Self-organization of two-dimensional incompressible viscous flow in a friction-free box.

Abstract

The process by which self-organization occurs for two-dimensional incompressible viscous flow in a friction-free box is investigated theoretically with the use of numerical simulations. It is shown by analytical and numerical eigenfunction spectrum analyses that two basic processes for the self-organization are the spectrum transfer by nonlinear couplings and the selective dissipation among the eigenmodes of the dissipative operator, and they yield spectrum accumulation at the lowest eigenmode. The third important process during nonlinear self-organization is an interchange between the dominant operators, which has hitherto been overlooked in conventional self-organization theories and which leads to a final self-similar coherent structure with the lowest eigenmode of the dissipative operator. \textcopyright{} 1996 The American Physical Society.