channel takes a value lying between 5/16 and 3/8 nearly