Self-Organization in the Two-Dimensional Kelvin-Helmholtz Instability

The evolution and relaxation of an initial shear flow subject to the Kelvin-Helmholtz instability are investigated via two-dimensional compressible hydrodynamic simulations and the calculus of variations. During the instability evolution the total kinetic energy remains almost constant, but the enstrophy decays rapidly by the selective dissipation with the artificial viscosity. The successive vortex pairings lead to the emergence of an isolated vortex and the initial shear flow relaxes toward a self-organized state, i.e., a nearly minimum enstrophy state in the incompressible fluid.