Nonlinear stability of the Kelvin-Stuart cat's eyes flow

Holm, D. D., J. E. Marsden and T. S. Ratiu

Lects. in Appl. Math., SIAM, 23, (1986), 171-186

Abstract:

Conditions which ensure the nonlinear stability of the Kelvin-Stuart cat's eyes solution for two dimensional ideal flow are given. The solution is periodic in the x -direction and is bounded by two streamlines, which contain the separatrix. in the y -direction. The stability conditions are given explicitly in terms of the solution parameters and the domain size. The method is based on a technique originally developed by Arnold [1969].