Stability of a Quadruple Vortex Street

The stability of a quadruple vortex street, i.e. a pair of double vortex streets in a perfect fluid is investigated for small disturbances. Permanent configurations are first determined; two of which are then examined in their stability—one is a symmetric arrangement of a pair of staggered (Kármán-type) double streets and the other is an antisymmetric arrangement of the pair. The stability curves are obtained for several values of ratio of the distance 2b₀ between the double streets to the spacing a between consecutive vorticies in a row. It is found that both types are neutrally stable for most of disturbances except unstable disturbances in very narrow ranges of a parameter specifying the disturbances mode, provided that b₀/a≳0.5 and b/a is taken to be about 0.28, where b is the breadth of the double street. The symmetric type is more stable than the antisymmetric one.