NONEXISTENCE OF LYAPUNOV FUNCTIONS AND THE INSTABILITY OF THE VONKARMAN VORTEX STREETS

The instability of the von Karman vortex streets and the existence of a global Lyapunov function at the special aspect ratio h/l = (1/pi)sin h-1 (1), are some of the difficulties with the well-known von Karman m odel. By consistently applying the principle of genericity, its shown that a new family of near-equilibrium periodic solutions of the von Ka rman model for aspect ratios near 0.281... supplies numerous theoretic al candidates for observed vortex trails. This set of solutions implie s that there is no global Lyapunov functions when h/l not-equal (1/pi) sinh-1 (1) which in turn leads to a rich variety of near-equilibrium solutions for the model.